From 0ae0fbebc89906b5e94e55677377e5f90ac5905d Mon Sep 17 00:00:00 2001 From: carlos Date: Thu, 4 May 2017 13:12:03 -0500 Subject: [PATCH 1/9] primer commit, progreso en runge kutta --- tareas/Carlos/Tarea6.ipynb | 187 +++++++++++++++++++++++++++++++++++++ 1 file changed, 187 insertions(+) create mode 100644 tareas/Carlos/Tarea6.ipynb diff --git a/tareas/Carlos/Tarea6.ipynb b/tareas/Carlos/Tarea6.ipynb new file mode 100644 index 0000000..06b622c --- /dev/null +++ b/tareas/Carlos/Tarea6.ipynb @@ -0,0 +1,187 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Tarea 6: Integración con Taylor" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Fecha de envío del PR inicial: **viernes 5 de mayo**\n", + "\n", + "Fecha de aceptación del PR: **martes 16 de mayo, antes de la clase**" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ejercicio 1\n", + "\n", + "Usando su implementación de polinomios de Taylor, escriban un integrador para la ecuación diferencial que se desarrolló en este ejemplo, esto es, $\\dot{x} = x^2$ con la condición inicial $x(0) = 3$. \n", + "\n", + "El integrador debe hacer las operaciones necesarias para obtener automáticamente los coeficientes $x_{[k]}$, *en cada paso de integración*, a partir de la condición inicial local. Un requisito básico para esto es que tengan una implementación de la función $P_\\alpha(x) = [g(x)]^\\alpha$ con $g(x)$ un polinomio de Taylor, que hicieron en la \"Tarea5\", y que funcione bien en particular para `alpha::Int`.\n", + "\n", + "La implementación debe consistir de varias funciones: \n", + "\n", + "- Una función donde se calculen los coeficientes $x_{[k]}$ de la expansión. Esta función deberá llamar a otra donde se implementan las recurrencias que imponen las ecuaciones de movimiento.\n", + "\n", + "- Una función donde se obtenga el paso de integración $h$ como se describió en el notebook 10.\n", + "\n", + "- Otra función donde se haga la suma usando el método de Horner.\n", + "\n", + "- Finalmente, una función que combine las funciones anteriores para hacer la integración desde un tiempo inicial a uno final. En este punto, *fingiremos ignorancia*, en el sentido de que el tiempo inicial es cero, y el tiempo final será $0.5$ (que está más allá de donde la solución está definida).\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Dado que conocemos la solución analítica de este problema, grafiquen como función de $t$ el error relativo de su integrador (respecto al valor del resultado analítico)." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ejercicio 2\n", + "\n", + "Repitan la integración del ejercicio anterior usando el método de Runge-Kutta de 4o orden con paso de integración fijo (que es lo más sofisticado que conocen hasta ahora) y comparen los resultados del error relativo con los obtenidos con el método de Taylor. En particular, finjan ignorancia de la misma manera que en el ejercicio anterior." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "runge_kutta_4" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\n", + "se hará el método de runge-kutta para resolver una ecuación diferencial de la forma dy/dx=f(x,y),\n", + "considerando el valor de una condicion inicial x_0, con cierto número de pasos, y cierto valor de y_0\n", + "\"\"\"\n", + "function runge_kutta_4(f,x_0,y_0,n)\n", + " x_f=1\n", + " a=zeros(n) #\"x\"\n", + " b=zeros(n) #\"y\"\n", + " h=(x_f-x_0)/n\n", + " a[1]=x_0\n", + " b[1]=y_0\n", + " for i in 1:n\n", + " k_1=f(a[i],b[i]) #condiciones necesarias para definir el siguiente valor de \"y\" y de \"x\"\n", + " k_2=f(a[i]+(h*(1/2)),b[i]+((1/2)*((k_1)*h)))\n", + " k_3=f(a[i]+(h*(1/2)),b[i]+((1/2)*((k_2)*h)))\n", + " k_4=f(a[i]+h,b[i]+((k_3)*h))\n", + " b[i+1]=a[i]+(1/6)*(h)*(k_1+2*k_2+2*k_3+k_4)\n", + " a[i+1]=a[i]+h\n", + " end\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "1.0e-14" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "1e-14" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "---" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Ejercicio 3\n", + "\n", + "Integra la ecuación de movimiento para el oscilador armónico, $\\ddot{x} = -2x$, con $x(0)=2$, $\\dot{x}(0)=0$, durante 10^4 periodos de oscilación (o sea, hasta $t_f = 10^4 \\cdot 2\\pi/\\sqrt{2}$, usando el método de Taylor y el método de Runge-Kutta de 4o orden con paso de integración constante. Compara cómo cambia la energía (respecto al valor al tiempo cero) en función del tiempo en ambos métodos." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "anaconda-cloud": {}, + "kernel_info": { + "name": "julia-0.5" + }, + "kernelspec": { + "display_name": "Julia 0.5.0", + "language": "julia", + "name": "julia-0.5" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "0.5.0" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} From 548ca3f4ca6eea61828dd43962ef9e72ce1da1ae Mon Sep 17 00:00:00 2001 From: carlos Date: Sun, 7 May 2017 17:17:42 -0500 Subject: [PATCH 2/9] =?UTF-8?q?gr=C3=A1fica=20de=20runge-kutta?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- tareas/Carlos/Tarea6.ipynb | 138 ++++++++++++++++++++++++++++++++++--- 1 file changed, 129 insertions(+), 9 deletions(-) diff --git a/tareas/Carlos/Tarea6.ipynb b/tareas/Carlos/Tarea6.ipynb index 06b622c..8462d18 100644 --- a/tareas/Carlos/Tarea6.ipynb +++ b/tareas/Carlos/Tarea6.ipynb @@ -78,18 +78,26 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: Method definition runge_kutta_4(Any, Any, Any, Any) in module Main at In[12]:6 overwritten at In[19]:6.\n", + "\u001b[1m\u001b[31mWARNING: replacing docs for 'runge_kutta_4 :: Tuple{Any,Any,Any,Any}' in module 'Main'.\u001b[0m\n" + ] + }, { "data": { "text/plain": [ "runge_kutta_4" ] }, - "execution_count": 2, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } @@ -100,9 +108,9 @@ "considerando el valor de una condicion inicial x_0, con cierto número de pasos, y cierto valor de y_0\n", "\"\"\"\n", "function runge_kutta_4(f,x_0,y_0,n)\n", - " x_f=1\n", - " a=zeros(n) #\"x\"\n", - " b=zeros(n) #\"y\"\n", + " x_f=0.1\n", + " a=zeros(n+1) #\"x\"\n", + " b=zeros(n+1) #\"y\"\n", " h=(x_f-x_0)/n\n", " a[1]=x_0\n", " b[1]=y_0\n", @@ -114,29 +122,115 @@ " b[i+1]=a[i]+(1/6)*(h)*(k_1+2*k_2+2*k_3+k_4)\n", " a[i+1]=a[i]+h\n", " end\n", + " return a,b\n", "end" ] }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: Method definition f(Any, " + ] + }, { "data": { "text/plain": [ - "1.0e-14" + "f (generic function with 1 method)" ] }, - "execution_count": 2, + "execution_count": 33, "metadata": {}, "output_type": "execute_result" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Any) in module Main at In[32]:1 overwritten at In[33]:1.\n" + ] } ], "source": [ - "1e-14" + "f(x,y)=y^2" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": { + "collapsed": false + }, + "outputs": [ 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", + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "using PyPlot\n", + "plot(R[1],R[2])\n", + "title(\"runge-kutta de cuarto orden con condición inicial x=0 y x(0)=3\")\n", + "xlabel(\"x\")\n", + "ylabel(\"x evaluada en y\")\n", + "show()" ] }, { @@ -155,6 +249,32 @@ "Integra la ecuación de movimiento para el oscilador armónico, $\\ddot{x} = -2x$, con $x(0)=2$, $\\dot{x}(0)=0$, durante 10^4 periodos de oscilación (o sea, hasta $t_f = 10^4 \\cdot 2\\pi/\\sqrt{2}$, usando el método de Taylor y el método de Runge-Kutta de 4o orden con paso de integración constante. Compara cómo cambia la energía (respecto al valor al tiempo cero) en función del tiempo en ambos métodos." ] }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "runge_kutta_4_2 (generic function with 1 method)" + ] + }, + "execution_count": 38, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function runge_kutta_4_2(f,x_0,y_0,y_1,n)\n", + " x_f=1\n", + " h=((x_f)-(x_0))/n\n", + " \n", + "end" + ] + }, { "cell_type": "code", "execution_count": null, From 20822c486662dc000aacf9f03b027c3527f00505 Mon Sep 17 00:00:00 2001 From: carlos Date: Mon, 8 May 2017 19:33:40 -0500 Subject: [PATCH 3/9] progreso en problema3 --- tareas/Carlos/Tarea6.ipynb | 82 +++++++++++++++++++++++++++++--------- 1 file changed, 63 insertions(+), 19 deletions(-) diff --git a/tareas/Carlos/Tarea6.ipynb b/tareas/Carlos/Tarea6.ipynb index 8462d18..31fa3b1 100644 --- a/tareas/Carlos/Tarea6.ipynb +++ b/tareas/Carlos/Tarea6.ipynb @@ -78,7 +78,7 @@ }, { "cell_type": "code", - "execution_count": 19, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -87,7 +87,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "WARNING: Method definition runge_kutta_4(Any, Any, Any, Any) in module Main at In[12]:6 overwritten at In[19]:6.\n", + "WARNING: Method definition runge_kutta_4(Any, Any, Any, Any) in module Main at In[1]:6 overwritten at In[4]:6.\n", "\u001b[1m\u001b[31mWARNING: replacing docs for 'runge_kutta_4 :: Tuple{Any,Any,Any,Any}' in module 'Main'.\u001b[0m\n" ] }, @@ -97,7 +97,7 @@ "runge_kutta_4" ] }, - "execution_count": 19, + "execution_count": 4, "metadata": {}, "output_type": "execute_result" } @@ -128,7 +128,7 @@ }, { "cell_type": "code", - "execution_count": 33, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -137,7 +137,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "WARNING: Method definition f(Any, " + "WARNING: Method definition f(Any" ] }, { @@ -146,7 +146,7 @@ "f (generic function with 1 method)" ] }, - "execution_count": 33, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" }, @@ -154,7 +154,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "Any) in module Main at In[32]:1 overwritten at In[33]:1.\n" + ", Any) in module Main at In[2]:1 overwritten at In[5]:1.\n" ] } ], @@ -164,7 +164,7 @@ }, { "cell_type": "code", - "execution_count": 34, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -172,10 +172,10 @@ { "data": { "text/plain": [ - "([0.0,1.0e-5,2.0e-5,3.0e-5,4.0e-5,5.0e-5,6.0e-5,7.0e-5,8.0e-5,9.0e-5 … 0.09991,0.09992,0.09993,0.09994,0.09995,0.09996,0.09997,0.09998,0.09999,0.1],[3.0,0.000270036,1.0e-5,2.0e-5,3.0e-5,4.0e-5,5.0e-5,6.0e-5,7.0e-5,8.0e-5 … 0.0999,0.09991,0.09992,0.09993,0.09994,0.09995,0.09996,0.09997,0.09998,0.09999])" + "([0.0,1.0e-5,2.0e-5,3.0e-5,4.0e-5,5.0e-5,6.0e-5,7.0e-5,8.0e-5,9.0e-5 … 0.09991,0.09992,0.09993,0.09994,0.09995,0.09996,0.09997,0.09998,0.09999,0.1],[3.0,9.00027e-5,1.0e-5,2.0e-5,3.0e-5,4.0e-5,5.0e-5,6.0e-5,7.0e-5,8.0e-5 … 0.0999001,0.0999101,0.0999201,0.0999301,0.0999401,0.0999501,0.0999601,0.0999701,0.0999801,0.0999901])" ] }, - "execution_count": 34, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -186,7 +186,7 @@ }, { "cell_type": "code", - "execution_count": 35, + "execution_count": 7, "metadata": { "collapsed": false }, @@ -197,7 +197,7 @@ "Tuple{Array{Float64,1},Array{Float64,1}}" ] }, - "execution_count": 35, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -208,16 +208,16 @@ }, { "cell_type": "code", - "execution_count": 37, + "execution_count": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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", "text/plain": [ - "PyPlot.Figure(PyObject )" + "PyPlot.Figure(PyObject )" ] }, "metadata": {}, @@ -251,30 +251,74 @@ }, { "cell_type": "code", - "execution_count": 38, + "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: Method definition runge_kutta_4_2(Any" + ] + }, { "data": { "text/plain": [ "runge_kutta_4_2 (generic function with 1 method)" ] }, - "execution_count": 38, + "execution_count": 16, "metadata": {}, "output_type": "execute_result" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + ", Any, Any, Any, Any) in module Main at In[15]:2 overwritten at In[16]:2.\n" + ] } ], "source": [ - "function runge_kutta_4_2(f,x_0,y_0,y_1,n)\n", + "function runge_kutta_4_2(f,x_0,y_0,y_1,n) #se aumenta un elemento más en la función de runge kutta, pero en principio es lo mismo\n", " x_f=1\n", " h=((x_f)-(x_0))/n\n", - " \n", + " x=zeros(n+1)\n", + " y=zeros(n+1)\n", + " yp=zeros(n+1)\n", + " x[1]=x_0\n", + " y[1]=y_0\n", + " yp[1]=y_1\n", + " g(x,y,yp)=z\n", + " k(x,y,yp)=f(x,y)\n", + " for i in 1:n\n", + " k_1=g(x[i],y[i],yp[i]) #las condiciones para definir \"x\", \"y\" y \"yprima\"\n", + " m_1=k(x[i],y[i],yp[i])\n", + " k_2=g(x[i]+((1/2)*h),y[i]+((k_1)*(1/2)*h),yp[i]+((m_1)*(1/2)*h))\n", + " m_2=k(x[i]+((1/2)*h),y[i]+((k_1)*(1/2)*h),yp[i]+((m_1)*(1/2)*h))\n", + " k_3=g(x[i]+((1/2)*h),y[i]+((k_2)*(1/2)*h),yp[i]+((m_2)*(1/2)*h))\n", + " m_3=k(x[i]+((1/2)*h),y[i]+((k_2)*(1/2)*h),yp[i]+((m_2)*(1/2)*h))\n", + " k_4=g(x[i]+h,y[i]+((k_3)*h),yp[i]+((m_3)*h)) \n", + " m_4=k(x[i]+h,y[i]+((k_3)*h),yp[i]+((m_3)*h))\n", + " x[i+1]=x[i]+h\n", + " y[i+1]=y[i]+(1/6)*(k_1+k_2+k_3+k_4)*h\n", + " yp[i+1]=yp[i]+(1/6)*(m_1+m_2+m_3+m_4)*h\n", + " end\n", + " return x,y\n", "end" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + }, { "cell_type": "code", "execution_count": null, From e8e66a791ad56da9de9384c45193b357e22e8dfe Mon Sep 17 00:00:00 2001 From: carlos Date: Mon, 8 May 2017 20:27:41 -0500 Subject: [PATCH 4/9] se elimina progreso de problema3 --- tareas/Carlos/Tarea6.ipynb | 96 +++++--------------------------------- 1 file changed, 11 insertions(+), 85 deletions(-) diff --git a/tareas/Carlos/Tarea6.ipynb b/tareas/Carlos/Tarea6.ipynb index 31fa3b1..7ecd617 100644 --- a/tareas/Carlos/Tarea6.ipynb +++ b/tareas/Carlos/Tarea6.ipynb @@ -78,26 +78,18 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "WARNING: Method definition runge_kutta_4(Any, Any, Any, Any) in module Main at In[1]:6 overwritten at In[4]:6.\n", - "\u001b[1m\u001b[31mWARNING: replacing docs for 'runge_kutta_4 :: Tuple{Any,Any,Any,Any}' in module 'Main'.\u001b[0m\n" - ] - }, { "data": { "text/plain": [ "runge_kutta_4" ] }, - "execution_count": 4, + "execution_count": 1, "metadata": {}, "output_type": "execute_result" } @@ -128,34 +120,20 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 2, "metadata": { "collapsed": false }, "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "WARNING: Method definition f(Any" - ] - }, { "data": { "text/plain": [ "f (generic function with 1 method)" ] }, - "execution_count": 5, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - ", Any) in module Main at In[2]:1 overwritten at In[5]:1.\n" - ] } ], "source": [ @@ -164,7 +142,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 3, "metadata": { "collapsed": false }, @@ -175,7 +153,7 @@ "([0.0,1.0e-5,2.0e-5,3.0e-5,4.0e-5,5.0e-5,6.0e-5,7.0e-5,8.0e-5,9.0e-5 … 0.09991,0.09992,0.09993,0.09994,0.09995,0.09996,0.09997,0.09998,0.09999,0.1],[3.0,9.00027e-5,1.0e-5,2.0e-5,3.0e-5,4.0e-5,5.0e-5,6.0e-5,7.0e-5,8.0e-5 … 0.0999001,0.0999101,0.0999201,0.0999301,0.0999401,0.0999501,0.0999601,0.0999701,0.0999801,0.0999901])" ] }, - "execution_count": 6, + "execution_count": 3, "metadata": {}, "output_type": "execute_result" } @@ -208,7 +186,7 @@ }, { "cell_type": "code", - "execution_count": 14, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -217,7 +195,7 @@ "data": { "image/png": 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", "text/plain": [ - "PyPlot.Figure(PyObject )" + "PyPlot.Figure(PyObject )" ] }, "metadata": {}, @@ -251,64 +229,12 @@ }, { "cell_type": "code", - "execution_count": 16, + "execution_count": null, "metadata": { "collapsed": false }, - "outputs": [ - { - "name": "stderr", - "output_type": "stream", - "text": [ - "WARNING: Method definition runge_kutta_4_2(Any" - ] - }, - { - "data": { - "text/plain": [ - "runge_kutta_4_2 (generic function with 1 method)" - ] - }, - "execution_count": 16, - "metadata": {}, - "output_type": "execute_result" - }, - { - "name": "stderr", - "output_type": "stream", - "text": [ - ", Any, Any, Any, Any) in module Main at In[15]:2 overwritten at In[16]:2.\n" - ] - } - ], - "source": [ - "function runge_kutta_4_2(f,x_0,y_0,y_1,n) #se aumenta un elemento más en la función de runge kutta, pero en principio es lo mismo\n", - " x_f=1\n", - " h=((x_f)-(x_0))/n\n", - " x=zeros(n+1)\n", - " y=zeros(n+1)\n", - " yp=zeros(n+1)\n", - " x[1]=x_0\n", - " y[1]=y_0\n", - " yp[1]=y_1\n", - " g(x,y,yp)=z\n", - " k(x,y,yp)=f(x,y)\n", - " for i in 1:n\n", - " k_1=g(x[i],y[i],yp[i]) #las condiciones para definir \"x\", \"y\" y \"yprima\"\n", - " m_1=k(x[i],y[i],yp[i])\n", - " k_2=g(x[i]+((1/2)*h),y[i]+((k_1)*(1/2)*h),yp[i]+((m_1)*(1/2)*h))\n", - " m_2=k(x[i]+((1/2)*h),y[i]+((k_1)*(1/2)*h),yp[i]+((m_1)*(1/2)*h))\n", - " k_3=g(x[i]+((1/2)*h),y[i]+((k_2)*(1/2)*h),yp[i]+((m_2)*(1/2)*h))\n", - " m_3=k(x[i]+((1/2)*h),y[i]+((k_2)*(1/2)*h),yp[i]+((m_2)*(1/2)*h))\n", - " k_4=g(x[i]+h,y[i]+((k_3)*h),yp[i]+((m_3)*h)) \n", - " m_4=k(x[i]+h,y[i]+((k_3)*h),yp[i]+((m_3)*h))\n", - " x[i+1]=x[i]+h\n", - " y[i+1]=y[i]+(1/6)*(k_1+k_2+k_3+k_4)*h\n", - " yp[i+1]=yp[i]+(1/6)*(m_1+m_2+m_3+m_4)*h\n", - " end\n", - " return x,y\n", - "end" - ] + "outputs": [], + "source": [] }, { "cell_type": "code", From 39c3fc1a4bd65533909ebb501d18abb3453382e6 Mon Sep 17 00:00:00 2001 From: carlos Date: Wed, 10 May 2017 21:15:55 -0500 Subject: [PATCH 5/9] =?UTF-8?q?progreso=20de=20problema=203=20con=20=C5=95?= =?UTF-8?q?eferencia?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- tareas/Carlos/Tarea6.ipynb | 107 +++++++++++++++++++++++++++++++------ 1 file changed, 90 insertions(+), 17 deletions(-) diff --git a/tareas/Carlos/Tarea6.ipynb b/tareas/Carlos/Tarea6.ipynb index 7ecd617..b8e8fdd 100644 --- a/tareas/Carlos/Tarea6.ipynb +++ b/tareas/Carlos/Tarea6.ipynb @@ -96,18 +96,18 @@ ], "source": [ "\"\"\"\n", - "se hará el método de runge-kutta para resolver una ecuación diferencial de la forma dy/dx=f(x,y),\n", - "considerando el valor de una condicion inicial x_0, con cierto número de pasos, y cierto valor de y_0\n", + "se hará el método de runge-kutta para resolver una ecuación diferencial de la forma dx/dt=f(x,t),\n", + "considerando el valor de una condicion inicial en t_0, con cierto número de pasos, y cierto valor en x_0\n", "\"\"\"\n", - "function runge_kutta_4(f,x_0,y_0,n)\n", - " x_f=0.1\n", - " a=zeros(n+1) #\"x\"\n", - " b=zeros(n+1) #\"y\"\n", - " h=(x_f-x_0)/n\n", - " a[1]=x_0\n", - " b[1]=y_0\n", + "function runge_kutta_4(f,t_0,x_0,n)\n", + " t_f=0.1\n", + " a=zeros(n+1) #\"t\"\n", + " b=zeros(n+1) #\"x\"\n", + " h=(t_f-t_0)/n\n", + " a[1]=t_0\n", + " b[1]=x_0\n", " for i in 1:n\n", - " k_1=f(a[i],b[i]) #condiciones necesarias para definir el siguiente valor de \"y\" y de \"x\"\n", + " k_1=f(a[i],b[i]) #condiciones necesarias para definir el siguiente valor de \"t\" y de \"x\"\n", " k_2=f(a[i]+(h*(1/2)),b[i]+((1/2)*((k_1)*h)))\n", " k_3=f(a[i]+(h*(1/2)),b[i]+((1/2)*((k_2)*h)))\n", " k_4=f(a[i]+h,b[i]+((k_3)*h))\n", @@ -229,21 +229,94 @@ }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": { "collapsed": false }, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "text/plain": [ + "runge_kutta_4_2 (generic function with 1 method)" + ] + }, + "execution_count": 6, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "function runge_kutta_4_2(f,t_0,x_0,y_0,n) #se aumenta un elemento más en la función de runge kutta, pero en principio es lo mismo\n", + " t_f=(10e4*2*pi)/(sqrt(2))\n", + " h=((t_f)-(t_0))/n\n", + " t=zeros(n+1)\n", + " x=zeros(n+1)\n", + " y=zeros(n+1)\n", + " t[1]=t_0\n", + " x[1]=x_0\n", + " y[1]=y_0\n", + " k(t,x,y)=y\n", + " g(t,x,y)=f(t,x)\n", + " for i in 1:n\n", + " k_1=g(t[i],x[i],y[i]) #las condiciones para definir \"x\", \"y\" y \"yprima\"\n", + " m_1=k(t[i],x[i],y[i])\n", + " k_2=g(t[i]+((1/2)*h),x[i]+((k_1)*(1/2)*h),y[i]+((m_1)*(1/2)*h))\n", + " m_2=k(t[i]+((1/2)*h),x[i]+((k_1)*(1/2)*h),y[i]+((m_1)*(1/2)*h))\n", + " k_3=g(t[i]+((1/2)*h),x[i]+((k_2)*(1/2)*h),y[i]+((m_2)*(1/2)*h))\n", + " m_3=k(t[i]+((1/2)*h),x[i]+((k_2)*(1/2)*h),y[i]+((m_2)*(1/2)*h))\n", + " k_4=g(t[i]+h,x[i]+((k_3)*h),y[i]+((m_3)*h)) \n", + " m_4=k(t[i]+h,x[i]+((k_3)*h),y[i]+((m_3)*h))\n", + " t[i+1]=t[i]+h\n", + " x[i+1]=x[i]+(1/6)*(k_1+k_2+k_3+k_4)*h\n", + " y[i+1]=y[i]+(1/6)*(m_1+m_2+m_3+m_4)*h\n", + " end\n", + " return x,y\n", + "end" + ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 7, "metadata": { - "collapsed": true + "collapsed": false }, - "outputs": [], - "source": [] + "outputs": [ + { + "data": { + "text/plain": [ + "g (generic function with 1 method)" + ] + }, + "execution_count": 7, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "g(x,t)=-2x" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "([2.0,-1.31593e5,-5.26377e5,-1.18435e6,-2.10551e6,-3.28987e6,-4.73741e6,-6.44814e6,-8.42206e6,-1.06592e7 … -1.29237e11,-1.29498e11,-1.29759e11,-1.3002e11,-1.30282e11,-1.30544e11,-1.30806e11,-1.31069e11,-1.31332e11,-1.31595e11],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 … 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "runge_kutta_4_2(g,0,2,0,1000)" + ] }, { "cell_type": "code", From 21767b49c197225e2e1a5c04239755a6aa71eecd Mon Sep 17 00:00:00 2001 From: carlos Date: Wed, 10 May 2017 21:48:49 -0500 Subject: [PATCH 6/9] se agregan modificaciones al problema 3, no obstante, la grafcacion esta mal --- tareas/Carlos/Tarea6.ipynb | 71 ++++++++++++++++++++++++++++---------- 1 file changed, 52 insertions(+), 19 deletions(-) diff --git a/tareas/Carlos/Tarea6.ipynb b/tareas/Carlos/Tarea6.ipynb index b8e8fdd..f985570 100644 --- a/tareas/Carlos/Tarea6.ipynb +++ b/tareas/Carlos/Tarea6.ipynb @@ -78,7 +78,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -89,7 +89,7 @@ "runge_kutta_4" ] }, - "execution_count": 1, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -120,7 +120,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -131,7 +131,7 @@ "f (generic function with 1 method)" ] }, - "execution_count": 2, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -142,7 +142,7 @@ }, { "cell_type": "code", - "execution_count": 3, + "execution_count": 7, "metadata": { "collapsed": false }, @@ -153,7 +153,7 @@ "([0.0,1.0e-5,2.0e-5,3.0e-5,4.0e-5,5.0e-5,6.0e-5,7.0e-5,8.0e-5,9.0e-5 … 0.09991,0.09992,0.09993,0.09994,0.09995,0.09996,0.09997,0.09998,0.09999,0.1],[3.0,9.00027e-5,1.0e-5,2.0e-5,3.0e-5,4.0e-5,5.0e-5,6.0e-5,7.0e-5,8.0e-5 … 0.0999001,0.0999101,0.0999201,0.0999301,0.0999401,0.0999501,0.0999601,0.0999701,0.0999801,0.0999901])" ] }, - "execution_count": 3, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -164,7 +164,7 @@ }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 8, "metadata": { "collapsed": false }, @@ -175,7 +175,7 @@ "Tuple{Array{Float64,1},Array{Float64,1}}" ] }, - "execution_count": 7, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } @@ -186,7 +186,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 9, "metadata": { "collapsed": false }, @@ -195,7 +195,7 @@ "data": { "image/png": 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", "text/plain": [ - "PyPlot.Figure(PyObject )" + "PyPlot.Figure(PyObject )" ] }, "metadata": {}, @@ -229,7 +229,7 @@ }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 1, "metadata": { "collapsed": false }, @@ -240,7 +240,7 @@ "runge_kutta_4_2 (generic function with 1 method)" ] }, - "execution_count": 6, + "execution_count": 1, "metadata": {}, "output_type": "execute_result" } @@ -270,13 +270,13 @@ " x[i+1]=x[i]+(1/6)*(k_1+k_2+k_3+k_4)*h\n", " y[i+1]=y[i]+(1/6)*(m_1+m_2+m_3+m_4)*h\n", " end\n", - " return x,y\n", + " return t,x\n", "end" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 2, "metadata": { "collapsed": false }, @@ -287,7 +287,7 @@ "g (generic function with 1 method)" ] }, - "execution_count": 7, + "execution_count": 2, "metadata": {}, "output_type": "execute_result" } @@ -298,7 +298,7 @@ }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 4, "metadata": { "collapsed": false }, @@ -306,16 +306,49 @@ { "data": { "text/plain": [ - "([2.0,-1.31593e5,-5.26377e5,-1.18435e6,-2.10551e6,-3.28987e6,-4.73741e6,-6.44814e6,-8.42206e6,-1.06592e7 … -1.29237e11,-1.29498e11,-1.29759e11,-1.3002e11,-1.30282e11,-1.30544e11,-1.30806e11,-1.31069e11,-1.31332e11,-1.31595e11],[0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0 … 0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0])" + "([0.0,444.288,888.577,1332.86,1777.15,2221.44,2665.73,3110.02,3554.31,3998.59 … 4.4029e5,440734.0,4.41178e5,4.41623e5,4.42067e5,4.42511e5,4.42955e5,4.434e5,443844.0,4.44288e5],[2.0,-1.31593e5,-5.26377e5,-1.18435e6,-2.10551e6,-3.28987e6,-4.73741e6,-6.44814e6,-8.42206e6,-1.06592e7 … -1.29237e11,-1.29498e11,-1.29759e11,-1.3002e11,-1.30282e11,-1.30544e11,-1.30806e11,-1.31069e11,-1.31332e11,-1.31595e11])" ] }, - "execution_count": 8, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "b=runge_kutta_4_2(g,0,2,0,1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "1-element Array{Any,1}:\n", + " PyObject " + ] + }, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "runge_kutta_4_2(g,0,2,0,1000)" + "plot(b[1],b[2])" ] }, { From d7cf26f9efe3276d5515b8551c2049fdd9131763 Mon Sep 17 00:00:00 2001 From: carlos Date: Thu, 11 May 2017 19:42:31 -0500 Subject: [PATCH 7/9] cambios en problema 2 y 3 --- tareas/Carlos/Tarea6.ipynb | 111 +++++++++++++++++++++++-------------- 1 file changed, 68 insertions(+), 43 deletions(-) diff --git a/tareas/Carlos/Tarea6.ipynb b/tareas/Carlos/Tarea6.ipynb index f985570..0c6e780 100644 --- a/tareas/Carlos/Tarea6.ipynb +++ b/tareas/Carlos/Tarea6.ipynb @@ -78,18 +78,26 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: Method definition runge_kutta_4(Any, Any, Any, Any) in module Main at In[39]:6 overwritten at In[40]:6.\n", + "\u001b[1m\u001b[31mWARNING: replacing docs for 'runge_kutta_4 :: Tuple{Any,Any,Any,Any}' in module 'Main'.\u001b[0m\n" + ] + }, { "data": { "text/plain": [ "runge_kutta_4" ] }, - "execution_count": 5, + "execution_count": 40, "metadata": {}, "output_type": "execute_result" } @@ -101,48 +109,65 @@ "\"\"\"\n", "function runge_kutta_4(f,t_0,x_0,n)\n", " t_f=0.1\n", - " a=zeros(n+1) #\"t\"\n", - " b=zeros(n+1) #\"x\"\n", + " t=zeros(n+1) #\"t\"\n", + " x=zeros(n+1) #\"x\"\n", + " g=zeros(n+1)#la funcion evaluada en t y x\n", " h=(t_f-t_0)/n\n", - " a[1]=t_0\n", - " b[1]=x_0\n", + " t[1]=t_0\n", + " x[1]=x_0\n", " for i in 1:n\n", - " k_1=f(a[i],b[i]) #condiciones necesarias para definir el siguiente valor de \"t\" y de \"x\"\n", - " k_2=f(a[i]+(h*(1/2)),b[i]+((1/2)*((k_1)*h)))\n", - " k_3=f(a[i]+(h*(1/2)),b[i]+((1/2)*((k_2)*h)))\n", - " k_4=f(a[i]+h,b[i]+((k_3)*h))\n", - " b[i+1]=a[i]+(1/6)*(h)*(k_1+2*k_2+2*k_3+k_4)\n", - " a[i+1]=a[i]+h\n", + " k_1=f(t[i],x[i]) #condiciones necesarias para definir el siguiente valor de \"t\" y de \"x\"\n", + " k_2=f(t[i]+(h*(1/2)),x[i]+((1/2)*((k_1)*h)))\n", + " k_3=f(t[i]+(h*(1/2)),x[i]+((1/2)*((k_2)*h)))\n", + " k_4=f(t[i]+h,x[i]+((k_3)*h))\n", + " x[i+1]=x[i]+(1/6)*(h)*(k_1+2*k_2+2*k_3+k_4)\n", + " t[i+1]=t[i]+h\n", + " g[i+1]=f(t[i],x[i])\n", + " \n", " end\n", - " return a,b\n", + " return t,g\n", "end" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 41, "metadata": { "collapsed": false }, "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "WARNING: Method definition f(Any" + ] + }, { "data": { "text/plain": [ "f (generic function with 1 method)" ] }, - "execution_count": 6, + "execution_count": 41, "metadata": {}, "output_type": "execute_result" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + ", Any) in module Main at In[37]:1 overwritten at In[41]:1.\n" + ] } ], "source": [ - "f(x,y)=y^2" + "f(t,x)=x^2" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 42, "metadata": { "collapsed": false }, @@ -150,21 +175,21 @@ { "data": { "text/plain": [ - "([0.0,1.0e-5,2.0e-5,3.0e-5,4.0e-5,5.0e-5,6.0e-5,7.0e-5,8.0e-5,9.0e-5 … 0.09991,0.09992,0.09993,0.09994,0.09995,0.09996,0.09997,0.09998,0.09999,0.1],[3.0,9.00027e-5,1.0e-5,2.0e-5,3.0e-5,4.0e-5,5.0e-5,6.0e-5,7.0e-5,8.0e-5 … 0.0999001,0.0999101,0.0999201,0.0999301,0.0999401,0.0999501,0.0999601,0.0999701,0.0999801,0.0999901])" + "([0.0,1.0e-7,2.0e-7,3.0e-7,4.0e-7,5.0e-7,6.0e-7,7.0e-7,8.0e-7,9.0e-7 … 0.0999991,0.0999992,0.0999993,0.0999994,0.0999995,0.0999996,0.0999997,0.0999998,0.0999999,0.1],[0.0,9.0,9.00001,9.00001,9.00002,9.00002,9.00003,9.00003,9.00004,9.00004 … 18.3672,18.3672,18.3672,18.3672,18.3673,18.3673,18.3673,18.3673,18.3673,18.3673])" ] }, - "execution_count": 7, + "execution_count": 42, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "R=runge_kutta_4(f,0,3,10000)" + "(t,x)=runge_kutta_4(f,0,3,1000000)" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 43, "metadata": { "collapsed": false }, @@ -175,7 +200,7 @@ "Tuple{Array{Float64,1},Array{Float64,1}}" ] }, - "execution_count": 8, + "execution_count": 43, "metadata": {}, "output_type": "execute_result" } @@ -186,16 +211,16 @@ }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ - "PyPlot.Figure(PyObject )" + "PyPlot.Figure(PyObject )" ] }, "metadata": {}, @@ -204,10 +229,10 @@ ], "source": [ "using PyPlot\n", - "plot(R[1],R[2])\n", - "title(\"runge-kutta de cuarto orden con condición inicial x=0 y x(0)=3\")\n", - "xlabel(\"x\")\n", - "ylabel(\"x evaluada en y\")\n", + "plot(t,x)\n", + "title(\"runge-kutta de cuarto orden con condición inicial t=0 y x(0)=3\")\n", + "xlabel(\"t\")\n", + "ylabel(\"x evaluada en t\")\n", "show()" ] }, @@ -229,7 +254,7 @@ }, { "cell_type": "code", - "execution_count": 1, + "execution_count": 46, "metadata": { "collapsed": false }, @@ -240,7 +265,7 @@ "runge_kutta_4_2 (generic function with 1 method)" ] }, - "execution_count": 1, + "execution_count": 46, "metadata": {}, "output_type": "execute_result" } @@ -276,7 +301,7 @@ }, { "cell_type": "code", - "execution_count": 2, + "execution_count": 47, "metadata": { "collapsed": false }, @@ -287,7 +312,7 @@ "g (generic function with 1 method)" ] }, - "execution_count": 2, + "execution_count": 47, "metadata": {}, "output_type": "execute_result" } @@ -298,7 +323,7 @@ }, { "cell_type": "code", - "execution_count": 4, + "execution_count": 51, "metadata": { "collapsed": false }, @@ -306,30 +331,30 @@ { "data": { "text/plain": [ - "([0.0,444.288,888.577,1332.86,1777.15,2221.44,2665.73,3110.02,3554.31,3998.59 … 4.4029e5,440734.0,4.41178e5,4.41623e5,4.42067e5,4.42511e5,4.42955e5,4.434e5,443844.0,4.44288e5],[2.0,-1.31593e5,-5.26377e5,-1.18435e6,-2.10551e6,-3.28987e6,-4.73741e6,-6.44814e6,-8.42206e6,-1.06592e7 … -1.29237e11,-1.29498e11,-1.29759e11,-1.3002e11,-1.30282e11,-1.30544e11,-1.30806e11,-1.31069e11,-1.31332e11,-1.31595e11])" + "([0.0,4.44288,8.88577,13.3286,17.7715,22.2144,26.6573,31.1002,35.5431,39.9859 … 4.44248e5,4.44253e5,4.44257e5,4.44262e5,4.44266e5,4.44271e5,444275.0,4.44279e5,4.44284e5,4.44288e5],[2.0,-11.1595,-50.6379,-116.435,-208.552,-326.987,-471.741,-642.814,-840.206,-1063.92 … -1.31571e11,-1.31574e11,-1.31576e11,-1.31579e11,-1.31582e11,-1.31584e11,-1.31587e11,-1.31589e11,-1.31592e11,-1.31595e11])" ] }, - "execution_count": 4, + "execution_count": 51, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "b=runge_kutta_4_2(g,0,2,0,1000)" + "(t,x)=runge_kutta_4_2(g,0,2,0,100000)" ] }, { "cell_type": "code", - "execution_count": 10, + "execution_count": 52, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "PyPlot.Figure(PyObject )" + "PyPlot.Figure(PyObject )" ] }, "metadata": {}, @@ -339,16 +364,16 @@ "data": { "text/plain": [ "1-element Array{Any,1}:\n", - " PyObject " + " PyObject " ] }, - "execution_count": 10, + "execution_count": 52, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "plot(b[1],b[2])" + "plot(t,x)" ] }, { From a0a69f08dda10632e47670422db1da8e3285c805 Mon Sep 17 00:00:00 2001 From: carlos Date: Mon, 15 May 2017 17:18:34 -0500 Subject: [PATCH 8/9] =?UTF-8?q?corrigiendo=20gr=C3=A1fica=20e=20insertando?= =?UTF-8?q?=20error=20relativo?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- tareas/Carlos/Tarea6.ipynb | 119 ++++++++++++++++++++++++++----------- 1 file changed, 83 insertions(+), 36 deletions(-) diff --git a/tareas/Carlos/Tarea6.ipynb b/tareas/Carlos/Tarea6.ipynb index 0c6e780..0a8c284 100644 --- a/tareas/Carlos/Tarea6.ipynb +++ b/tareas/Carlos/Tarea6.ipynb @@ -78,7 +78,7 @@ }, { "cell_type": "code", - "execution_count": 40, + "execution_count": 24, "metadata": { "collapsed": false }, @@ -87,7 +87,7 @@ "name": "stderr", "output_type": "stream", "text": [ - "WARNING: Method definition runge_kutta_4(Any, Any, Any, Any) in module Main at In[39]:6 overwritten at In[40]:6.\n", + "WARNING: Method definition runge_kutta_4(Any, Any, Any, Any) in module Main at In[14]:6 overwritten at In[24]:6.\n", "\u001b[1m\u001b[31mWARNING: replacing docs for 'runge_kutta_4 :: Tuple{Any,Any,Any,Any}' in module 'Main'.\u001b[0m\n" ] }, @@ -97,7 +97,7 @@ "runge_kutta_4" ] }, - "execution_count": 40, + "execution_count": 24, "metadata": {}, "output_type": "execute_result" } @@ -108,10 +108,9 @@ "considerando el valor de una condicion inicial en t_0, con cierto número de pasos, y cierto valor en x_0\n", "\"\"\"\n", "function runge_kutta_4(f,t_0,x_0,n)\n", - " t_f=0.1\n", - " t=zeros(n+1) #\"t\"\n", - " x=zeros(n+1) #\"x\"\n", - " g=zeros(n+1)#la funcion evaluada en t y x\n", + " t_f=0.333\n", + " t=Array(Number,1) #\"t\"\n", + " x=Array(Number,1) #\"x\"\n", " h=(t_f-t_0)/n\n", " t[1]=t_0\n", " x[1]=x_0\n", @@ -120,18 +119,18 @@ " k_2=f(t[i]+(h*(1/2)),x[i]+((1/2)*((k_1)*h)))\n", " k_3=f(t[i]+(h*(1/2)),x[i]+((1/2)*((k_2)*h)))\n", " k_4=f(t[i]+h,x[i]+((k_3)*h))\n", - " x[i+1]=x[i]+(1/6)*(h)*(k_1+2*k_2+2*k_3+k_4)\n", - " t[i+1]=t[i]+h\n", - " g[i+1]=f(t[i],x[i])\n", - " \n", + " m=x[i]+(1/6)*(h)*(k_1+2*k_2+2*k_3+k_4)\n", + " push!(x,m)\n", + " n=t[i]+h\n", + " push!(t,n)\n", " end\n", - " return t,g\n", + " return t,x\n", "end" ] }, { "cell_type": "code", - "execution_count": 41, + "execution_count": 15, "metadata": { "collapsed": false }, @@ -149,7 +148,7 @@ "f (generic function with 1 method)" ] }, - "execution_count": 41, + "execution_count": 15, "metadata": {}, "output_type": "execute_result" }, @@ -157,7 +156,7 @@ "name": "stderr", "output_type": "stream", "text": [ - ", Any) in module Main at In[37]:1 overwritten at In[41]:1.\n" + ", Any) in module Main at In[10]:1 overwritten at In[15]:1.\n" ] } ], @@ -167,7 +166,7 @@ }, { "cell_type": "code", - "execution_count": 42, + "execution_count": 25, "metadata": { "collapsed": false }, @@ -175,21 +174,21 @@ { "data": { "text/plain": [ - "([0.0,1.0e-7,2.0e-7,3.0e-7,4.0e-7,5.0e-7,6.0e-7,7.0e-7,8.0e-7,9.0e-7 … 0.0999991,0.0999992,0.0999993,0.0999994,0.0999995,0.0999996,0.0999997,0.0999998,0.0999999,0.1],[0.0,9.0,9.00001,9.00001,9.00002,9.00002,9.00003,9.00003,9.00004,9.00004 … 18.3672,18.3672,18.3672,18.3672,18.3673,18.3673,18.3673,18.3673,18.3673,18.3673])" + "(Number[0,0.000333,0.000666,0.000999,0.001332,0.001665,0.001998,0.002331,0.002664,0.002997 … 0.330003,0.330336,0.330669,0.331002,0.331335,0.331668,0.332001,0.332334,0.332667,0.333],Number[3,3.003,3.00601,3.00902,3.01204,3.01506,3.01809,3.02113,3.02417,3.02722 … 300.27,333.629,375.327,428.937,500.412,600.468,750.525,1000.52,1499.73,2978.76])" ] }, - "execution_count": 42, + "execution_count": 25, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(t,x)=runge_kutta_4(f,0,3,1000000)" + "R_K=runge_kutta_4(f,0,3,1000)" ] }, { "cell_type": "code", - "execution_count": 43, + "execution_count": 18, "metadata": { "collapsed": false }, @@ -197,10 +196,10 @@ { "data": { "text/plain": [ - "Tuple{Array{Float64,1},Array{Float64,1}}" + "Tuple{Array{Number,1},Array{Number,1}}" ] }, - "execution_count": 43, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" } @@ -211,16 +210,16 @@ }, { "cell_type": "code", - "execution_count": 44, + "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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cuTOio6PvdxVUWrRoEQ4cOHDPv9WrVyuWqb/0r6ovlqGh4T27Q3Tq1Am9evXCt99+qygrKCjAvn37MGXKlHseBx0cHPDvf/8bBw4cwIABAxATE4NNmzYpXSrMz88HAKV9WZ3Y75ynXn0dd17yDg8PV2u7HThwQOU6fPPNN/jtt9/w+eefw8/PDxUVFWpdPq7X7i7PeXh4PHAdHTt2VHpd/8HW90FKTk4GAHh7ezdY1tvbW+nLFx8fj6KiItjZ2al8r5ycHABAUVGR0g5lYGCg1Lz63//+F6WlpdiwYYPSQfphSUlJwdKlS/Hzzz836ItVVFTU5LLJycno1atXg/LOnTsrvY6PjweARjsF3vnFVeXmzZsYN25ck/NoQpN11tPTU+sSSr3k5GT4+Pg0uLOnvmm/fh9rbFmg4fYzMDCAp6dng2WdnZ0bXJqpn8fHx0ep3NbWtsHBMD4+HpcuXYKtra3KeOr34Xr3+v40Rp3PT9Pt1pZiaewzAXDPH/Xc3FwUFxcrLnGoq7F9Cajri3LixAmlsvq+Q3eytLR8oP6Z9/MZ3bx5E05OTkrHSHXU94P6/PPPkZiYqPRjeuedXc3B39//nsnu3epP1KqqqhpMq6ysVNml4W5Tp07FK6+8guTkZLi5uSEyMhI1NTV47rnn1Iph0qRJ2LZtG/bs2YPnn3++0Utb4q7uL/eK/c557q7jzmTO0dERjo6OasWqSp8+fRT/nzRpkuL7uGrVKrWWb3dJk6qdSiKRqOzf1Fj2qaurq7JcVR33IpfLYWdnp5T536n+ADRv3jylDqShoaFKHQr79euHmJgYrF+/HhMmTGhwsGjsDEKTDLsxMpkMw4YNQ0FBAf71r3/B19cXJiYmSE9Px/Tp0+/rVmBV6uvZunUrHBwcGkzX9PZqVdTdTpqu851nsK2NOgfapsjlcgwbNgyLFi1SOf3uQRCb8/vzoBhL82psHVqizpbYLitXrsTbb7+NmTNnYsWKFbCysoKOjg7mz5/fbMexenefCDfmzhPk+mQhMzOzwXyZmZlq9bmaNGkSXnvtNXz77bdYsmQJtm3bhu7du6tMjFXJz89XdKaPjY2FXC5XOrbVJ5d3J7VWVlaQSqWNxg6gQfz1ddzZN6miouKeJ+L1VP1O3MnS0hKDBw/Gt99+y6RJE5aWliqbeps6m2+Km5sbADS4w0NVmZeXFw4ePIh+/fo1+eO1aNEipU56d5/te3t746OPPsKgQYMwYsQIHDp0SKlDXf38d98loGodG0scGiu/fPkybty4gS1btmDq1KmK8saaR+/m5uamaEW6092PafDy8gJQd8fD0KFD1ar77uXvNZCZutvpQde5XmPb1M3NDZcuXWpwQLp+/bpiemPqp8XFxcHT01NRXl1djcTERLW2XX0d8fHxSnXk5uY2OBh6eXmhtLT0vj4TTajz+T3Idmvtsdz5mdztXo80sbW1hZmZmcYD+d25L93dwhsXF9ds27O5eXl54ffff2/Q4fledu7cibCwMHz99ddK5YWFhRrfKAI0fSnw7hPhxtx5ghwQEAA9PT1ERUVhwoQJinmqq6sRExOjVNYYKysrjB49Gt9++y2mTJmCkydPajTA7ssvv4ySkhJERERg8eLFWLNmDRYsWKCY3rFjRxgZGSExMVFpOR0dHQQGBirdvVjv7Nmz8PT0VPrNAqCoo741CAB27NjRoDtBY9RJrDVJwoB2NORAU7y8vHD9+nXk5uYqyi5evHhfw78DddlyQECA4pJZvT/++AOXL19WmnfChAmQyWRYsWJFg3pqa2sVP97+/v4YOnSo4i8kJKTB/I899hj27t2La9euYcyYMUpnMfUJx539S2QyGb744osG9ZiYmKjcierHFbo7oag/E7xzBxVCYO3atQ3qUGXUqFE4c+YM/vzzT0VZbm5ug9a38PBwmJmZYeXKlaipqWlQz52fnyrjxo3DxYsXVd6iXR+7utvpQde5XmPbetSoUcjKysKOHTsUZbW1tVi3bh1MTU0RGhraaJ1Dhw6FgYEBPvvsM6X4vv76axQVFWH06NH3jGvo0KHQ19fHunXrlOpQdXCdMGECTp8+jd9//73BtMLCQtTW1t7z/dShzuf3INuttcfi6OiI4OBgbNmyRWmfOXDgAGJjY5tcVkdHB2PHjsUvv/yi8kersR+X7t27w87ODhs3blS6rLJv3z5cu3ZNrX1JG8aNGwchBJYvX95gWlM/pLq6ug2mR0ZGNhheQV2NHTOB++vTZG5ujqFDh2Lbtm1Kd5Bt3boVpaWliiEO7uW5555DbGws/vnPf0JXVxeTJk1Sa7mdO3dix44d+OCDD/DGG29g0qRJeOutt3Djxg3FPPr6+ujevbvK/ezpp5/GuXPnlKbFxcXh8OHDKmM/f/48zM3N0aVLF0XZ/fZpurubAFA33MehQ4cavZtSFbY0AZg5cyY++eQThIeHY9asWcjJycHGjRvRpUsXFBcX31edK1euxJNPPol+/fphxowZuH37NtavX4+AgAClRCo0NBQvvPACIiIiEBMTg+HDh0NfXx/x8fGIjIzE2rVr8fTTT6v9vr1798ZPP/2EUaNG4emnn8bu3buhr6+PLl26oHfv3li8eLHi7Ou7775T+YMWEhKCHTt2YMGCBejRowdMTU0xZswYeHl5wcLCAhs3bkSHDh1gYmKCXr16wdfXF15eXli4cCHS09NhZmaGH374Qe1+DIsWLcLWrVsxYsQIzJs3TzHkQP2Zej0zMzNs2LABzz33HLp164ZJkybB1tYWKSkp2LNnD/r164f169c3+j7//Oc/sXPnTowfPx4zZ85ESEgICgoK8PPPP2Pjxo0ICgpSezs96Drfa1s///zz+M9//oPp06fj/PnzcHd3x86dOxVnhXefkd3J1tYWixcvxvLlyzFixAg88cQTiIuLw+eff44ePXo0eVvxnXUsXLgQERERePzxxzFq1ChcuHAB+/bta3DG/c9//hM///wzHn/8cUyfPh0hISEoKyvD5cuXsXPnTiQlJd3XWfrd1Pn8HmS7tYVYIiIiMHr0aPTv3x8zZ85EQUEB1q1bhy5dutzzMRorV67E/v37ERoaiueffx5+fn7IzMxEZGQkTpw4oTR0QD19fX18+OGHmDFjBkJDQzF58mTFkAPu7u547bXXNF6HhyEsLAzPPfccPvvsM8THx2PEiBGQy+U4fvw4wsLCGn1W5+OPP453330XM2bMQN++fXH58mV8++23Sq2tmggODoauri4+/PBDFBUVQSqVYvDgwbCzs7uvPk0A8P7776Nv376KzzEtLQ2rV6/G8OHDMWLECLXqGD16NKytrREZGYmRI0c22qf2Tjk5OZg7d67S9lu/fj2OHDmC6dOn48SJE4oW1SeffBJvvvkmiouLlfqavvTSS/jyyy8xevRoLFy4EPr6+vjkk09gb2+P119/vcF7HjhwAGPGjGmWPk2BgYEYMmQIgoODYWlpifj4eHz99deoqanBBx98oH5Fat9n18bVDzmQm5urcvq2bduEp6enMDAwEMHBweL3339vdMiBjz/+uMHyuOv2XiGE+O6774Svr68wMDAQ/v7+YteuXWLcuHHC19e3wfJffPGFCAkJEUZGRqJDhw4iMDBQLFq0SGRkZNxz3XDHkAP1fvrpJ6GnpycmTpyouJ3y5s2bYujQoUIqlQp7e3uxZMkSceDAgQa3xJaWlopnnnlGWFhYNLiV+aeffhL+/v5CT09P6Zbb2NhYMXToUGFqaipsbGzEnDlzxMWLF9W6LVcIIS5duiRCQ0OFoaGhcHZ2FitWrBBff/11o7f/h4eHC3Nzc2FoaCi8vLzE9OnTRVRU1D3fJz8/X7zyyivC2dlZGBgYCBcXFzFt2jSRl5enmEfd7aTuOk+bNk2YmJiojKepbZ2dnS1mzJghbGxshIGBgQgMDFRrW9Zbv3698PX1Ffr6+sLe3l7MnTtX3L59W2me0NBQ0aVLF5XLy2QysXz5cuHo6CiMjIzEoEGDxJUrVxrcpi1E3XAQixcvFt7e3sLAwEDY2NiIvn37ilWrVonq6mohhObfH1XU+fzU2W5tOZYffvhB+Pn5CalUKvz9/cWPP/7Y4FjV2LLJycli6tSpwtbWVkilUuHp6SlefvllxS39qobWEEKIHTt2iK5duwqpVCqsrKzElClTRFpamtI8je3n9cfee2lsyIHIyEil+VTd7q9q/Wtra8XHH3+sOAbb2tqKkSNHivPnzyvmUTXkwOuvv67Y5/v16ydOnz7dIDZ1hxwQQogvv/xSeHp6Cl1d3UaHH9DU8ePHRd++fYWhoaGwtbUVL7/8cpPDkKjy0ksvCQBi+/btas3/1FNPiQ4dOoikpCSl8vqhMT788ENFWXZ2ttDT0xNbt25tUE9qaqp4+umnhZmZmTA1NRWPP/64iI+PbzDftWvXBABx8OBBjdarMe+8847o3r27sLS0FHp6esLJyUlMmjRJXLp0SaN6JEK0oV6Gj4Dg4GDY2tpq3PeFiIioubz22mv4+uuvkZWV1SKPTZo1axZu3LiB48eP39fy8+fPx7Fjx3D+/PlW9XBo9mlqITU1NQ0u6Rw9ehQXL15U+cgWIiKih6GyshLbtm3DuHHjWuw5k++8847iCQSays/Px1dffYX33nuvVSVMAMCWphaSlJSEoUOH4tlnn4WTkxOuX7+OjRs3wtzcHFeuXGn2MT+IiIiakpOTg4MHD2Lnzp3YvXs3oqOjERwcrO2w2hR2BG8hlpaWCAkJwVdffYXc3FyYmJhg9OjR+OCDD5gwERHRQxcbG4spU6bAzs4On332GROm+8CWJiIiIiI1sE8TERERkRqYNBERERGpgX2aVJDL5cjIyECHDh1aXc99IiIiUk0IgZKSEjg5ObXI8z6ZNKmQkZEBV1dXbYdBRERE9yE1NRUuLi7NXi+TJhXqH2+QmpqqNAQ8ERERtV7FxcVwdXVttkcm3Y1Jkwr1l+TMzMyYNBEREbUxLdW1hh3BiYiIiNTApImIiIhIDUyaiIiIiNTApImIiIhIDUyaiIiIiNTApImIiIhIDUyaiIiIiNTApImIiIhIDUyaiIiIiNTApImIiIhIDUyaiIiIiNTApImIiIhIDUyaiIiI6KGKzShGRmGFtsPQGJMmIiIieigqa2T4YN91jFl/Am/vvgIhhLZD0oietgMgIiKiR9+J+Dy8ufsykvPLAQBSfR1U1cphqK+r5cjUx6SJiIiIWkxBWTXe2xOLH6PTAQCO5oZ498kADPO313JkmmPSRERERM1OCIGd59Owcu813C6vgUQCTOvjjoXhnWEqbZvpR9uMmoiIiFqthJwSLNl1BX8mFgAAfB06IOKpQHTtaKnlyB4MkyYiIiJqFpU1Mqw/nID/HLuJGpmAkb4uXhvmgxn9PKCv2/bvPWPSRERERA/sjxu5eHv3FaQU1HX0Hupnh2VPdIGLpbGWI2s+TJqIiIjovuUUV2L5r7HYcykTQF1H72VPdMFwf3tIJBItR9e8mDQRERGRxmRygW/PJuPj3+JQUlULHQkwo58HXhvWqc129L6XR3OtiIiIqMVcSS/Cm7su42JaEQAgyNUC748NQICzuZYja1lMmoiIiEgtxZU1+PTADWw5lQS5ADpI9bBoRGc808sNujqP1qU4VZg0ERERUZOEENh1IR0r915HXmkVAGBMkBPeHu0HOzNDLUf38DBpIiIiokZdyyzG0p+u4FzSbQCAp40Jlj3RBQM72Wo5sodPq4MmHDt2DGPGjIGTkxMkEgl2796tNF0ikaj8+/jjjxutc/PmzQ3mNzRsP1kwERFRcyiqqMGyn6/i8XUncC7pNoz0dbFoRGfsmz+gXSZMgJZbmsrKyhAUFISZM2fiqaeeajA9MzNT6fW+ffswa9YsjBs3rsl6zczMEBcXp3j9qN3ySERE1FLkcoEfL6Tjg33XkFdaDQAYFeiAN0f7w9nCSMvRaZdWk6aRI0di5MiRjU53cHBQev3TTz8hLCwMnp6eTdYrkUgaLEtERERNi82ouxQXlfzTaz6wAAAgAElEQVTXpThbEyx/ogsG+LTPlqW7tZk+TdnZ2dizZw+2bNlyz3lLS0vh5uYGuVyObt26YeXKlejSpUuj81dVVaGqqkrxuri4uFliJiIiaguKKmrwyf44bD2TDLkAjA108eoQH8zs5wEDvbb/+JPm0maSpi1btqBDhw4qL+PdqXPnzti0aRMee+wxFBUVYdWqVejbty+uXr0KFxcXlctERERg+fLlLRE2ERFRqyWXC/wQnYYP9l1HflndpbjRjznirdF+cDRv35fiVJEIIYS2gwDqLqnt2rULY8eOVTnd19cXw4YNw7p16zSqt6amBn5+fpg8eTJWrFihch5VLU2urq4oKiqCmZmZRu9HRETUFlxIuY1lv8TiYmohAMDbzhTLn+iCft42Wo7s/hUXF8Pc3LzFfr/bREvT8ePHERcXhx07dmi8rL6+Prp27YqEhIRG55FKpZBKpQ8SIhERUZuQXVyJD/ddx48X0gEAJn9dipvBS3H31CaSpq+//hohISEICgrSeFmZTIbLly9j1KhRLRAZERFR21BZI8PXJxLx7yMJKK+WAQDGh7jgn+Gd29UAlQ9Cq0lTaWmpUgtQYmIiYmJiYGVlhY4dOwKoa2qLjIzE6tWrVdYxdepUODs7IyIiAgDw7rvvonfv3vD29kZhYSE+/vhjJCcnY/bs2S2/QkRERK2MEAK/X83G+3tjkVpQAQDo2tECy8Z0QZCrhZaja1u0mjRFRUUhLCxM8XrBggUAgGnTpmHz5s0AgO+++w5CCEyePFllHSkpKdDR+bs58fbt25gzZw6ysrJgaWmJkJAQnDp1Cv7+/i23IkRERK3Q9axivPtLLE7dzAcA2JtJsXikH54MduIYhveh1XQEb01auiMZERFRSyooq8YnB+Kw/WwK5AIw0NPBCwM98WKoF0ykbaJnzn1hR3AiIiJSS41Mjm1nkvHpgRsorqwFUDea9+KRfnC1MtZydG0fkyYiIqI2TgiBo3G5WLn3GuJzSgEAfo5meGeMP3p7Wms5ukcHkyYiIqI2LDajGCv3XsOJhDwAgKWxPhaGd8akHh2hq8N+S82JSRMREVEblF1cidX74xB5Pg1CAAa6Opjezx0vh3nD3Ehf2+E9kpg0ERERtSHl1bX44tgt/OePW6ioqRtvafRjjnhjhC/7LbUwJk1ERERtgEwu8MP5NKzaH4eckrpHf3XraIE3R/sjxM1Sy9G1D0yaiIiIWrkT8Xl4f+81XMssBgC4WhnhjRF+GBXowPGWHiImTURERK1UfHYJVu69hiNxuQCADoZ6+Mdgb0zr6w6pnq6Wo2t/mDQRERG1MjkllVh7MB7fnUuFTC6gpyPBs73d8OoQH1iZGGg7vHaLSRMREVErUVJZgy+P3cKXxxMVnbyH+9vjjZG+8LQ11XJ0xKSJiIhIy6pqZdh+NgXrDiegoKwaABDkaoHFI305OGUrwqSJiIhIS+RygZ8vZmD1gTikFlQAADxtTLBoRGeEd2En79aGSRMREdFDJoTAsfg8fLjvOmL/uiPOroMU84d2woTuLtDT1dFyhKQKkyYiIqKH6GJqIT787TpO3cwHAHSQ6uHFQV6Y0c8dxgb8WW7N+OkQERE9BIl5ZVi1Pw57LmUCqHvsyXN93PBymDfviGsjmDQRERG1oJziSqw7nID//ZmCWrmARAL8X1dnLBjWCS6WfOxJW8KkiYiIqAXcLqvGxj9uYsvpJFTWyAEAYZ1tsWiEL/wczbQbHN0XJk1ERETNqKSyBl8dT8TXJxJRWlULoO4Zcf8M90UfLw4f0JYxaSIiImoGFdUy/Pd0Ejb8cROF5TUAAH9HMywM74SwznYcPuARwKSJiIjoAVTVyrDjXCrWHU5AbkkVAMDL1gQLhnXGyAAH6OgwWXpUMGkiIiK6D7UyOX68kI61B+ORXlg3MKWLpRHmDfHB/3V15lhLjyAmTURERBqQywX2XM7Epwdv4FZuGYC6gSn/MdgbE3t0hIEek6VHFZMmIiIiNQghcPBaDj45cAPX/hrF29JYH3MHeeG53u4wMtDVcoTU0pg0ERERNUEIgUPXcrDm0A1cSa9LlkylepgzwBMz+7ujg6G+liOkh4VJExERkQpCCBy+noM1B+NxOb0IAGBsoIupfdzxwkBPWHIU73aHSRMREdEdhBA4EleXLF1KU06W5gzwgLWpVMsRkrYwaSIiIoLqZMlIXxdT+7rh+QGeTJaISRMREbVvQggcjcvFmoM3cPHOZKmPG54fyGSJ/sakiYiI2iUhBI7eyMWag/G4mFoI4O9kac5AT9gwWaK7MGkiIqJ2pf4y3NpDCYpkyVBfB1P7uON5JkvUBCZNRETULsjlAr9fzcL6Iwm4mlE3dIChvg6e6+2G5wd6wbYDkyVqGpMmIiJ6pNXK5PjlUgb+feQmEnJKAdTdDTelV0cmS6QRJk1ERPRIqq6V48foNHx+9CZSCsoBAB0M9TCjrztm9PPgOEukMSZNRET0SKmskeG7P1Pwn2O3kFlUCaDucSezB3jiuT5uMOMI3nSfmDQREdEjobSqFt+eScaXxxORV1oFoO5Bus8P9MQzvTrC2IA/efRgtPoo5mPHjmHMmDFwcnKCRCLB7t27laZPnz4dEolE6W/EiBH3rDcyMhK+vr4wNDREYGAg9u7d21KrQEREWlZUXoO1B+PR/8PDiNh3HXmlVXC2MMKKsQE4tigMswd4MmGiZqHVvaisrAxBQUGYOXMmnnrqKZXzjBgxAt98843itVTadIe9U6dOYfLkyYiIiMDjjz+O7du3Y+zYsYiOjkZAQECzxk9ERNqTU1yJTSeTsO1MMkqragEAHjYmeGmQF8Z2dYa+rlbbBegRJBFCCG0HAQASiQS7du3C2LFjFWXTp09HYWFhgxaopkycOBFlZWX49ddfFWW9e/dGcHAwNm7cqFYdxcXFMDc3R1FREczMzNRfCSIianGJeWX44thN/HA+HdUyOQCgs30HvDzYG6MDHaGrI9FyhKQtLf373erbK48ePQo7OztYWlpi8ODBeO+992Btbd3o/KdPn8aCBQuUysLDw5tMvKqqqlBVVaV4XVxc/OCBExFRs7qUVoiNf9zEvitZqD/dD3GzxIuhXhjiawcdJkvUwlp10jRixAg89dRT8PDwwM2bN7FkyRKMHDkSp0+fhq6ursplsrKyYG9vr1Rmb2+PrKysRt8nIiICy5cvb9bYiYjowQkhcCIhDxv/uImTCfmK8sG+dpg7yAs93K20GB21N606aZo0aZLi/4GBgXjsscfg5eWFo0ePYsiQIc32PosXL1ZqnSouLoarq2uz1U9ERJqRyQX2XcnExj9u4kp6Xeu/ro4ETwQ54YVQT/g6sOsEPXytOmm6m6enJ2xsbJCQkNBo0uTg4IDs7GylsuzsbDg4ODRar1QqvWcHcyIianmVNTL8EJ2GL47dQnJ+3YCUhvo6mNSjI2YP8ICLpbGWI6T2rE0lTWlpacjPz4ejo2Oj8/Tp0weHDh3C/PnzFWUHDhxAnz59HkaIRER0H4oqavDt2WRsOpGkGGPJwlgf0/q4Y1pfd1hx9G5qBbSaNJWWliIhIUHxOjExETExMbCysoKVlRWWL1+OcePGwcHBATdv3sSiRYvg7e2N8PBwxTJTp06Fs7MzIiIiAADz5s1DaGgoVq9ejdGjR+O7775DVFQUvvjii4e+fkRE1LTUgnJ8czIJO86loKxaBgBwMjfEnIGemNjDleMrUaui1b0xKioKYWFhitf1/YqmTZuGDRs24NKlS9iyZQsKCwvh5OSE4cOHY8WKFUqX0lJSUqCj8/dYHH379sX27dvx1ltvYcmSJfDx8cHu3bs5RhMRUSsSk1qIL4/fwr7LmZD/dSdcJ3tTvBjqhTFBThxjiVqlVjNOU2vCcZqIiJqfTC5w8Fo2vjp+C+eSbivK+3vbYPYAD4R2soVEwmED6P61+3GaiIiobauolmHn+VR8fSIRSX917tbXlWBMkBNm9/eEvxNPTqltYNJEREQtIqekEv89lYxtZ5NRWF4DADAz1MOU3m6Y3tcd9maGWo6QSDNMmoiIqFnFZZXgq+O38FNMhuIxJ65WRpjVzwPju7vCRMqfHmqbuOcSEdEDE0LgeHwevjqRiGM3chXl3TpaYM4ATwzv4sBnwlGbx6SJiIjuW3l1LX6ITsfmk4m4mVsGANCRAOFdHDB7gCdC3Cy1HCFR82HSREREGkstKMd/Tydhx7lUFFfWAgBMpXp4OsQFM/t5oKM1R+6mRw+TJiIiUosQAmduFWDzqUQciM1WjK/kbm2MaX3d8XSICzoY6ms3SKIWxKSJiIiaVFkjw88xGfjmVBKuZRYrygf42GB6X3eEdbaDDvsrUTvApImIiFTKKqrE1jNJ+N+fqSgoqwZQ9/Dcp7q5YEZfd/jYd9ByhEQPF5MmIiJSEEIgOqUQm08lYd/lTNT+dQ3O2cIIU/u4YWIPV1gY8+G51D4xaSIiorpLcBczsPV0Mi6nFynKe3pYYWY/dwz1s4cenwdH7RyTJiKidiw5vwzbziTj+6g0FFXUjdptoKuDJ4KdML2vOwKczbUcIVHrwaSJiKidkckF/riRg/+eTsYfN3JR/9h2ZwsjPNvbDRO6u8DaVKrdIIlaISZNRETtREFZNb6PSsW3Z5ORWlChKA/tZIupfdwwqLMdR+0magKTJiKiR1xMaiH+ezoJv17KRHVt3bPgzI30MaG7C6b0coO7jYl2AyRqI5g0ERE9guo7dm87k4xLaX937A5wNsPU3u4YE+QEIwNdLUZI1PYwaSIieoTcyi3F//5MQeT5NBSW/92x+/HHHPFcHzcEu1pAIuElOKL7waSJiKiNq6qV4fer2fjf2RScvpWvKHe2MMKU3h0xsbsrO3YTNQMmTUREbVRiXhm++6tVqX7EbokECOtsh2d6dkSYLzt2EzUnJk1ERG1Ida0c+2OzsP1sCk7d/LtVyd5Miok9OmJiD1c4WxhpMUKiRxeTJiKiNiAprwz/O5eCnVFpyL+jVWlQJ1tM7tkRg33tOGI3UQtj0kRE1EpV18pxIDYb2/9MxsmEu1qVurtiQg9XuFgaazFCovaFSRMRUSuTlFeG786lYuf5VOSV/t2qFPpXq9IQtioRaQWTJiKiVqCiWoZ9VzKx41wqziYWKMptO9S1Kk3s4QpXK7YqEWkTkyYiIi0RQuBSWhF2RKXil5gMlFTVAqhrVRro81erkp8d9NmqRNQqMGkiInrIbpdVY9eFdHwflYrrWSWKclcrI0wIccW4EBc48Q44olaHSRMR0UMgkwucTMjDjqhUHLiajWpZ3TPgDPR0MDLAARO7u6K3pzV0OK4SUavFpImIqAWlFpQj8nwafjifhvTCCkV5gLMZJnZ3xRNBzjA31tdihESkLiZNRETNrLJGhv2x2fj+XCpO3syDEHXl5kb6GBvshAk9XNHFyVy7QRKRxpg0ERE1AyEEolMK8UN0Gn69mIHiylrFtP7eNpjQwxXD/e1hqK+rxSiJ6EEwaSIiegDphRXYFZ2GH6LTkZhXpih3tjDCuBAXjA9x4VABRI8IJk1ERBoqq6rFb1ey8EN0Gk7fyldcfjM20MWIAAc83c2FnbqJHkFMmoiI1CCXC5xJzMcP59Ox70omyqtliml9PK0xLsQFIwMcYCLlYZXoUcVvNxFRExLzyvBjdBp+jE5XuvvN3doY47q54P+6OfP5b0TthFaHmT127BjGjBkDJycnSCQS7N69WzGtpqYG//rXvxAYGAgTExM4OTlh6tSpyMjIaLLOzZs3QyKRKP0ZGhq29KoQ0SOkqKIG28+mYNyGUwhbdRTrDicgvbACHQz1MLlnR/wwtw+OLByEfwzxYcJE1I5otaWprKwMQUFBmDlzJp566imlaeXl5YiOjsbbb7+NoKAg3L59G/PmzcMTTzyBqKioJus1MzNDXFyc4rVEwn4FRNS0qloZjsblYveFdBy6noPq2rrBJ3UkwMBOthjXzQXDePcbUbum1aRp5MiRGDlypMpp5ubmOHDggFLZ+vXr0bNnT6SkpKBjx46N1iuRSODg4NCssRLRo0cuFziXVIDdMenYcylTaZiATvamGNfNBWO7OsPejK3VRNTG+jQVFRVBIpHAwsKiyflKS0vh5uYGuVyObt26YeXKlejSpUuj81dVVaGqqkrxuri4uNliJqLWJy6rBLsupOOXixlK/ZTszaR4MtgZTwY7wd/RjK3URKSkzSRNlZWV+Ne//oXJkyfDzMys0fk6d+6MTZs24bHHHkNRURFWrVqFvn374urVq3BxcVG5TEREBJYvX95SoRNRK5BZVIGfYjKw+0K60kNyO0j1MDLQAWODndHL0xq6HCaAiBohEaJ+hBHtkkgk2LVrF8aOHdtgWk1NDcaNG4e0tDQcPXq0yaRJ1bJ+fn6YPHkyVqxYoXIeVS1Nrq6uKCoq0ui9iKh1KaqowW9XMrHrQjrOJhYoxlPS15UgrLMdxnZ1xmBfO/ZTInpEFBcXw9zcvMV+v1t9S1NNTQ0mTJiA5ORkHD58WOONoK+vj65duyIhIaHReaRSKaRS6YOGSkStQFWtDEeu5+KnGOUO3QDQ08MKY4OdMSrQARbGBlqMkojaoladNNUnTPHx8Thy5Aisra01rkMmk+Hy5csYNWpUC0RIRK1BjUyOUzfz8evFDPx2NQsld3XoHtvVGU8EOXF4ACJ6IFpNmkpLS5VagBITExETEwMrKys4Ojri6aefRnR0NH799VfIZDJkZWUBAKysrGBgUHeWOHXqVDg7OyMiIgIA8O6776J3797w9vZGYWEhPv74YyQnJ2P27NkPfwWJqMXI/rrz7ZeLGdh3JQsFZdWKaQ5mhngy2AlPBjvDz7EDO3QTUbPQatIUFRWFsLAwxesFCxYAAKZNm4Zly5bh559/BgAEBwcrLXfkyBEMGjQIAJCSkgIdnb/H6Lx9+zbmzJmDrKwsWFpaIiQkBKdOnYK/v38Lrw0RtTQhBGJSC/HLxUzsuZyB7OK/+yJamxhgVKAjxgQ5obubJZ/7RkTNrtV0BG9NWrojGRGpTwiB2Mxi/HIxE79eykDa7b+HCDAz1MOIAAeMCXJCH09r6Olq9SEHRKRl7b4jOBG1Twk5Jfj5r0TpVm6ZotzEQBfD/O0xJsgJA3xsYaDHRImIHg4mTUTUaqTkl+OXSxn45WKG0lhKUj0dDPa1w5ggJ4R1toORAYcIIKKHT+OkydPTE+fOnWtwJ1thYSG6deuGW7duNVtwRPToS8orw57Lmdh3JRNX0v8ejV9fV4KBPrYYE+SEof72MJXyHI+ItEvjo1BSUhJkMlmD8qqqKqSnpzdLUET0aLuZW4q9lzKx90oWrmX+nSjpSIC+XjYYE+SI8C4cS4mIWhe1k6b6O9kA4Pfff4e5ubnitUwmw6FDh+Du7t6swRHRoyM+u6SuRelyFuKy/770pqsjQV8va4wKdMRwf3tYm3KgWSJqndROmuofbyKRSDBt2jSlafr6+nB3d8fq1aubNzoiarOEEIjLLlG0KCXklCqm6elI0N/HBqMCHDHM3x6WJmxRIqLWT+2kSS6vexSBh4cHzp07BxsbmxYLiojapvrhAfb+1aJ0K+/vu94MdHUwwMcGIwMdMczPHubG+lqMlIhIcxr3aUpMTGyJOIiojRJC4FJaEfZdycK+K5lIzi9XTDPQ00FoJ1uMCnTAED97mBkyUSKitou3oxCRxmplcvyZWIDfr2Zhf2w2MosqFdOkejoY1NkWowIdMdjXDh2YKBHRI4JJExGppbJGhmM3cvH71Wwcup6NwvIaxTRjA11FohTW2Q4mHB6AiB5BPLIRUaOKKmpw+Ho2fr+SjT9u5KKi5u/hRiyN9THUzx7hXRzQ38cGhvoccJKIHm1MmohISU5xJX6Pzcb+q1k4fTMftfK/H0/pZG6I4V0cEN7FAT3cLfmsNyJqV+4raZLL5UhISEBOTo7irrp6AwcObJbAiOjhScwrw+9Xs/D71SxcSClUmuZjZ4rwvxKlAGczSCQSLUVJRKRdGidNZ86cwTPPPIPk5GQIIZSmSSQSlaOFE1HrIpcLXE4vwsFr2fj9ahZuZJcqTQ92tfgrUbKHp62plqIkImpdNE6aXnzxRXTv3h179uyBo6MjzzqJ2ojKGhlOJuTh4LVsHLqWg5ySKsU0PR0JentaI7yLPYb5O8DB3FCLkRIRtU4aJ03x8fHYuXMnvL29WyIeImpGuSVVOHw9Gwev5eB4fC4qa/6+nG5ioIvQzrYY6mePIb4cbJKI6F40Tpp69eqFhIQEJk1ErZAQAjeyS3HwWjYOXstGTGoh7ryK7mRuiKH+9hjiZ4/enlaQ6vGONyIidWmcNP3jH//A66+/jqysLAQGBkJfX/ns9LHHHmu24Ijo3mr+GmiyPlFKLahQmv6Yi3lda5KfHfwd2ZGbiOh+ScTdvbnvQUen4S3GEokEQohHpiN4cXExzM3NUVRUBDMzM22HQ9RAUXkNjt7IwcFrOTgal4OSylrFNAM9HfT3tsEQPzsM8bVn/yQiajda+vebz54jagOEEIjPKcWR6zk4fD0H55NvK42fZG1iUJck+dljgI8NjA04BBsRUXPT+Mjq5ubWEnEQ0V0qqmU4fSsPh6/n4Mj1XKQXKl9262Rv+tdlN3sEu1pAV4eX3YiIWtJ9nY5u3boVGzduRGJiIk6fPg03NzesWbMGHh4eePLJJ5s7RqJ2I7WgHEfi6lqTTt/MR1Xt33e7GejpoI+nNQb72iGssx06WhtrMVIiovZH46Rpw4YNWLp0KebPn4/3339f0YfJwsICa9asYdJEpIHqWjmikgsUl91u5pYpTXe2MEKYry3COtuhr5cNjAx4txsRkbZonDStW7cOX375JcaOHYsPPvhAUd69e3csXLiwWYMjehTlFFfiaFwujsTl4Hh8Hkqr/u7ErasjQXc3S4T52mGwrx187Ex5txsRUStxXx3Bu3bt2qBcKpWirKxMxRJE7VutTI6LaUX4Iy4Hh+NycCW9WGm6jakBQjvVJUn9fWxgbsRBJomIWiONkyYPDw/ExMQ06BD+22+/wc/Pr9kCI2rLMosqcOxGLo7dyMPx+FwU3zEkAAAEuZhjUOe6RCnQ2Rw67MRNRNTqaZw0LViwAC+//DIqKyshhMCff/6J//3vf4iIiMBXX33VEjEStXqVNTKcSyrAH3G5OBaf2+ABuGaGehjgY4swXzuEdrKFbQepliIlIqL7pXHSNHv2bBgZGeGtt95CeXk5nnnmGTg5OWHt2rWYNGlSS8RI1OoIIXArr0yRJJ25la/0XDeJBAhysUBoJ1sM7GSLIBdz6Ok2HBiWiIjaDo1HBL9TeXk5SktLYWdn15wxaR1HBCdVSiprcDIhH8fic/FHXMNxk+w6SBVJUn9vG1iaGGgpUiKi9qnVjQh+J2NjYxgbc6wYejTJ5QJXM4oVSVJ0ivIo3Aa6OujhYalIlDrbd+CdbkREjzA+a4HoDumFFTgZn4fjCXk4lZCH/LJqpekeNiZ/JUk26O1pzceVEBG1IzziU7tWVFGDM7fycSI+DycT8nArT3nYDBMDXfT1tsHATrYI9bHlKNxERO0YkyZqV6pr5biQchsnEvJwIiEPF1MLcccVN+hIgCBXCwzwtkFfbxt062gJAz124CYiIiZN9IgTQuBGdimOx+fiZEIeziYWoLxapjSPp40J+vvYoJ933SU3Di5JRESq3FfSVFZWhj/++AMpKSmorlbu8/Hqq682S2BE9yurqBInEuout51IyENuSZXSdGsTA/TztkF/bxv087GBs4WRliIlIqK2ROOk6cKFCxg1ahTKy8tRVlYGKysr5OXlwdjYGHZ2dholTceOHcPHH3+M8+fPIzMzE7t27cLYsWMV04UQeOedd/Dll1+isLAQ/fr1w4YNG+Dj49NkvZGRkXj77beRlJQEHx8ffPjhhxg1apSmq0ptRFFFDc7eysepm/k4kZCHhBzlgSUN9XXQ08Ma/b2t0d/bFr4OHTgCNxERaUzjpOm1117DmDFjsHHjRpibm+PMmTPQ19fHs88+i3nz5mlUV1lZGYKCgjBz5kw89dRTDaZ/9NFH+Oyzz7BlyxZ4eHjg7bffRnh4OGJjY2FoaKiyzlOnTmHy5MmIiIjA448/ju3bt2Ps2LGIjo5GQECApqtLrVBZVS3OJRXg9M26ROlqRpFSvySJBHjM2VxxyS3EzRJSPV3tBUxERI8EjQe3tLCwwNmzZ9G5c2dYWFjg9OnT8PPzw9mzZzFt2jRcv379/gKRSJRamoQQcHJywuuvv46FCxcCAIqKimBvb4/Nmzc3Ovr4xIkTUVZWhl9//VVR1rt3bwQHB2Pjxo1qxcLBLVuXyhoZopNv49TNfJy+lY+LqYVK4yUBgKetCfp4WqO/tw36eFnDwpgDSxIRtTetbnBLfX196OjU3U1kZ2eHlJQU+Pn5wdzcHKmpqc0WWGJiIrKysjB06FBFmbm5OXr16oXTp083mjSdPn0aCxYsUCoLDw/H7t27G32vqqoqVFX93e+luLi40Xmp5VXXynExrfCvlqQ8RKcUorpWrjSPq5UR+nhao69XXZJkb6a65ZGIiKi5aJw0de3aFefOnYOPjw9CQ0OxdOlS5OXlYevWrc16+SsrKwsAYG9vr1Rub2+vmNbYcpouExERgeXLlz9AtPQgamVyXM0oVrQknUssQEWN8h1u9mbSugTJ0xp9vKzhasXxkoiI6OHSOGlauXIlSkpKAADvv/8+pk6dirlz58LHxwebNm1q9gAfhsWLFyu1ThUXF8PV1VWLET3a5HKB61klOH0rH6dv5uHsrQKUVNUqzWNlYqBIkPp6WcPDxoSPKCEiIq3SOGnq3r274v92dnb47bffmjWgeg4ODgCA7OxsODo6Ksqzs7MRHBzc5HLZ2dlKZdnZ2Yr6VJFKpZBKpQ8YMeerbW4AAB+cSURBVDWmViZHbGYxzt4qwNnEApxLKkBRRY3SPB0M9dDbsy5B6uNljU52vMONiIhal1Y7uKWHhwccHBxw6NAhRZJUXFyMs2fPYu7cuY0u16dPHxw6dAjz589XlB04cAB9+vRp8ZipTo1MjktpRTibmI8/EwsQlXQbpXe1JJkY6KK7uxX6etX1S/J3MoMukyQiImrF1EqaunbtqvalkejoaLXfvLS0FAkJCYrXiYmJiImJgZWVFTp27Ij58+fjvffeg4+Pj2LIAScnJ6WxnKZOnQpnZ2dEREQAAObNm4fQ0FCsXr0ao0ePxnfffYeoqCh88cUXasdFmqmskeFiaiH+TKxrSTqffLtBn6QOhnro6W6FXp5W6OVhjS5OZtDT5eNJiIio7VArabozSamsrMTnn38Of39/RevNmTNncPXqVbz00ksavXlUVBTCwsIUr+v7FU2bNg2bN2/GokWLUFZWhueffx6FhYXo378/fvvtN6UxmlJSUhR38wFA3759sX37drz11ltYsmQJfHx8sHv3bo7R1IwqqmWITrmNs4kFOHsrHxdSG97dZmmsj54edQlSL08r+DqwJYmIiNo2jcdpmj17NhwdHbFixQql8nfeeQepqalttjP4nThOk7LSqlpEJdW1Iv2ZWIBLaYWokSnvNjamUvTytEJvDyv08rSGt60p+yQREdFD1dK/3xonTebm5oiKimrwKJP4+Hh0794dRUVFzRqgNrT3pCmnpBJRSbdxLqmuP1JsZjFkdw0m6WhuiF5/JUi9PKx4dxsREWldqxvc0sjICCdPnmyQNJ08ebLRR5tQ6yWEwM3cMkQlFeBc0m1EJRcgOb+8wXyuVkZ1l9o8rNDb0xoulkZMkoiIqF3ROGmaP38+5s6di+joaPTs2RMAcPbsWWzatAlvv/12swdIzau6Vo4rGUWKJOl88m0UlFUrzSORAH4OZujhbokQdyv0cLeEo7mRliImIiJqHTROmt544w14enpi7dq12LZtGwDAz88P33zzDSZMmNDsAdKDKa6sQXTybcXltpjUQlTd1WlbqqeDYFcL9PSwQnd3K3TtaAEzQ30tRUxERNQ6adynqT1oy32aMosq6i6z/dWSdD2rGHd/wpbG+uj+VwtSd3crBDiZw0CPt/8TEVHb1ur6NFHrUSOT43pmCc4nFyA6pRDnk28jvbCiwXxu1sbo7vZ3kuRly07bREREmtI4aZLJZPj000/x/fffIyUlBdXVyv1hCgoKmi04UpZfWoXolEJEp9T1RbqUVojKGuVLbToSoIuTObq7W6KHuxW6u1nCzowd9ImIiB6UxknT8uXL8dVXX+H111/HW2+9hTfffBNJSUnYvXs3li5d2hIxtksyuUBcVgmiU27X/SXfRpKKu9rMDPXQzc3y/9u79+goyvuP459c2IWUJEAhF8wGQpSqXEoByQmoBA1ERVuxVY6giNei0UJQqVRbONoatKJQBaOiBK2KtAhesEgIRouEopBQFIgi0SAksfRANoAkgTy/P/yxx5VAZ2EnO0ner3PmHHbmmc33+QrO58w+mdXA5O+2Acmd1NHNDUQAAIIt4DVNqamp+stf/qLRo0crOjpapaWlvn3r16/XK6+8YletzSYUa5pqDjVo0659KvlqnzZW7NPmXTXHfV+bJJ0V1/G7gNSjkwb16KxeXXmIJAAAkgPXNFVVValfv36SpI4dO/oeZnn55ZfzyAGLGhuNvvjPgf+/g7RfGyv2acc3B44b19EdqQGeThqY3EkDe3TWzzydFRvFb7UBABAKAYempKQkVVZWKjk5WampqVq1apUGDhyojz76SG63244aW436I42a9vfNWrP9G3kPH38XKaXrj/Sz5O/uIA1M7qze8dF8XxsAAA4RcGgaM2aMCgsLlZaWprvuukvXXXednn/+eVVUVCgnJ8eOGluNbZVeLS/dI0nq0C5CP/XE+tYi/Sy5k37ckdAJAIBTBRyaZs2a5fvz2LFjlZycrOLiYp111lm64oorglpca3P0e8vHtswcpcgIno0EAEBLcdq/ZpWenq709PRg1NJmJHeJIjABANDCBByaXnzxxZMenzBhwikXAwAA4FQBh6bJkyf7vW5oaNChQ4fkcrkUFRVFaAIAAK1SwJ8R7du3z287cOCAysrKdP755+vVV1+1o0YAAICQC8rCmrPOOkuzZs067i4UAABAaxG01ciRkZHas2dPsN4OAADAUQJe0/Tmm2/6vTbGqLKyUk899ZSGDRsWtMIAAACcJODQdOWVV/q9DgsLU7du3XTRRRdp9uzZQSsMAADASQIOTY2NjXbUAQAA4Gg8YREAAMACS3eapk6davkNH3/88VMuBgAAwKkshaaSkhJLbxYWFnZaxQAAADiVpdD03nvv2V0HAACAo7GmCQAAwIKAf3tOkj7++GMtWbJEFRUVqq+v9zv2+uuvB6UwAAAAJwn4TtPixYs1dOhQbdu2TcuWLVNDQ4M+/fRTrVmzRrGxsXbUCAAAEHIBh6aHH35YTzzxhN566y25XC7NnTtX27dv1zXXXKPk5GQ7agQAAAi5gEPTF198odGjR0uSXC6XDh48qLCwMOXk5OjZZ58NeoEAAABOEHBo6ty5s2prayVJZ5xxhj755BNJ0v79+3Xo0KHgVgcAAOAQAS8Ev/DCC1VQUKB+/frp6quv1uTJk7VmzRoVFBTo4osvtqNGAACAkAs4ND311FM6fPiwJOn+++9Xu3bttG7dOv3yl7/UAw88EPQCAQAAnCDg0NSlSxffn8PDw3XfffcFtSAAAAAnCnhNU2ZmpvLz8+X1eu2o5zg9e/ZUWFjYcVt2dnaT44uKipocX1VV1Sz1AgCA1ing0NSnTx9Nnz5dCQkJuvrqq/XGG2+ooaHBjtokSR999JEqKyt9W0FBgSTp6quvPul5ZWVlfufFxcXZViMAAGj9Ag5Nc+fO1e7du7V8+XL96Ec/0oQJExQfH6/bbrtN77//ftAL7NatmxISEnzb22+/rdTUVA0fPvyk58XFxfmdFx7ON8YAAIBTd0pJIjw8XKNGjVJ+fr6qq6v1zDPPaMOGDbrooouCXZ+f+vp6/fWvf9VNN92ksLCwk44dMGCAEhMTNXLkSH344YcnHVtXVyev1+u3AQAAfN9p3X6pqqpSXl6eHnnkEf373//WeeedF6y6mrR8+XLt379fEydOPOGYxMRE5eXlaenSpVq6dKk8Ho8yMjK0adOmE56Tm5ur2NhY3+bxeGyoHgAAtGRhxhgTyAler1dLly7VK6+8oqKiIvXq1Uvjx4/X+PHjlZqaaledkqSsrCy5XC699dZbAZ03fPhwJScn66WXXmryeF1dnerq6nyvvV6vPB6PampqFBMTc1o1f9+min26av46JXeJ0gfTRgTtfQEAwHfX79jY2KBfv48J+JED8fHx6ty5s8aOHavc3FwNHjw46EU15auvvtLq1av1+uuvB3zukCFDtHbt2hMed7vdcrvdp1MeAABo5QIOTW+++aYuvvjiZl9YvXDhQsXFxfm+9y4QpaWlSkxMtKEqAADQVgQcmkaOHKkjR45ozZo1+uKLLzRu3DhFR0drz549iomJUceOHYNeZGNjoxYuXKgbbrhBkZH+JU+fPl27d+/Wiy++KEmaM2eOUlJS1KdPHx0+fFgLFizQmjVrtGrVqqDXBQAA2o6AQ9NXX32lSy65RBUVFaqrq9PIkSMVHR2tRx55RHV1dcrLywt6katXr1ZFRYVuuumm445VVlaqoqLC97q+vl533323du/eraioKPXv31+rV6/WiBGsIQIAAKcu4NA0efJkDR48WJs3b9aPf/xj3/4xY8bo1ltvDWpxx4waNUonWq+en5/v93ratGmaNm2aLXUAAIC2K+DQ9M9//lPr1q2Ty+Xy29+zZ0/t3r07aIUBAAA4ScCruRsbG3X06NHj9n/99deKjo4OSlEAAABOE3BoGjVqlObMmeN7HRYWpgMHDmjGjBm67LLLglocAACAUwT88dzs2bOVlZWlc889V4cPH9a4ceP0+eefq2vXrnr11VftqBEAACDkAg5NSUlJ2rx5s1577TVt3rxZBw4c0M0336zx48erQ4cOdtQIAAAQcgGHJkmKjIz0fXUKAABAW9C8j/UGAABooQhNAAAAFhCaAAAALCA0AQAAWBBwaHrvvfdOeOyZZ545rWIAAACcKuDQdMkll+jee+9VQ0ODb9/evXt1xRVX6L777gtqcQAAAE5xSneali1bpvPOO09bt27VihUr1LdvX3m9XpWWltpRIwAAQMgFHJqGDh2q0tJS9e3bVwMHDtSYMWOUk5OjoqIi9ejRw44aAQAAQu6UFoJ/9tln+vjjj5WUlKTIyEiVlZXp0KFDwa4NAADAMQIOTbNmzVJ6erpGjhypTz75RBs2bFBJSYn69++v4uJiO2oEAAAIuYBD09y5c7V8+XI9+eSTat++vfr27asNGzboqquuUkZGhg0lAgAAhF7A3z23ZcsWde3a1W9fu3bt9Oc//1mXX3550AoDAABwkoDvNP0wMH3f8OHDT6sYAAAAp+KJ4AAAABYQmgAAACwgNAEAAFhAaAIAALCA0AQAAGABoQkAAMACQhMAAIAFhCYAAAALCE0AAAAWEJoAAAAsIDQBAABYQGgCAACwgNAEAABgAaEJAADAAkITAACABYQmAAAACxwdmmbOnKmwsDC/7eyzzz7pOUVFRRo4cKDcbrfOPPNM5efnN0+xAACgVYsMdQH/S58+fbR69Wrf68jIE5dcXl6u0aNHa9KkSXr55ZdVWFioW265RYmJicrKymqOcgEAQCvl+NAUGRmphIQES2Pz8vKUkpKi2bNnS5LOOeccrV27Vk888cRJQ1NdXZ3q6up8r71e7+kVDQAAWh1HfzwnSZ9//rm6d++uXr16afz48aqoqDjh2OLiYmVmZvrty8rKUnFx8Ul/Rm5urmJjY32bx+MJSu0AAKD1cHRoSktLU35+vlauXKmnn35a5eXluuCCC1RbW9vk+KqqKsXHx/vti4+Pl9fr1bfffnvCnzN9+nTV1NT4tl27dgV1HgAAoOVz9Mdzl156qe/P/fv3V1pamnr06KElS5bo5ptvDtrPcbvdcrvdQXs/AADQ+jj6TtMPderUSb1799aOHTuaPJ6QkKDq6mq/fdXV1YqJiVGHDh2ao0QAANBKtajQdODAAe3YsUOJiYlNHk9PT1dhYaHfvoKCAqWnpzdHeQAAoBVzdGi655579P777+vLL7/UunXrNGbMGEVGRuraa6+V9N1apAkTJvjGT5o0STt37tS0adO0fft2zZ8/X0uWLFFOTk6opgAAAFoJR69p+vrrr3Xttdfqv//9r7p166bzzz9f69evV7du3SRJlZWVfr9Nl5KSohUrVignJ0dz585VUlKSFixYwDOaAADAaXN0aFq8ePFJjzf1tO+MjAyVlJTYVBEAAGirHP3xHAAAgFMQmgAAACwgNAEAAFhAaAIAALCA0AQAAGABoQkAAMACQhMAAIAFhCYAAAALCE0AAAAWEJoAAAAsIDQBAABYQGgCAACwgNAEAABgAaEJAADAAkITAACABYQmAAAACwhNAAAAFhCaAAAALCA0AQAAWEBoAgAAsIDQBAAAYAGhCQAAwAJCEwAAgAWEJgAAAAsITQAAABYQmgAAACwgNAEAAFhAaAIAALCA0AQAAGABoQkAAMACQhMAAIAFhCYAAAALCE0AAAAWEJoAAAAscHRoys3N1Xnnnafo6GjFxcXpyiuvVFlZ2UnPKSoqUlhY2HFbVVVVM1UNAABaI0eHpvfff1/Z2dlav369CgoK1NDQoFGjRungwYP/89yysjJVVlb6tri4uGaoGAAAtFaRoS7gZFauXOn3Oj8/X3Fxcdq4caMuvPDCk54bFxenTp062VkeAABoQxx9p+mHampqJEldunT5n2MHDBigxMREjRw5Uh9++OFJx9bV1cnr9fptAAAA39diQlNjY6OmTJmiYcOGqW/fviccl5iYqLy8PC1dulRLly6Vx+NRRkaGNm3adMJzcnNzFRsb69s8Ho8dUwAAAC1YmDHGhLoIK26//Xb94x//0Nq1a5WUlBTQucOHD1dycrJeeumlJo/X1dWprq7O99rr9crj8aimpkYxMTGnVff3barYp6vmr1Nylyh9MG1E0N4XAAB8d/2OjY0N+vX7GEevaTrmzjvv1Ntvv60PPvgg4MAkSUOGDNHatWtPeNztdsvtdp9OiQAAoJVzdGgyxuiuu+7SsmXLVFRUpJSUlFN6n9LSUiUmJga5OgAA0JY4OjRlZ2frlVde0RtvvKHo6Gjfs5ZiY2PVoUMHSdL06dO1e/duvfjii5KkOXPmKCUlRX369NHhw4e1YMECrVmzRqtWrQrZPAAAQMvn6ND09NNPS5IyMjL89i9cuFATJ06UJFVWVqqiosJ3rL6+Xnfffbd2796tqKgo9e/fX6tXr9aIEawhAgAAp67FLARvTnYtJGMhOAAA9rF7IXiLeeQAAABAKBGaAAAALCA0AQAAWEBoAgAAsIDQBAAAYAGhCQAAwAJCEwAAgAWEJgAAAAsITQAAABYQmgAAACwgNAEAAFhAaAIAALCA0AQAAGABoQkAAMACQhMAAIAFhCYAAAALCE0AAAAWEJoAAAAsIDQBAABYQGgCAACwgNAEAABgAaEJAADAAkITAACABYQmAAAACwhNAAAAFhCaAAAALCA0AQAAWEBoAgAAsIDQBAAAYAGhCQAAwAJCEwAAgAWEJgAAAAsITQAAABYQmgAAACwgNAEAAFjQIkLTvHnz1LNnT7Vv315paWnasGHDSccXFRVp4MCBcrvdOvPMM5Wfn988hQIAgFbL8aHptdde09SpUzVjxgxt2rRJP/3pT5WVlaVvvvmmyfHl5eUaPXq0RowYodLSUk2ZMkW33HKL3n333WauHAAAtCaOD02PP/64br31Vt14440699xzlZeXp6ioKL3wwgtNjs/Ly1NKSopmz56tc845R3feead+9atf6YknnmjmygEAQGvi6NBUX1+vjRs3KjMz07cvPDxcmZmZKi4ubvKc4uJiv/GSlJWVdcLxklRXVyev1+u3AQAAfJ+jQ9PevXt19OhRxcfH++2Pj49XVVVVk+dUVVU1Od7r9erbb79t8pzc3FzFxsb6No/HE5wJ/ECYJHdkuFyRjm47AABoAldvSdOnT1dNTY1v27Vrly0/52fJnVX2x0u1eupwW94fAADYJzLUBZxM165dFRERoerqar/91dXVSkhIaPKchISEJsfHxMSoQ4cOTZ7jdrvldruDUzQAAGiVHH2nyeVyadCgQSosLPTta2xsVGFhodLT05s8Jz093W+8JBUUFJxwPAAAgBWODk2SNHXqVD333HNatGiRtm3bpttvv10HDx7UjTfeKOm7j9YmTJjgGz9p0iTt3LlT06ZN0/bt2zV//nwtWbJEOTk5oZoCAABoBRz98ZwkjR07Vv/5z3/0hz/8QVVVVRowYIBWrlzpW+xdWVmpiooK3/iUlBStWLFCOTk5mjt3rpKSkrRgwQJlZWWFagoAAKAVCDPGmFAX4TRer1exsbGqqalRTExMqMsBAAAW2H39dvzHcwAAAE5AaAIAALCA0AQAAGABoQkAAMACQhMAAIAFhCYAAAALCE0AAAAWEJoAAAAsIDQBAABY4PivUQmFYw9J93q9Ia4EAABYdey6bdeXnRCamlBbWytJ8ng8Ia4EAAAEqra2VrGxsUF/X757rgmNjY3as2ePoqOjFRYWFtT39nq98ng82rVrF99rZyP63Dzoc/Ogz82HXjcPu/psjFFtba26d++u8PDgr0DiTlMTwsPDlZSUZOvPiImJ4R9kM6DPzYM+Nw/63HzodfOwo8923GE6hoXgAAAAFhCaAAAALIiYOXPmzFAX0dZEREQoIyNDkZF8Omon+tw86HPzoM/Nh143j5bYZxaCAwAAWMDHcwAAABYQmgAAACwgNAEAAFhAaAIAALCA0HSa5s2bp549e6p9+/ZKS0vThg0bTjq+qKhIAwcOlNvt1plnnqn8/Pzjxvztb3/T2Wefrfbt26tfv3565513bKq+5Qh2n5977jldcMEF6ty5szp37qzMzMz/+Z5thR1/p49ZvHixwsLCdOWVVwa56pbHjj7v379f2dnZSkxMlNvtVu/evdv8/z/s6POcOXP0k5/8RB06dJDH41FOTo4OHz5s0wxahkD6XFlZqXHjxql3794KDw/XlClTmhznyGuhwSlbvHixcblc5oUXXjCffvqpufXWW02nTp1MdXV1k+N37txpoqKizNSpU83WrVvNk08+aSIiIszKlSt9Yz788EMTERFhHn30UbN161bzwAMPmHbt2pktW7Y017Qcx44+jxs3zsybN8+UlJSYbdu2mYkTJ5rY2Fjz9ddfN9e0HMmOXh9TXl5uzjjjDHPBBReYX/ziF3ZPxdHs6HNdXZ0ZPHiwueyyy8zatWtNeXm5KSoqMqWlpc01Lcexo88vv/yycbvd5uWXXzbl5eXm3XffNd27dzc5OTnNNS3HCbTP5eXl5je/+Y1ZtGiRGTBggJk8efJxY5x6LSQ0nYYhQ4aY7Oxs3+ujR4+a7t27m9zc3CbHT5s2zfTp08dv39ixY01WVpbv9TXXXGNGjx7tNyYtLc38+te/DmLlLYsdff6hI0eOmOjoaLNo0aLgFN1C2dXrI0eOmKFDh5oFCxaYG264oc2HJjv6/PTTT5tevXqZ+vp6e4pugezoc3Z2trnooov8xkydOtUMGzYsiJW3LIH2+fuGDx/eZGhy6rWQj+dOUX19vTZu3KjMzEzfvvDwcGVmZqq4uLjJc4qLi/3GS1JWVpbfeCtj2hK7+vxDhw4dUkNDg7p06RKcwlsgO3v94IMPKi4uTjfffHPwC29h7Orzm2++qfT0dGVnZys+Pl59+/bVww8/rKNHj9ozEYezq89Dhw7Vxo0bfR8/7dy5U++8844uu+wyG2bhfKfSZyucei1sOY/hdJi9e/fq6NGjio+P99sfHx+v7du3N3lOVVVVk+O9Xq++/fZbdejQ4YRjqqqqgjuBFsKuPv/Qb3/7W3Xv3v24f6RtiV29Xrt2rZ5//nmVlpbaVntLYlefd+7cqTVr1mj8+PF65513tGPHDt1xxx1qaGjQjBkzbJuPU9nV53Hjxmnv3r06//zzZYzRkSNHNGnSJP3ud7+zbS5Odip9tsKp10LuNKHNmzVrlhYvXqxly5apffv2oS6nVamtrdX111+v5557Tl27dg11Oa1aY2Oj4uLi9Oyzz2rQoEEaO3as7r//fuXl5YW6tFalqKhIDz/8sObPn69Nmzbp9ddf14oVK/TQQw+FujQ0A+40naKuXbsqIiJC1dXVfvurq6uVkJDQ5DkJCQlNjo+JifHd/TjRmBO9Z2tnV5+PeeyxxzRr1iytXr1a/fv3D27xLYwdvS4tLdWXX36pK664wne8sbFRkhQZGamysjKlpqYGeSbOZtff6cTERLVr104RERG+Meecc46qqqpUX18vl8sV5Jk4m119/v3vf6/rrrtOt9xyiySpX79+OnjwoG677Tbdf//9Cg9vW/ciTqXPVjj1Wti2/usGkcvl0qBBg1RYWOjb19jYqMLCQqWnpzd5Tnp6ut94SSooKPAbb2VMW2JXnyXp0Ucf1UMPPaSVK1dq8ODBwS++hbGj12effba2bNmi0tJS3/bzn/9cI0aMUGlpqTwej30Tcii7/k4PGzZMO3bs8IVSSfrss8+UmJjY5gKTZF+fDx06dNwXzB4LqqYNfpXrqfTZCsdeC0O6DL2FW7x4sXG73SY/P99s3brV3HbbbaZTp06mqqrKGGPMfffdZ66//nrf+GO/znrvvfeabdu2mXnz5jX5yIHIyEjz2GOPmW3btpkZM2Y44tcsQ8mOPs+aNcu4XC7z97//3VRWVvq22traZp+fk9jR6x/it+fs6XNFRYWJjo42d955pykrKzNvv/22iYuLM3/84x+bfX5OYUefZ8yYYaKjo82rr75qdu7caVatWmVSU1PNNddc0+zzc4pA+2yMMSUlJaakpMQMGjTIjBs3zpSUlJhPP/3Ud9yp10JC02l68sknTXJysnG5XGbIkCFm/fr1vmM33HCDGT58uN/49957zwwYMMC4XC7Tq1cvs3DhwuPec8mSJaZ3797G5XKZPn36mBUrVtg8C+cLdp979OhhJB23zZgxw/7JOJwdf6e/j9D0HTv6vG7dOpOWlmbcbrfp1auX+dOf/mSOHDli80ycLdh9bmhoMDNnzjSpqammffv2xuPxmDvuuMPs27evGWbjXIH2uan///bo0cNvjBOvhWHGtMH7iQAAAAFiTRMAAIAFhCYAAAALCE0AAAAWEJoAAAAsIDQBAABYQGgCAACwgNAEAABgAaEJAADAAkITAACABYQmAG1KRkaGpkyZEuoyALRAhCYAAAAL+O45AG3GxIkTtWjRIr995eXl6tmzZ2gKAtCiEJoAtBk1NTW69NJL1bdvXz344IOSpG7duikiIiLElQFoCSJDXQAANJfY2Fi5XC5FRUUpISEh1OUAaGFY0wQAAGABoQkAAMACQhOANsXlcuno0aOhLgNAC0RoAtCm9OzZU//617/05Zdfau/evWpsbAx1SQBaCEITgDblnnvuUUREhM4991x169ZNFRUVoS4JQAvBIwcAAAAs4E4TAACABYQmAAAACwhNAAAAFhCaAAAALCA0AQAAWEBoAgAAsIDQBAAAYAGhCQAAwAJCEwAAgAWEJgAAAAsITQAAABb8H5FUG+XOSG1FAAAAAElFTkSuQmCC", + "image/png": 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", "text/plain": [ - "PyPlot.Figure(PyObject )" + "PyPlot.Figure(PyObject )" ] }, "metadata": {}, @@ -229,13 +228,61 @@ ], "source": [ "using PyPlot\n", - "plot(t,x)\n", + "plot(R_K[1],R_K[2])\n", "title(\"runge-kutta de cuarto orden con condición inicial t=0 y x(0)=3\")\n", "xlabel(\"t\")\n", "ylabel(\"x evaluada en t\")\n", "show()" ] }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Ahora, se debe evaluar el error relativo con este método." + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "Error=[]\n", + "for i in 1:length(R_K[1])\n", + " valor=abs((R_K[2][i])-(3/(1-(3*R_K[1][i])))) #se usa el resultado de la forma analítica\n", + " push!(Error,valor)\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plot(R_K[1],Error)\n", + "title(\"error absoluto del método de Runge-Kutta con respecto a la solución analítica\")\n", + "xlabel(\"t\")\n", + "ylabel(\"el valor de Runge-Kutta menos la función analitica\")\n", + "show()" + ] + }, { "cell_type": "markdown", "metadata": {}, @@ -254,7 +301,7 @@ }, { "cell_type": "code", - "execution_count": 46, + "execution_count": 5, "metadata": { "collapsed": false }, @@ -265,7 +312,7 @@ "runge_kutta_4_2 (generic function with 1 method)" ] }, - "execution_count": 46, + "execution_count": 5, "metadata": {}, "output_type": "execute_result" } @@ -301,7 +348,7 @@ }, { "cell_type": "code", - "execution_count": 47, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -312,7 +359,7 @@ "g (generic function with 1 method)" ] }, - "execution_count": 47, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" } @@ -323,7 +370,7 @@ }, { "cell_type": "code", - "execution_count": 51, + "execution_count": 7, "metadata": { "collapsed": false }, @@ -334,7 +381,7 @@ "([0.0,4.44288,8.88577,13.3286,17.7715,22.2144,26.6573,31.1002,35.5431,39.9859 … 4.44248e5,4.44253e5,4.44257e5,4.44262e5,4.44266e5,4.44271e5,444275.0,4.44279e5,4.44284e5,4.44288e5],[2.0,-11.1595,-50.6379,-116.435,-208.552,-326.987,-471.741,-642.814,-840.206,-1063.92 … -1.31571e11,-1.31574e11,-1.31576e11,-1.31579e11,-1.31582e11,-1.31584e11,-1.31587e11,-1.31589e11,-1.31592e11,-1.31595e11])" ] }, - "execution_count": 51, + "execution_count": 7, "metadata": {}, "output_type": "execute_result" } @@ -345,7 +392,7 @@ }, { "cell_type": "code", - "execution_count": 52, + "execution_count": 8, "metadata": { "collapsed": false }, @@ -354,7 +401,7 @@ "data": { "image/png": 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", "text/plain": [ - "PyPlot.Figure(PyObject )" + "PyPlot.Figure(PyObject )" ] }, "metadata": {}, @@ -364,10 +411,10 @@ "data": { "text/plain": [ "1-element Array{Any,1}:\n", - " PyObject " + " PyObject " ] }, - "execution_count": 52, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } From 866b8bd431f856889343f758cf2d9ac6897c2e6a Mon Sep 17 00:00:00 2001 From: carlos Date: Mon, 15 May 2017 20:15:49 -0500 Subject: [PATCH 9/9] =?UTF-8?q?se=20intent=C3=B3=20modificar=20las=20gr?= =?UTF-8?q?=C3=A1ficas=20de=20runge=20kutta,=20no=20obstante=20los=20resul?= =?UTF-8?q?tados=20dan=20mucho=20que=20desear,=20el=20problema=203=20se=20?= =?UTF-8?q?modifico=20y=20no=20se=20aprecia=20cambio=20aparente?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- tareas/Carlos/Tarea6.ipynb | 188 ++++++++++++++++++++----------------- 1 file changed, 100 insertions(+), 88 deletions(-) diff --git a/tareas/Carlos/Tarea6.ipynb b/tareas/Carlos/Tarea6.ipynb index 0a8c284..b2bde5d 100644 --- a/tareas/Carlos/Tarea6.ipynb +++ b/tareas/Carlos/Tarea6.ipynb @@ -78,7 +78,7 @@ }, { "cell_type": "code", - "execution_count": 24, + "execution_count": 17, "metadata": { "collapsed": false }, @@ -87,8 +87,12 @@ "name": "stderr", "output_type": "stream", "text": [ - "WARNING: Method definition runge_kutta_4(Any, Any, Any, Any) in module Main at In[14]:6 overwritten at In[24]:6.\n", - "\u001b[1m\u001b[31mWARNING: replacing docs for 'runge_kutta_4 :: Tuple{Any,Any,Any,Any}' in module 'Main'.\u001b[0m\n" + "WARNING: Method definition runge_kutta_4(Any) in module Main at In[13]:6 overwritten at In[17]:6.\n", + "WARNING: Method definition runge_kutta_4(Any, Any) in module Main at In[13]:6 overwritten at In[17]:6.\n", + "WARNING: Method definition runge_kutta_4(Any, Any, Any) in module Main at In[13]:6 overwritten at In[17]:6.\n", + "WARNING: Method definition runge_kutta_4(Any, Any, Any, Any) in module Main at In[13]:6 overwritten at In[17]:6.\n", + "WARNING: Method definition runge_kutta_4(Any, Any, Any, Any, Any) in module Main at In[13]:6 overwritten at In[17]:6.\n", + "\u001b[1m\u001b[31mWARNING: replacing docs for 'runge_kutta_4 :: Union{Tuple{Any,Any,Any,Any,Any},Tuple{Any,Any,Any,Any},Tuple{Any,Any,Any},Tuple{Any,Any},Tuple{Any}}' in module 'Main'.\u001b[0m\n" ] }, { @@ -97,7 +101,7 @@ "runge_kutta_4" ] }, - "execution_count": 24, + "execution_count": 17, "metadata": {}, "output_type": "execute_result" } @@ -107,8 +111,7 @@ "se hará el método de runge-kutta para resolver una ecuación diferencial de la forma dx/dt=f(x,t),\n", "considerando el valor de una condicion inicial en t_0, con cierto número de pasos, y cierto valor en x_0\n", "\"\"\"\n", - "function runge_kutta_4(f,t_0,x_0,n)\n", - " t_f=0.333\n", + "function runge_kutta_4(f,t_0=0,x_0=0,t_f=1,n=100)\n", " t=Array(Number,1) #\"t\"\n", " x=Array(Number,1) #\"x\"\n", " h=(t_f-t_0)/n\n", @@ -120,9 +123,13 @@ " k_3=f(t[i]+(h*(1/2)),x[i]+((1/2)*((k_2)*h)))\n", " k_4=f(t[i]+h,x[i]+((k_3)*h))\n", " m=x[i]+(1/6)*(h)*(k_1+2*k_2+2*k_3+k_4)\n", + " if (m!=Inf && m!=-Inf)\n", " push!(x,m)\n", - " n=t[i]+h\n", + " n=x_0+h*i\n", " push!(t,n)\n", + " else \n", + " break\n", + " end\n", " end\n", " return t,x\n", "end" @@ -130,7 +137,7 @@ }, { "cell_type": "code", - "execution_count": 15, + "execution_count": 18, "metadata": { "collapsed": false }, @@ -148,7 +155,7 @@ "f (generic function with 1 method)" ] }, - "execution_count": 15, + "execution_count": 18, "metadata": {}, "output_type": "execute_result" }, @@ -156,7 +163,7 @@ "name": "stderr", "output_type": "stream", "text": [ - ", Any) in module Main at In[10]:1 overwritten at In[15]:1.\n" + ", Any) in module Main at In[14]:1 overwritten at In[18]:1.\n" ] } ], @@ -166,7 +173,7 @@ }, { "cell_type": "code", - "execution_count": 25, + "execution_count": 19, "metadata": { "collapsed": false }, @@ -174,10 +181,10 @@ { "data": { "text/plain": [ - "(Number[0,0.000333,0.000666,0.000999,0.001332,0.001665,0.001998,0.002331,0.002664,0.002997 … 0.330003,0.330336,0.330669,0.331002,0.331335,0.331668,0.332001,0.332334,0.332667,0.333],Number[3,3.003,3.00601,3.00902,3.01204,3.01506,3.01809,3.02113,3.02417,3.02722 … 300.27,333.629,375.327,428.937,500.412,600.468,750.525,1000.52,1499.73,2978.76])" + "(Number[0,13.0,23.0],Number[3,2.9384e18,1.2568e306])" ] }, - "execution_count": 25, + "execution_count": 19, "metadata": {}, "output_type": "execute_result" } @@ -188,38 +195,16 @@ }, { "cell_type": "code", - "execution_count": 18, - "metadata": { - "collapsed": false - }, - "outputs": [ - { - "data": { - "text/plain": [ - "Tuple{Array{Number,1},Array{Number,1}}" - ] - }, - "execution_count": 18, - "metadata": {}, - "output_type": "execute_result" - } - ], - "source": [ - "typeof(ans)" - ] - }, - { - "cell_type": "code", - "execution_count": 26, + "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ - "PyPlot.Figure(PyObject )" + "PyPlot.Figure(PyObject )" ] }, "metadata": {}, @@ -244,7 +229,7 @@ }, { "cell_type": "code", - "execution_count": 30, + "execution_count": 6, "metadata": { "collapsed": false }, @@ -259,16 +244,16 @@ }, { "cell_type": "code", - "execution_count": 32, + "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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", "text/plain": [ - "PyPlot.Figure(PyObject )" + "PyPlot.Figure(PyObject )" ] }, "metadata": {}, @@ -301,7 +286,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 8, "metadata": { "collapsed": false }, @@ -309,46 +294,21 @@ { "data": { "text/plain": [ - "runge_kutta_4_2 (generic function with 1 method)" + "g (generic function with 1 method)" ] }, - "execution_count": 5, + "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "function runge_kutta_4_2(f,t_0,x_0,y_0,n) #se aumenta un elemento más en la función de runge kutta, pero en principio es lo mismo\n", - " t_f=(10e4*2*pi)/(sqrt(2))\n", - " h=((t_f)-(t_0))/n\n", - " t=zeros(n+1)\n", - " x=zeros(n+1)\n", - " y=zeros(n+1)\n", - " t[1]=t_0\n", - " x[1]=x_0\n", - " y[1]=y_0\n", - " k(t,x,y)=y\n", - " g(t,x,y)=f(t,x)\n", - " for i in 1:n\n", - " k_1=g(t[i],x[i],y[i]) #las condiciones para definir \"x\", \"y\" y \"yprima\"\n", - " m_1=k(t[i],x[i],y[i])\n", - " k_2=g(t[i]+((1/2)*h),x[i]+((k_1)*(1/2)*h),y[i]+((m_1)*(1/2)*h))\n", - " m_2=k(t[i]+((1/2)*h),x[i]+((k_1)*(1/2)*h),y[i]+((m_1)*(1/2)*h))\n", - " k_3=g(t[i]+((1/2)*h),x[i]+((k_2)*(1/2)*h),y[i]+((m_2)*(1/2)*h))\n", - " m_3=k(t[i]+((1/2)*h),x[i]+((k_2)*(1/2)*h),y[i]+((m_2)*(1/2)*h))\n", - " k_4=g(t[i]+h,x[i]+((k_3)*h),y[i]+((m_3)*h)) \n", - " m_4=k(t[i]+h,x[i]+((k_3)*h),y[i]+((m_3)*h))\n", - " t[i+1]=t[i]+h\n", - " x[i+1]=x[i]+(1/6)*(k_1+k_2+k_3+k_4)*h\n", - " y[i+1]=y[i]+(1/6)*(m_1+m_2+m_3+m_4)*h\n", - " end\n", - " return t,x\n", - "end" + "g(x,t)=-2x" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 9, "metadata": { "collapsed": false }, @@ -356,21 +316,48 @@ { "data": { "text/plain": [ - "g (generic function with 1 method)" + "runge_kutta_4_2 (generic function with 5 methods)" ] }, - "execution_count": 6, + "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "g(x,t)=-2x" + "function runge_kutta_4_2(f,x_0=2,y_0=0,t_f=1,n=1000)\n", + " t_0=0\n", + " h=(t_f-t_0)/(n)\n", + " t=zeros(Number,n)\n", + " x=zeros(Number,length(t))\n", + " y=zeros(Number,length(t))\n", + "\n", + " for i in 1:n\n", + " t[i]=i*h\n", + " end\n", + " x[1]=x_0\n", + " y[1]=y_0\n", + " a(t,x,y)=y\n", + " b(t,x,y)=f(t,x)\n", + " for i in 1:length(t)-1\n", + " k1=a(t[i],x[i],y[i])\n", + " l1=b(t[i],x[i],y[i])\n", + " k2=a((t[i]+((1/2)*h)),x[i]+((1/2)*(k1)*h),y[i]+((1/2)*(l1)*h))\n", + " l2=b((t[i]+((1/2)*h)),x[i]+((1/2)*(k1)*h),y[i]+((1/2)*(l1)*h))\n", + " k3=a((t[i]+((1/2)*h)),x[i]+((1/2)*(k2)*h),y[i]+((1/2)*(l2)*h))\n", + " l3=b((t[i]+((1/2)*h)),x[i]+((1/2)*(k2)*h),y[i]+((1/2)*(l2)*h))\n", + " k4=a((t[i]+h),(x[i]+h*(k3)),(y[i]+h*(l3)))\n", + " l4=b((t[i]+h),(x[i]+h*(k3)),(y[i]+h*(l3)))\n", + " x[i+1]=x[i]+(1/6)*(h)*(k1+(2*k2)+(2*k3)+k4)\n", + " y[i+1]=y[i]+(1/6)*(h)*(l1+(2*l2)+(2*l3)+l4)\n", + " end\n", + " return t,x\n", + "end" ] }, { "cell_type": "code", - "execution_count": 7, + "execution_count": 10, "metadata": { "collapsed": false }, @@ -378,49 +365,74 @@ { "data": { "text/plain": [ - "([0.0,4.44288,8.88577,13.3286,17.7715,22.2144,26.6573,31.1002,35.5431,39.9859 … 4.44248e5,4.44253e5,4.44257e5,4.44262e5,4.44266e5,4.44271e5,444275.0,4.44279e5,4.44284e5,4.44288e5],[2.0,-11.1595,-50.6379,-116.435,-208.552,-326.987,-471.741,-642.814,-840.206,-1063.92 … -1.31571e11,-1.31574e11,-1.31576e11,-1.31579e11,-1.31582e11,-1.31584e11,-1.31587e11,-1.31589e11,-1.31592e11,-1.31595e11])" + "(Number[4442.88,8885.77,13328.6,17771.5,22214.4,26657.3,31100.2,35543.1,39985.9,44428.8],Number[2,1.28185e21,2.16307e104,Inf,Inf,Inf,Inf,Inf,Inf,Inf])" ] }, - "execution_count": 7, + "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ - "(t,x)=runge_kutta_4_2(g,0,2,0,100000)" + "RK2=runge_kutta_4_2(f,2,0,(10^4)*(2*pi/(sqrt(2))),10)" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { - "image/png": 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", + "image/png": 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YK1euICoqCgEBAQpnSAu2xZMnTxAWFoYRI0bAwsJCNtzLywtdu3bFwYMHFeb7+ueuXbt2eP78uez75k0VlEgLOyump6dX6hJqce7cuYM1a9Zg+fLlSp99u3TpEp4+fYpPPvlErh+Ln58fXF1dZd+T+vr60NHRQWhoaJGl65CQEKSkpGDmzJkKfWKUvSXHq5/bnJwcPH/+HA0aNICZmRkuX74sG1aaz+jrymM/Ke1xoOCMzeHDh0tVIn0TLF0V4fUvG1NTU+jp6Smc/jM1NcXz589l/0dGRuLWrVuwsrIqdL6v9isoTEJCAtLT09GoUSOFYW5ubpBKpXj06BHc3d3x8OFDWRnrVa9P+/Dhw0LbdXR0UL9+fdnwouLJyMiAi4tLoct59YMQGRkJIUSh4wKl73jn5ORUqvGK8/r2KzigFnwxFbznBg0aKEzboEEDuS+QyMhIJCUlwdrautBlFWzTpKQkuS9rHR0duS+PX375BampqVi/fr1cMlBRoqOjMXfuXOzbt0/hC7qkmvi9e/cKvUXCqx4+fAgXFxe5ZBqA7Eqc1/ezkrZRSX788Uc4OzsjMjIS586dK7RkWxo+Pj5KjZ+Xl4eEhAS5NgsLC4W+OXFxcfDz84OpqSl27doFTU1NhXm1bdsW48ePx3fffQdfX1+MGjWqxOXfu3cPAODh4VHkOEV95oH87XH48GGFjv7FbQ8TE5MS4ypJwfZ5ta9igczMzDJvv1dNnjwZbdq0KXFfLUxx68zV1VV2Wbuuri6WLl2KadOmwcbGBm+//TZ69uyJYcOGyUplpdlGpZWRkYHAwEBs2bIFMTExcuX8Vz+3pfmMvq489pPSHgecnJwwdepUfPPNN/j111/Rrl079O7dW9Y3VpVqdKJz6tQpLF++HP/99x+ePHmC4OBg2bDCvpReb8vMzERERAQSExOhpaWFnj17QiqVwtPTE998841svPDwcKxfvx4PHz5EcHAwmjZtWuS9PAr68Pzxxx/46quvVPAuK45UKoVEIsHff/9d6Pp79cxJcQr7wpNIJIX218nLyyt0HoUtH0CZ+vxIpVJYW1vj119/LXR4QVI7efJkuY63HTp0kHUgBvIPamFhYVi3bh0GDRoklwQBRf/qKuo9KiMvLw9du3bFixcv8Pnnn8PV1RWGhoaIiYnBiBEjiuzAXp7edBuFhobKDprXrl1D69atyxRHXFxcqcYzNTWFvr4+Hj16pJCMnzhxQq6zfFJSErp3747ExEScPn0a9vb2hc4zKytLto/cu3cP6enpsj4XFU2Vn5nC2NnZAcg/i1CnTh25YU+ePJE7M10Wx48fx6FDh/Dnn3/KddTNzc1FRkYGHjx4AAsLC5UkbQEBAejVqxf27NmDw4cPY86cOQgMDMTx48fRtGnTN57/qyZOnIgtW7YgICAArVu3hqmpKSQSCYYMGVIpP7fKHAdWrlyJESNGYO/evThy5AgmTZqEwMBAXLhwAQ4ODiqLuUYnOmlpafD29saoUaPQr18/pafPy8uDhoYGatWqJSt3ODs7Izw8HF26dIFEIkFUVBT69OmDcePGYfTo0Th27BhGjx4NOzs7hQPbgwcPsHDhQmhoaCA1NVVheREREdDQ0JB9SdSrVw+RkZEK471+X4Z69erJ2l8th2VnZyMqKqrYX7RWVlbQ19cv1XKcnZ0hhICTkxMaNmxY5DzLwtzcvNCSRnFno4pTsE7u3r2rMOz1NmdnZxw9ehRt27Yt9lfnjBkz8MEHH8jF/KoGDRpg2bJl6NixI959910cO3ZM7mqVgvFfvxKusPdYVFJUVPu1a9dw584d/Pzzzxg2bJisPSQkpMj38ypnZ+cS7wNTr149XL16FVKpVO6sTsE9TwrWuSoUdNzt1q0bdHR0MH36dPj6+pZpGQUH4JJs2bIFI0aMgK2trcJ68/b2lv2dmZmJXr164c6dOzh69CgaN25c5DznzZuHW7duYcWKFfj8888xc+ZMfPvtt8XGUXDRwvXr14v87L76mX9dREQELC0tK/y2DU2aNAGQXyJ6NamJjY3F48ePZRdllFV0dDQAFPpdHhMTAycnJ6xatQoBAQGFTv/qOivoalDg9u3bCvuWs7Mzpk2bhmnTpiEyMhJNmjTBypUrsX37drltVNhZY2Xs2rULw4cPl7vCNzMzU+F7ojSf0deVx36i7HHA09MTnp6emD17Ns6dO4e2bdtiw4YNWLRokVLLLU6N7qPTvXt3LFq0qNCaJpD/a2v69OmoXbs2tm/fjoyMDLlf6IaGhmjYsCHMzc1lpywHDRqEmJgY/PDDDwCADRs2wMnJCStXroSjoyNGjhyJAQMGYNWqVTA0NJTtrHl5eXj//ffx1VdfoXbt2oiLi5P7VRIfH48dO3bgnXfekf0i6dGjBy5cuIB///1XNl5CQoLCmQcfHx/o6Ojg22+/lft19uOPPyIpKQl+fn5FriNNTU34+vpiz549si8SALh16xYOHz4sN26/fv2gqamJBQsWKPwKFELIlfiU5ezsjIiICLmSQXh4OM6ePVum+dnb28PDw0NWTipw8uRJXLt2TW7cQYMGIS8vDwsXLlSYT25urmwbNm7cGD4+PrJX8+bNFcb38vLCwYMHcevWLfTq1Uuu1FXw5Xjq1ClZW15eHjZt2qQwH0NDw0LLTQVfSq9/CRb8snp1uwghFC5HLkr//v0RHh4ud9bz1fkA+ftjXFwc/vjjD9mw3NxcrF27FkZGRujQoUOpllUaY8aMgVQqxY8//ohNmzZBS0sLH330UZnOPijbR0dPT09uO/v4+MiS1Ly8PAwePBjnz59HUFBQsWeZ/vnnH6xYsQIBAQGYNm0aPvvsM6xbt06hL9PrmjVrBicnJ6xevVphOxe8fzs7OzRp0gQ///yz3DjXr1/HkSNH0KNHD6XX05tyd3eHq6srNm3aJHeWcv369ZBIJBgwYMAbzb9z584IDg5WeFlZWaFFixYIDg5Gr169ipy+RYsWsLa2xoYNG+TKa3///Tdu3bol+55MT09HZmam3LTOzs4wNjaWTdetWzcYGxsjMDBQYVxl91FNTU2FadauXatwprc0n9HXlcd+UtrjQHJyssIdsT09PaGhoVFoefONlHt35yoCgAgODpb1LE9ISBCjR48Wbdq0EadOnRL9+vUTOjo6QldXV9y5c0c2XYcOHYS7u7sYPny46NOnj8jLyxM9evQQEolEDBkyRDg7O4v27duLcePGCQsLC3Hx4kXx008/CRMTE9GjRw9haGgoVq5cKfr16ye7oqp3795CU1NT1K5dW3z99ddi6dKlon79+kJXV1dcuHBBtuzY2FhRq1YtYW5uLubPny+WL18uXFxchJeXl8KVDwXvq1u3bmLdunVi4sSJQlNTU7Rs2VJkZ2cXu27Cw8OFnp6eqFu3rliyZIlYtGiRsLGxkS3nVYGBgQKAaNOmjVi2bJlYv369mDFjhnBxcSn2KoVXY0xISFAYdvPmTaGhoSGaNm0q1q1bJ+bOnSusra2Fp6dnoVddFbYsvHY1w759+4REIhFeXl5i1apVYu7cucLCwkJ4eHgIR0dHuWk//vhjAUB0795drFq1Sqxbt05MnjxZ2Nvbl+qqAbxy1ZUQQhw7dkzo6uqKHj16yK3/t99+WxgYGIh58+aJNWvWiNatW4vmzZsrXHW1bNkyAUBMmTJF7NixQ+zbt08IkX/liJmZmWjUqJHYvHmz+O2338T9+/dFdna2cHZ2FpaWluLrr78Wa9euFR07dhTe3t6luqIoJSVFNG7cWGhqaooxY8aIDRs2iMWLF4u3335bhIWFCSHyrw5xc3MTOjo6Ytq0aWLt2rWiQ4cOAoBYvXp1mbZRYX766ScBQO6qte3btwsA4rvvvit22vI2efJkAUD06tVLbNu2TeFVICMjQzRq1Ei4urrKrsrJysoS7u7uwsnJSaSmpha7nEOHDgltbW1Rr149MX/+fLFx40YxZcoU0a1bN9k4ISEhQktLS7i6uorly5eLr776SlhZWQlzc3Nx//592XhFfe6KugrwdYmJiWLhwoVi4cKF4t133xUAxLRp08TChQvF2rVr5cb966+/hEQiEZ07dxabNm0SkyZNEhoaGmLMmDHFLuNNlPaqKyH+/z2/9dZbYvXq1WLWrFnCwMBAODo6yq5wu3LlirCwsBDjxo0T3377rfj+++9F165dBQCxa9cu2bw2b94sAAgPDw+xePFisX79ejFu3Di5K5lKc9XVsGHDhKamppg8ebLYuHGjGDFihHBwcBC1atWSu2q3NJ/Rwq66Ko/9pDTHgeDgYFG7dm0REBAgvv/+e/Htt9+Kli1bCm1tbXH+/PlSba/SYqLzP68nOleuXBGampoiJiZGCJG/QxoaGoouXbqIWbNmyaZ7PdERIv9gs3TpUuHu7i4kEonQ19cXzZs3FwsWLBBJSUniwIEDAoAICwsT7du3F7q6ugKAGDx4sGxZHTp0EL6+vsLIyEgYGBiITp06iXPnzinEffXqVdGhQwehp6cnateuLRYuXCh+/PHHQr+g1q1bJ1xdXYW2trawsbER48ePV7g8tSgnT54UzZs3Fzo6OqJ+/fpiw4YNsnX1ut27d4t33nlHGBoaCkNDQ+Hq6iomTJggbt++Xewyikt0hMg/mNWvX1/o6OiIJk2aiMOHDxd5eXlpD6K///67cHV1FTo6OqJx48YiODhY9O/fX7i6uipMv2nTJtG8eXOhr68vjI2Nhaenp5gxY4aIjY0t9n0VLPvVREeI/MuptbS0xODBg2WX/d+7d0/4+PgIXV1dYWNjI7744gsREhKikOikpqaKoUOHCjMzM4XL4ffu3SsaN24stLS05L7Ubt68KXx8fISRkZGwtLQUY8aMEeHh4aW+dPr58+fi008/FbVr1xY6OjrCwcFBDB8+XDx79kw2Tnx8vBg5cqSwtLQUOjo6wtPTU2Heb5LoPHr0SJiamopevXopDOvbt68wNDSU+3KuaAWJXVGvAlOmTBGamppyt4YQQohLly4JLS0tMX78+BKXdebMGdG1a1dhbGwsDA0NhZeXl0JicfToUdG2bVuhr68vTExMRK9evcTNmzflxnnTRKdgexb2KuwWCMHBwaJJkyZCV1dXODg4iNmzZ5f4Y+tNKJPoCCHEH3/8IZo2bSp0dXWFhYWFeP/998Xjx49lw589eyYmTJggXF1dhaGhoTA1NRVvvfWW2Llzp8K89u3bJ9q0aSNb/61atRK//fabbHhpEp2XL1/KPlNGRkbC19dXREREiHr16incnqSkz2hhiY4Q5bOflHQcuH//vhg1apRwdnYWenp6wsLCQnTq1EkcPXpUYT2+KYkQKuppVsVJJBIEBwfD398fQP7N5Hr27KlQn8zKykK/fv3kTs8DkN0U7fVnVzVs2BAjR47ErFmzZG0HDx6En58f0tPTkZubCy8vL3z//ffo3r17sfOiitGkSRNYWVmVuv8KERFVXjW6M3JxUlNToampif/++0+h53hprx4CAFtbW8THx8u1xcfHw8TEBPr6+ggLC8ODBw/kascFPem1tLRw+/ZtWd8NUq2cnBxIJBK5u6qGhoYiPDxcpR3hiIhIfZjoFKFp06bIy8vD06dPZTcyK4vWrVsr3HQpJCRE1knR1dVVofPr7NmzkZKSgjVr1ihchkmqExMTAx8fH3zwwQewt7dHREQENmzYAFtbW5XctJCIiNSvRic6qampcpcSR0VFISwsDBYWFmjYsCHef/99DBs2DCtXrkTTpk2RkJCAY8eOwcvLS9YD/+bNm8jOzsaLFy+QkpIie3JvwaWU48aNw7p16zBjxgyMGjUKx48fx86dO2V32Sx4mOSrCu52qoqbTVHRzM3N0bx5c2zevBkJCQkwNDSEn58flixZglq1aqk7PCIiUoEa3Uen4MFwrxs+fDi2bt2KnJwcLFq0CL/88gtiYmJgaWmJt99+GwsWLJDdN8fR0bHQ+5y8ulpDQ0MxZcoU3Lx5Ew4ODpgzZ06RNwwE2EeHiIhIVWp0okNERETVW42+YSCTKJqsAAAgAElEQVQRERFVbzWuj45UKkVsbCyMjY2VfoosERERqYcQAikpKbC3t1d4eHBxalyiExsbyyuZiIiIqqhHjx4p9dDPGpfoFDxE8dGjRyp5ii0RERGVv+TkZNSpU0fuYcilUeMSnYJylYmJCRMdIiKiKkbZbifsjExERETVFhMdIiIiqraY6BAREVG1xUSHiIiIqi0mOkRERFRtMdEhIiKiaouJDhEREVVbTHSIiIio2mKiQ0RERNUWEx0iIiKqtpjoEBERUbXFRIeIiIiqLSY6REREpDLn7j5DenauusOQYaJDREREKnEvIRUjt17Eu6tP42lyprrDAcBEh4iIiFQgTyowPSgcWblSOFoawspYV90hAWCiQ0RERCqw+fR9XIlOhLGuFpb294REIlF3SACY6BAREdEbioxPwcqQOwCAOb0aw85UX80R/T8mOkRERFRmuXlSTA8KR3auFJ0aWWFgcwd1hySHiQ4RERGV2abT9xH+OAkmeloI7OdVaUpWBZjoEBERUZncjkvB6pBIAMD83u6wNdVTc0SKmOgQERGR0nIKSlZ5Uvi4WaNv09rqDqlQTHSIiIhIaRtC7+FaTBJM9bWxuG/lucrqdUx0iIiISCm3niTj2+P5Jauv+rjD2qTylawKMNEhIiKiUsvJk2LaznDk5An4utugt7e9ukMqFhMdIiIiKrXvTtzFzSfJMDfQxiL/yluyKsBEh4iIiErlekwS1h2/CwD4qo9HpXnMQ3GY6BAREVGJsnPzr7LKlQr08LRFTy87dYdUKkx0iIiIqETrjkciIi4FtQx1sLCPR6UvWRVgokNERETFuvY4Cd+F3gMALPT3QC2jyl+yKsBEh4iIiIqUlZuHaUFhyJMK9PSyQw/PqlGyKsBEh4iIiIq05mgk7sSnwtJIB1/18VB3OEpjokNERESFCn+UiA0n80tWi/w9YWGoo+aIlMdEh4iIiBRk5uRhWlA4pALwb2KPdz1s1R1SmTDRISIiIgWrjt7B3aepsDLWxfze7uoOp8yY6BAREZGcy9Ev8cOp+wCAxX09YWZQ9UpWBdSa6AQGBqJly5YwNjaGtbU1/P39cfv27RKnCw0NRbNmzaCrq4sGDRpg69at5R8sERFRDZCZk4fp/ytZ9WtWG10b26g7pDei1kTn5MmTmDBhAi5cuICQkBDk5OSgW7duSEtLK3KaqKgo+Pn5oVOnTggLC0NAQABGjx6Nw4cPV2DkRERE1dPKI7dxPyENNia6mNez6pasCkiEEELdQRRISEiAtbU1Tp48ifbt2xc6zueff44DBw7g+vXrsrYhQ4YgMTERhw4dKnEZycnJMDU1RVJSEkxMTFQWOxERUVV36cELDNx4HkIAW0a0RCdXa3WHJFPW43el6qOTlJQEALCwsChynPPnz8PHx0euzdfXF+fPny90/KysLCQnJ8u9iIiISF5Gdn7JSghgYHOHSpXkvIlKk+hIpVIEBASgbdu28PAo+oZEcXFxsLGRrxfa2NggOTkZGRkZCuMHBgbC1NRU9qpTp47KYyciIqrqlh2OwIPn6bAz1cPsno3VHY7KVJpEZ8KECbh+/Tp+//13lc531qxZSEpKkr0ePXqk0vkTERFVdf/cf46t5x4AAJb094KpvrZ6A1IhLXUHAACffvop9u/fj1OnTsHBwaHYcW1tbREfHy/XFh8fDxMTE+jr6yuMr6urC13dqvPwMSIiooqUnp2Lz3ZdhRDAkJZ10KGhlbpDUim1ntERQuDTTz9FcHAwjh8/DicnpxKnad26NY4dOybXFhISgtatW5dXmERERNXW0r8jEP0iHfamevjSz03d4aicWhOdCRMmYPv27dixYweMjY0RFxeHuLg4ub42s2bNwrBhw2T/jxs3Dvfv38eMGTMQERGB77//Hjt37sSUKVPU8RaIiIiqrHP3nuHn8w8BAMsGeMNYr/qUrAqoNdFZv349kpKS0LFjR9jZ2clef/zxh2ycJ0+eIDo6Wva/k5MTDhw4gJCQEHh7e2PlypXYvHkzfH191fEWiIiIqqS0rFzM2HUVAPD+W3XxjoulmiMqH5XqPjoVgffRISIiAmbvuYbtF6LhYK6PQwHtYaRbKbrtFqla3EeHiIiIyt+ZyGfYfiG/WrJsgFelT3LeBBMdIiKiGiQlMwef784vWQ1rXQ9tnKtnyaoAEx0iIqIaZPHBW4hJzEBdCwN8/q6rusMpd0x0iIiIaohTdxLw27/5N85dPsALhtW4ZFWAiQ4REVENkPxKyWpEG0e8Vb+WmiOqGEx0iIiIaoBF+2/iSVImHGsZYMa7jdQdToVhokNERFTNnYh4ip2XHkMiAZYP9IaBTvUvWRVgokNERFSNJaXnYOaf+SWrj9o6oaWjhZojqlhMdIiIiKqxr/bfRHxyFupbGmK6b80pWRVgokNERFRNHb0Zj92XH0PjfyUrPW1NdYdU4ZjoEBERVUOJ6dmYFXwNADCmXX00r2eu5ojUg4kOERFRNTR/3w0kpGTB2coQU7o2VHc4asNEh4iIqJo5fCMOe8JioSEBVg5qUiNLVgWY6BAREVUjL9Ky8eX/SlYfd3BGkzpmao5IvZjoEBERVSPz9t3As9RsNLQxQoCPi7rDUTsmOkRERNXE39ee4K/wWGhqSLBioDd0tWpuyaoAEx0iIqJq4HlqFmbvuQ4A+KSjM7wcanbJqgATHSIiompg7t4beJ6WDVdbY0zszJJVASY6REREVdz+q7E4cO0JtP5XstLR4uG9ANcEERFRFZaQkoU5/ytZTejUAB61TdUcUeXCRIeIiKiKEkJg9p5reJmeg8Z2JpjQqYG6Q6p0mOgQERFVUfvCY3H4Rjy0NVmyKgrXCBERURX0NDkTc/feAABM7OyCxvYmao6ocmKiQ0REVMUIIfBF8DUkZeTAo7YJxnd0VndIlRYTHSIioiom+EoMjt56Cm1NCVYObAJtTR7Oi8I1Q0REVIXEJ2di/r78klWAT0M0sjVWc0SVGxMdIiKiKkIIgVl/XkNyZi68HUzxcfv66g6p0mOiQ0REVEXs+u8xjkc8hY6mBlYM9IYWS1Yl4hoiIiKqAp4kZeCrv24CAKZ2awgXG5asSoOJDhERUSUnhMDnu68hJSsXTeuaYUw7lqxKi4kOERFRJbfz0iOcupMAHS0NLB/gDU0NibpDqjKY6BAREVViMYkZWLj/FgDgs26N0MDaSM0RVS1MdIiIiCopIQQ+33UVqVm5aF7PHKPecVJ3SFUOEx0iIqJKase/0Thz9xn0tDWwfIAXS1ZlwESHiIioEnr0Ih2LD+SXrGb4uqK+FUtWZcFEh4iIqJKRSgU+330Vadl5aOVogRFtHNUdUpXFRIeIiKiS+fWfhzh37zn0tTWxbIAXNFiyKjMmOkRERJVI9PN0LD4YAQCY2d0VjpaGao6oamOiQ0REVElIpQLTd4UjIycPb9e3wIdv11N3SFUeEx0iIqJK4pfzD/Bv1AsY6Ghi+QBvlqxUgIkOERFRJfDgWRqWHMovWc3q4YY6FgZqjqh6YKJDRESkZnlSgelB4cjMkaJtg1p4v1VddYdUbTDRISIiUrMtZ6Nw6eFLGOpoYml/XmWlSkx0iIiI1Oh+QiqWH74NAPjSrzEczFmyUiUmOkRERGpSULLKypWinYsl3mtVR90hVTtMdIiIiNTkxzP3cTk6Eca6Wlja3wsSCUtWqsZEh4iISA3uPk3BiiN3AABzejaGvZm+miOqnpjoEBERVbDcPCmmBV1Fdq4UHRtZYWALB3WHVG0x0SEiIqpgP5yOQvijRBjraWFJP5asyhMTHSIiogp0Jz4Fq0LyS1bzernD1lRPzRFVb0x0iIiIKkhOnhTTdoYjO0+KLq7W6N+strpDqvaY6BAREVWQjSfv4VpMEkz1tbG4nydLVhWAiQ4REVEFiIhLxppjkQCA+b0bw8aEJauKwESHiIionBWUrHLyBLo2toF/E5asKgoTHSIionL2/Yl7uBGbDDMDbXzd14MlqwrERIeIiKgc3YhNwtrj+SWrr/p4wNqYJauKxESHiIionGTn5pescqUC3T1s0cvLTt0h1ThMdIiIiMrJuhN3ERGXAgtDHSz0Z8lKHZjoEBERlYPrMUn47sRdAMDCPh6wNNJVc0Q1ExMdIiIiFcvKzcO0neHIkwr4ednBjyUrtWGiQ0REpGLfHovE7fgUWBrpYGEfD3WHU6Mx0SEiIlKh8EeJ2HDyPgBgkb8HLAx11BxRzcZEh4iISEUyc/IwPSi/ZNXb2x7verBkpW5MdIiIiFRk9dFIRD5NhaWRLhb0dld3OAQmOkRERCpxOfolNp26BwBY3NcD5ixZVQpMdIiIiN5QQclKKoC+TWujm7utukOi/2GiQ0RE9Ia+CbmD+wlpsDbWxbxejdUdDr1CrYnOqVOn0KtXL9jb20MikWDPnj3Fjh8aGgqJRKLwiouLq6CIiYiI5P338AV+OJ1/lVVgP0+YGbBkVZmoNdFJS0uDt7c3vvvuO6Wmu337Np48eSJ7WVtbl1OERERERcvIzsP0oKsQAhjQ3AFd3GzUHRK9RkudC+/evTu6d++u9HTW1tYwMzMrh4iIiIhKb/nh24h6lgZbEz3M6cmSVWVUJfvoNGnSBHZ2dujatSvOnj1b7LhZWVlITk6WexEREb2pf6NeYMu5KABAYH9PmOprqzkiKkyVSnTs7OywYcMG7N69G7t370adOnXQsWNHXL58uchpAgMDYWpqKnvVqVOnAiMmIqLqKD07F5/tCocQwOAWddCpEbtQVFYSIYRQdxAAIJFIEBwcDH9/f6Wm69ChA+rWrYtt27YVOjwrKwtZWVmy/5OTk1GnTh0kJSXBxMTkjWImIqKaaf6+G9h67gHsTfVwaEp7mOjxbE55S05OhqmpqdLHb7X20VGFVq1a4cyZM0UO19XVha6ubgVGRERE1dn5e8+x9dwDAMDSAV5Mciq5KlW6KkxYWBjs7PgsESIiKn9pWbmYsTscAPBeq7po52Kl5oioJGo9o5Oamoq7d+/K/o+KikJYWBgsLCxQt25dzJo1CzExMfjll18AAKtXr4aTkxPc3d2RmZmJzZs34/jx4zhy5Ii63gIREdUgS/6OwKMXGahtpo8v/dzUHQ6VgloTnUuXLqFTp06y/6dOnQoAGD58OLZu3YonT54gOjpaNjw7OxvTpk1DTEwMDAwM4OXlhaNHj8rNg4iIqDycvfsM2y48BAAsG+AFI90q3/ujRqg0nZErSlk7MxERUc2VkpmDd1efRkxiBj58ux4W+nuoO6Qap6zH7yrfR4eIiKi8LT4YgZjEDNSx0MfM7q7qDoeUwESHiIioGKfuJOC3f/O7USzr7w1DlqyqFCY6RERERUjOzMHM3VcBACPaOKK1cy01R0TKYqJDRERUhK/330JsUibq1TLAjHcbqTscKgMmOkRERIU4cfsp/rj0CBIJsHyANwx0WLKqipjoEBERvSYpIwezdl8DAIxs44RWThZqjojKSulEp379+nj+/LlCe2JiIurXr6+SoIiIiNRp4f6biEvOhJOlIT7zZcmqKlM60Xnw4AHy8vIU2rOyshATE6OSoIiIiNTl2K147PrvMSQSYMVAL+jraKo7JHoDpS447tu3T/b34cOHYWpqKvs/Ly8Px44dg6Ojo0qDIyIiqkiJ6dmY9Wd+yWpMu/poXo8lq6qu1ImOv78/AEAikWD48OFyw7S1teHo6IiVK1eqNjoiIqIKtOCvm3iakoX6VoaY2rWhusMhFSh1oiOVSgEATk5OuHjxIiwtLcstKCIioop25EYcgq/EQEMCrBjoDT1tlqyqA6WvlYuKiiqPOIiIiNTmZVo2vgi+DgAY294ZzeqaqzkiUhVeXk5ERDXevH038Cw1Cy7WRgjwcVF3OKRCTHSIiKhGO3T9CfaFx0JTQ8KSVTXERIeIiGqs56lZ+PJ/JatxHerDu46ZmiMiVWOiQ0RENdbcfTfwPC0bjWyMMakLS1bVUZke3CGVSnH37l08ffpUdjVWgfbt26skMCIiovK0/2osDlx9Ak0NCVYO8oauFktW1ZHSic6FCxcwdOhQPHz4EEIIuWESiaTQuyYTERFVJgkpWZizJ79kNaFTA3jUNi1hCqqqlE50xo0bhxYtWuDAgQOws7ODRCIpj7iIiIjKhRACc/Zcx8v0HLjZmeDTTg3UHRKVI6UTncjISOzatQsNGnDHICKiquevq09w6EYctDQkWDHQCzpa7K5anSm9dd966y3cvXu3PGIhIiIqV09TMjF3b37JamJnF7jbs2RV3Sl9RmfixImYNm0a4uLi4OnpCW1tbbnhXl5eKguOiIhIVYQQ+DL4OhLTc+Bub4JPOjmrOySqABLxeo/iEmhoKJ4EkkgkEEJUic7IycnJMDU1RVJSEkxMTNQdDhERVZDgK48x5Y9waGtK8NfEd+Bqy2NAVVLW4zefdUVERNVefHIm5u+7CQCY3MWFSU4NonSiU69evfKIg4iIqFwIIfDFn9eQlJEDz9qmGNeBJauapExdzbdt24a2bdvC3t4eDx8+BACsXr0ae/fuVWlwREREb2r35Rgci3gKHU0NrBzkDS1NXmVVkyi9tdevX4+pU6eiR48eSExMlPXJMTMzw+rVq1UeIBERUVk9ScrAgr9uAACmdG2IhjbGao6IKprSic7atWvxww8/4Msvv4Sm5v/fLrtFixa4du2aSoMjIiIqKyEEZu6+hpTMXHjXMcOYdk7qDonUQOlEJyoqCk2bNlVo19XVRVpamkqCIiIielNBlx7j5J0E6GhpYOVAL5asaiilt7qTkxPCwsIU2g8dOgQ3NzeVBEVERPQmYhIzsHB//lVW07s1RANrlqxqKqWvupo6dSomTJiAzMxMCCHw77//4rfffkNgYCA2b95cHjESERGVWn7J6ipSsnLRrK4ZPnqnvrpDIjVSOtEZPXo09PX1MXv2bKSnp2Po0KGwt7fHmjVrMGTIkPKIkYiIqNR++/cRTkc+g66WBlYM9IamBh8+XZMpfWfkV6WnpyM1NRXW1taqjKlc8c7IRETV1+OX6fBddQpp2XmY7eeG0e14Nqe6qLA7I7/KwMAABgYGbzILIiIilZBKBWbsuoq07Dy0dDTHyLa8yorKeMNAIiKiyubXf6Nx7t5z6GlrYPkAlqwoHxMdIiKq8qKfpyPw4C0AwOfvusLR0lDNEVFlwUSHiIiqNKlU4LNd4UjPzkMrJwsMb+2o7pCoEmGiQ0REVdq2Cw/xT9QLGOhoYsUAb2iwZEWvKFNn5LS0NJw8eRLR0dHIzs6WGzZp0iSVBEZERFSSB8/SsOTvCADArO6uqFuLF8iQPKUTnStXrqBHjx5IT09HWloaLCws8OzZMxgYGMDa2pqJDhERVYiCklVGTh7aONfC+2/VU3dIVAkpXbqaMmUKevXqhZcvX0JfXx8XLlzAw4cP0bx5c6xYsaI8YiQiIlKw5dwDXHzwEoY6mlja34slKyqU0olOWFgYpk2bBg0NDWhqaiIrKwt16tTBsmXL8MUXX5RHjERERHLuJ6Ri+eH8ktUXfm6oY8GSFRVO6URHW1sbGhr5k1lbWyM6OhoAYGpqikePHqk2OiIiotfkSQU+23UVmTlSvNPAEkNb1VV3SFSJKd1Hp2nTprh48SJcXFzQoUMHzJ07F8+ePcO2bdvg4eFRHjESERHJ/HQmCv89fAkjXS0sHeAFiYQlKyqa0md0Fi9eDDs7OwDA119/DXNzc4wfPx4JCQnYtGmTygMkIiIqcPdpKpYfuQ0AmO3nhtpm+mqOiCo7pc/otGjRQva3tbU1Dh06pNKAiIiICpMnFZgeFI7sXCnaN7TC4JZ11B0SVQG8YSAREVUJP5y+j7BHiTDW08LS/p4sWVGplOqMTtOmTUu9Q12+fPmNAiIiInpdZHwKvjlyBwAwt2dj2JmyZEWlU6pEx9/fX/Z3ZmYmvv/+ezRu3BitW7cGAFy4cAE3btzAJ598Uj5REhFRjZWbJ8W0oHBk50nR2dUaA5o7qDskqkJKlejMmzdP9vfo0aMxadIkLFy4UGEcXl5ORESqtvHUfVx9nAQTPS0s7suSFSlH6T46QUFBGDZsmEL7Bx98gN27d6skKCIiIgCIiEvG6qP5Jav5vd1ha6qn5oioqlE60dHX18fZs2cV2s+ePQs9Pe6ARESkGjl5UkwPCkdOnoCPmw36Nq2t7pCoClL68vKAgACMHz8ely9fRqtWrQAA//zzD3766SfMmTNH5QESEVHNtD70Hq7HJMPMQBuL+3mwZEVlonSiM3PmTNSvXx9r1qzB9u3bAQBubm7YsmULBg0apPIAiYio5rkRm4Rvj0UCABb0doe1MSsGVDZKJzoAMGjQICY1RERULrJzpZgedBW5UgFfdxv09rZXd0hUhfGGgUREVKl8d+Iubj1JhrmBNhb58yorejNKn9HJy8vDqlWrsHPnTkRHRyM7O1tu+IsXL1QWHBER1SzXY5Lw3Ym7AICF/h6wMtZVc0RU1Sl9RmfBggX45ptvMHjwYCQlJWHq1Kno168fNDQ0MH/+/HIIkYiIaoKs3DxMDwpHrlSgh6ctenqxZEVvTulE59dff8UPP/yAadOmQUtLC++99x42b96MuXPn4sKFC+URIxER1QBrj91FRFwKahnqYGEfD3WHQ9WE0olOXFwcPD09AQBGRkZISkoCAPTs2RMHDhxQbXRERFQjXH2ciPUn7wEAFvl7oJYRS1akGkonOg4ODnjy5AkAwNnZGUeOHAEAXLx4Ebq63DGJiEg5Wbl5mLYzHHlSgV7e9ujuaafukKgaUTrR6du3L44dOwYAmDhxIubMmQMXFxcMGzYMo0aNUnmARERUva0+GonIp6mwNNLFV73d1R0OVTMSIYR4kxmcP38e58+fh4uLC3r16qWquMpNcnIyTE1NkZSUBBMTE3WHQ0RUo12Jfon+689BKoCNHzaHr7utukOiSqqsx+8y3TDwVa1bt0br1q3fdDZERFTDZObkX2UlFYB/E3smOVQulE50fvnll2KHF/ZkcyIiotetCrmDewlpsDLWxXyWrKicKF26Mjc3l/s/JycH6enp0NHRgYGBQaW/YSBLV0RE6vffwxcYsOE8hAA2D2sBn8Y26g6JKrmyHr+V7oz88uVLuVdqaipu376Nd955B7/99puysyMiohomIzsP04OuQgigX7PaTHKoXKnkWVcuLi5YsmQJJk+erNR0p06dQq9evWBvbw+JRII9e/aUOE1oaCiaNWsGXV1dNGjQAFu3bi1j1EREpA4rjtxG1LM02JjoYl5PlqyofKnsoZ5aWlqIjY1Vapq0tDR4e3vju+++K9X4UVFR8PPzQ6dOnRAWFoaAgACMHj0ahw8fLkvIRERUwS4+eIGfzkYBAJb084KpgbaaI6LqTunOyPv27ZP7XwiBJ0+eYN26dWjbtq1S8+revTu6d+9e6vE3bNgAJycnrFy5EgDg5uaGM2fOYNWqVfD19VVq2UREVLHSs3PxWVA4hAAGtXBAJ1drdYdENYDSiY6/v7/c/xKJBFZWVujcubMsASkv58+fh4+Pj1ybr68vAgICipwmKysLWVlZsv+Tk5PLLT4iIiraskO38eB5OuxM9TC7Z2N1h0M1hNKJjlQqLY84SiUuLg42NvKd1mxsbJCcnIyMjAzo6+srTBMYGIgFCxZUVIhERFSIC/efY+u5BwCAJf29YKLHkhVVDJX10amsZs2ahaSkJNnr0aNH6g6JiKhGScvKxWe7wgEA77Wqgw4NrdQcEdUkpTqjM3Xq1FLP8JtvvilzMCWxtbVFfHy8XFt8fDxMTEwKPZsDALq6unzYKBGRGi09FIFHLzJQ20wfX/RwU3c4VMOUKtG5cuVKqWYmkUjeKJiStG7dGgcPHpRrCwkJ4SMoiIgqqXN3n+GX8w8BAEv7e8GYJSuqYKVKdE6cOFEuC09NTcXdu3dl/0dFRSEsLAwWFhaoW7cuZs2ahZiYGNljJ8aNG4d169ZhxowZGDVqFI4fP46dO3fiwIED5RIfERGVXWpWLj7bdRUA8P5bdfGOi6WaI6KaSK19dC5duoSmTZuiadOmAPJLZE2bNsXcuXMBAE+ePEF0dLRsfCcnJxw4cAAhISHw9vbGypUrsXnzZl5aTkRUCS0+eAsxiRlwMNfHLJasSE2UftYVkJ+g7Ny5E9HR0cjOzpYb9ueff6osuPLAZ10REZW/05EJ+PDHfwEAO8a8hTbOPJtDb6bCnnX1+++/o02bNrh16xaCg4ORk5ODGzdu4Pjx4zA1NVV2dkREVM2kZObg8/+VrIa3rsckh9RK6URn8eLFWLVqFf766y/o6OhgzZo1iIiIwKBBg1C3bt3yiJGIiKqQrw/cQmxSJupaGODz7q7qDodqOKUTnXv37sHPzw8AoKOjg7S0NEgkEkyZMgWbNm1SeYBERFR1hN5+it8v5t+vbPkALxjoKH1fWiKVUjrRMTc3R0pKCgCgdu3auH79OgAgMTER6enpqo2OiIiqjKSMHMzcfQ0AMLKtI96qX0vNERGV4REQ7du3R0hICDw9PTFw4EBMnjwZx48fR0hICLp06VIeMRIRURWwaP9NxCVnwrGWAWb4smRFlYPSic66deuQmZkJAPjyyy+hra2Nc+fOoX///pg9e7bKAyQiosrveEQ8gv57DIkEWDHQG/o6muoOiQhAGRIdCwsL2d8aGhqYOXOmSgMiIqKqJSn9/0tWH7V1QgtHixKmIKo4SvfR8fHxwdatW5GcnFwe8RARURWz4K8beJqShfqWhpju20jd4RDJUTrRcXd3x6xZs2Bra4uBAwdi7969yMnJKY/YiIiokgu5GY8/r8RAQwKsGOQNPW2WrKhyUTrRWbNmDWJiYrBnzx4YGhpi2LBhsLGxwdixY3Hy5MnyiJGIiCqhl2nZ+CI4v2Q1pn19NKtrruaIiBSV6VlXGhoa6NatG8YB3Y8AAB4nSURBVLZu3Yr4+Hhs3LgR//77Lzp37qzq+IiIqJKa/9cNJKRkoYG1Eab4NFR3OESFeqM7OcXFxeH333/H9u3bcfXqVbRq1UpVcRERUSV26Hoc9obF5pesBrJkRZWX0md0kpOTsWXLFnTt2hV16tTB+vXr0bt3b0RGRuLChQvlESMREVUiL9KyMXtPfslqXAdnNKljpuaIiIqm9BkdGxsbmJubY/DgwQgMDESLFi3KIy4iIqqk5u69jmep2WhoY4TJPi7qDoeoWEonOvv27UOXLl2goVGm7j1ERFSFHbj6BPuvPoGmhgQrBzaBrhZLVlS5KZ2tdO3aFVKpFEePHsXGjRtlz72KjY1FamqqygMkIqLK4VlqFubszX++4ScdneHpYKrmiIhKpvQZnYcPH+Ldd99FdHQ0srKy0LVrVxgbG2Pp0qXIysrChg0byiNOIiJSIyEE5uy5jhdp2XC1NcbEzixZUdWg9BmdyZMno0WLFnj58iX09fVl7X379sWxY8dUGhwREVUO+68+wd/X46ClIcGKgd7Q0WL3BaoalD6jc/r0aZw7dw46Ojpy7Y6OjoiJiVFZYEREVDk8TcmUlawmdGoAj9osWVHVoXRKLpVKkZeXp9D++PFjGBsbqyQoIiKqHIQQ+DL4OhLTc9DYzgQTOjVQd0hESlE60enWrRtWr14t+18ikSA1NRXz5s1Djx49VBocERGp196wWITcjIe2JktWVDUpXbpauXIlfH190bhxY2RmZmLo0KGIjIyEpaUlfvvtt/KIkYiI1OBpcibm7bsBAJjU2QWN7U3UHBGR8pROdBwcHBAeHo4//vgD4eHhSE1NxUcffYT3339frnMyERFVXUIIfBF8DUkZOfCsbYpxHZ3VHRJRmUiEEELdQVSk5ORkmJqaIikpCSYm/HVCRFSY3f89xrSgcOhoauCvie+gkS37YJJ6lfX4zWIrERHJiUvKxPy/8ktWk31cmORQlcZEh4iIZIQQmPnnVaRk5sLbwRQft6+v7pCI3ggTHSIikgn67zFCbydAR0sDKwZ6Q0uThwmq2rgHExERACA2MQML/7oJAJjatSFcbFiyoqpP6UTnxIkTRQ7buHHjGwVDRETqIYTA57uvIiUrF03rmmFMO5asqHpQOtF599138dlnnyEnJ0fW9uzZM/Tq1QszZ85UaXBE/9fencdHVd/7H39nX4AkQsiCBBIUQQgJm2DQXrFGgQuCgBuXKtLW+7P1Z4Wwa8WVxVKtuMFVb1vb2hZwwQUKQgAVGwlbwh62QDAmYTOZsGSb+d4/gNEoIGBmTubM6/l4zB9zzvfMfM75Mpk38zlnBoB3/HPtAX2267DCTresggIDrC4JaBCX9InOe++9p2uuuUbbtm3TokWLlJqaKofDoby8PE/UCADwoC+/PqFpi7ZLkib066ArWja1uCKg4Vx00OnTp4/y8vKUmpqq7t27a+jQoRo7dqxWrVqltm3beqJGAICHnGlZHauuU8+2l2n0dSlWlwQ0qEs6GXnnzp1at26dWrdureDgYBUUFOjEiRMNXRsAwMPeWlOkz3cfUXhIoGbRsoINXXTQmTlzpjIyMnTzzTdry5Ytys3N1caNG5WWlqacnBxP1AgA8IADR09o+uJTLauJ/ToqJbaJxRUBDe+ig87s2bO1cOFCvfTSSwoPD1dqaqpyc3M1bNgw9e3b1wMlAgAamstlNOHtfJ2ocapXcnPd1yfZ6pIAj7joH/XcvHmzYmNj6y0LCQnRrFmzNGjQoAYrDADgOX9bs19f7D2qiJAgzbojTYG0rGBTF/2JzndDzrfdcMMNP6oYAIDn7T9yXDMW75AkTR7QUW1b0LKCffHNyADgR1wuowkLNulkrVPXtmuue67lalnYG0EHAPzIn/+9T7n7jioyNEizbk+nZQXbI+gAgJ8oPHxcv1t6qmX1yH9eraTmkRZXBHgeQQcA/IDTZTRhQb6qal267soWGtm7jdUlAV5B0AEAP/Cnzwu1bv/XahIapGeHpykggJYV/ANBBwBsbvfBY5q1tECS9NtBndT6MlpW8B8EHQCwMefpLwasrnPpJ+1jdfc1SVaXBHgVQQcAbOyNz/ZqY1G5moUF07KCXyLoAIBN7Sqr1HPLdkqSHhvUSa1iIiyuCPA+gg4A2FCd06XxC/JVU+dS3w4tdUfP1laXBFiCoAMANvQ/n+5V/pcVahYerJnDaFnBfxF0AMBmCkorNXv5LknSE7d2VkJ0uMUVAdYh6ACAjdSeaVk5XbqpY5yGdb/c6pIASxF0AMBG5q7ao83FFYqOCNH0YV1oWcHvEXQAwCa2feXQiytOtayeHNxZ8VG0rACCDgDYwJmWVa3T6JZO8RrStZXVJQGNAkEHAGzglZW7ta3EoZjIED0zNJWWFXAaQQcAfNyW4gq9vGK3JOmpIamKa0bLCjiDoAMAPqym7lTLqs5lNCA1QbemJVpdEtCoEHQAwIe9tGKXdpRWqnmTUD19Gy0r4LsIOgDgozZ/WaFXV+2RJD09JFWxTcMsrghofAg6AOCDquucGrcgT06X0cC0RA2kZQWcFUEHAHzQ7OW7tLPsmGKbhurpIalWlwM0WgQdAPAxeQfKNfeTUy2rZ27rouZNQi2uCGi8CDoA4EOqap0aNz9PLiMN6dpK/VMTrC4JaNQIOgDgQ/6wfKf2HDqu2KZheuLWzlaXAzR6BB0A8BHr93+t1z/dK0maPjRVl9GyAn4QQQcAfEBVrVMTFuTLZaRh3S7XLZ1pWQEXgqADAD7g90sLtPfwccU1C9PjtKyAC2Z50HnllVeUnJys8PBw9e7dW7m5ueccu2rVKgUEBHzvVlpa6sWKAcC71u07qv/9vFCSNHN4F0VHhlhcEeA7LA068+bNU1ZWlh5//HFt2LBB6enp6tevnw4ePHje7QoKClRSUuK+xcXFealiAPCukzVOjV+QL2Ok23u01k87xltdEuBTLA06zz//vO6//36NHj1anTp10ty5cxUZGak//vGP590uLi5OCQkJ7ltgoOUfTAGAR/xu6Q7tO3JCCVHhemxQJ6vLAXyOZQmhpqZG69evV2Zm5jfFBAYqMzNTOTk55922a9euSkxM1M0336zPP//8vGOrq6vlcDjq3QDAF3yx94j+9Pk+SadbVhG0rICLZVnQOXz4sJxOp+Lj638MGx8ff85zbhITEzV37ly98847euedd5SUlKS+fftqw4YN53yeGTNmKDo62n1LSkpq0P0AAE84UVOniW9vkiTdfU2S+nagRQ9cimCrC7gYHTp0UIcOHdz3+/Tpoz179ugPf/iD/vrXv551mylTpigrK8t93+FwEHYANHrP/muHio6eUKvocD068GqrywF8lmVBJzY2VkFBQSorK6u3vKysTAkJF/79EL169dLq1avPuT4sLExhYWGXXCcAeNu/9xzWmzn7JUnP3p6mZuG0rIBLZVnrKjQ0VD169FB2drZ7mcvlUnZ2tjIyMi74cfLy8pSYmOiJEgHA645Vf9Oy+q/ebfST9i0trgjwbZa2rrKysjRq1Cj17NlTvXr10gsvvKDjx49r9OjRkk61nYqLi/WXv/xFkvTCCy8oJSVFnTt3VlVVld544w2tWLFCH3/8sZW7AQANZsbi7fry65O6PCZCj/wnLSvgx7I06Nx11106dOiQpk6dqtLSUnXt2lVLlixxn6BcUlKioqIi9/iamhqNGzdOxcXFioyMVFpampYvX64bb7zRql0AgAazetdhvbXm1N+8WbenqWmYT51GCTRKAcYYY3UR3uRwOBQdHa2KigpFRUVZXQ4ASJIqq2rV/4XPVFx+Uvdc21ZP35ZqdUlAo3Kp79980x4ANALTF29XcflJJTWP0OQBHa0uB7ANgg4AWOyTnYf0j9wDkqRZt6erCS0roMEQdADAQo6qWk1+59RVVvf1Sda17VpYXBFgLwQdALDQMx9tU0lFldq2iNTE/h1+eAMAF4WgAwAWWbnjoOav+1IBAadaVpGhtKyAhkbQAQALVJyo1eR3T7Wsfn5dinqlNLe4IsCeCDoAYIEnP9qqMke12sU20fhbaFkBnkLQAQAvW76tTO9uKD7VsrojTRGhQVaXBNgWQQcAvKj8RI2mvLdZknT/T9qpR1taVoAnEXQAwIue+GCrDlVW64qWTZR181VWlwPYHkEHALxk6dZSLcz7SoEB0u/vSFd4CC0rwNMIOgDgBUeP1+jR0y2r//6PK9StzWUWVwT4B4IOAHjB4x9s1eFjNWof11RjMttbXQ7gNwg6AOBhizeX6MP8rxQUGEDLCvAygg4AeNDhY9X67cItkqRf3XCF0pNiLK4I8C8EHQDwoKnvb9HR4zXqmNBMD910pdXlAH6HoAMAHvLRpq+0eHOpu2UVFkzLCvA2gg4AeMChymo9drpl9eCNVyr18miLKwL8E0EHABqYMUa/XbhZX5+o1dWJUfr/N9KyAqxC0AGABvZB/ldaurVMwYEBeu6OdIUG86cWsAqvPgBoQAcdVZr6/lZJ0kM/ba9OraIsrgjwbwQdAGggxhg98t5mVZysVedWUfr1jVdYXRLg9wg6ANBA3ttYrOXbDyokKEDP3ZmukCD+xAJW41UIAA2gtKJKT3xwqmU1JvMqdUygZQU0BgQdAPiRjDGa8u4mOarqlNY6Wv/vP9pZXRKA0wg6APAjvb3+S60sOKTQoED9/o50BdOyAhoNXo0A8COUVJzUUx9ukySNvfkqXRXfzOKKAHwbQQcALpExRpPe2azK6jp1TYrR/T9JsbokAN9B0AGASzRv7QF9uvOQQoNpWQGNFa9KALgExeUn9cyi7ZKk8bdcpSvjmlpcEYCzIegAwEUyxmjS25t0rLpO3dvE6BfXc5UV0FgRdADgIv09t0irdx9W2OmWVVBggNUlATgHgg4AXIQDR09o2umW1cT+HdWuJS0roDEj6ADABXK5jCa+vUknapy6Jvkyje6TbHVJAH4AQQcALtBba/YrZ+8RhYcEatbt6QqkZQU0egQdALgARUdOaPriHZKkyf07Kjm2icUVAbgQBB0A+AEul9H4t/N1stap3inNdW9GstUlAbhABB0A+AFv5uxTbuFRRYYG0bICfAxBBwDOY9/h43p2yamW1ZQBHdWmRaTFFQG4GAQdADgHp8to/IJ8VdW61OeKFhrZu63VJQG4SAQdADiHP31eqHX7v1aT0CA9OzyNlhXggwg6AHAWew4d06ylBZKkRwd2UlJzWlaALyLoAMB3OF1GExbkq7rOpZ+0j9WIXklWlwTgEhF0AOA7/nf1Xm0oKlfTsGDNHJ6mgABaVoCvIugAwLfsPlip33+8U5L02KCrdXlMhMUVAfgxCDoAcFqd06VxCzapps6lG65qqTt70rICfB1BBwBOe+2zvco/UK5m4cGaObwLLSvABgg6ACBpZ1mlXli2S5I0dVAnJUbTsgLsgKADwO/VOl0aNz9fNU6XftoxTrf3aG11SQAaCEEHgN/7n0/2aHNxhaLCgzVjGC0rwE4IOgD82vYSh2Znn2pZPTmks+Kjwi2uCEBDIugA8Fu1TpfGL8hXrdMo8+p43db1cqtLAtDACDoA/NarK/do61cOxUSGaPqwVFpWgA0RdAD4pa1fVeilFadbVoM7K64ZLSvAjgg6APxOTd2pq6zqXEb9OydocHorq0sC4CEEHQB+5+UVu7SjtFKXRYbo6dtoWQF2RtAB4Fe2FFfolVV7JElP35aqls3CLK4IgCcRdAD4jeo6p8bNz5fTZTSwS6IGpdGyAuyOoAPAb7yYvUsFZZVq0SRUTw3pbHU5ALyAoAPAL+QfKNec0y2rZ25LVYumtKwAf0DQAWB7VbVOjVuQL5eRbk1vpQFdEq0uCYCXEHQA2N4Ly3dp98Fjim0apqcG07IC/AlBB4CtbSj6Wq99eqplNX1oqi5rEmpxRQC8iaADwLaqap0af7plNbTb5bqlc4LVJQHwMoIOANt67uMC7T10XC2bhenxWztZXQ4ACxB0ANjS+v1H9cbqQknSjKFdFBNJywrwRwQdALZzssap8Qs2yRhpePfWyuwUb3VJACxiedB55ZVXlJycrPDwcPXu3Vu5ubnnHb9q1Sp1795dYWFhuvLKK/XnP//ZO4UC8Bmzlhao8PBxxUeFaSotK8CvWRp05s2bp6ysLD3++OPasGGD0tPT1a9fPx08ePCs4wsLCzVw4EDdeOONysvL05gxY/TLX/5SS5cu9XLlABqrNXuP6E//PtWymjk8TdERIRZXBMBKAcYYY9WT9+7dW9dcc41efvllSZLL5VJSUpIeeughTZ48+XvjJ02apEWLFmnLli3uZXfffbfKy8u1ZMmSC3pOh8Oh6OhoVVRUKCoqqmF2RJLTZVRScbLBHg/AxatzGt37x1wVHT2hO3u21u9uT7e6JAAN5FLfv4M9WNN51dTUaP369ZoyZYp7WWBgoDIzM5WTk3PWbXJycpSZmVlvWb9+/TRmzJhzPk91dbWqq6vd9x0Ox4+s/OyOHK/W9c+u9MhjA7g4idHh+u0gWlYALAw6hw8fltPpVHx8/ZME4+PjtWPHjrNuU1paetbxDodDJ0+eVERExPe2mTFjhp588smGK/w8woItP+UJ8HtNwoL13J3pigqnZQXAwqDjLVOmTFFWVpb7vsPhUFJSUoM/T1yzcBU8M6DBHxcAAFw6y4JObGysgoKCVFZWVm95WVmZEhLO/u2lCQkJZx0fFRV11k9zJCksLExhYfxKMQAA/siyXktoaKh69Oih7Oxs9zKXy6Xs7GxlZGScdZuMjIx64yVp2bJl5xwPAAD8m6UnlWRlZen111/Xm2++qe3bt+tXv/qVjh8/rtGjR0s61Xa699573eMfeOAB7d27VxMnTtSOHTv06quvav78+Ro7dqxVuwAAABoxS8/Rueuuu3To0CFNnTpVpaWl6tq1q5YsWeI+4bikpERFRUXu8SkpKVq0aJHGjh2r2bNnq3Xr1nrjjTfUr18/q3YBAAA0YpZ+j44VPPU9OgAAwHMu9f2b66EBAIBtEXQAAIBtEXQAAIBtEXQAAIBtEXQAAIBtEXQAAIBtEXQAAIBtEXQAAIBtEXQAAIBtWfoTEFY480XQDofD4koAAMCFOvO+fbE/6OB3QefIkSOSpKSkJIsrAQAAF6uyslLR0dEXPN7vgk7z5s0lSUVFRRd1oOBZDodDSUlJOnDgAL9B1kgwJ40T89L4MCfeYYxRZWWlWrVqdVHb+V3QCQw8dVpSdHQ0/yAboaioKOalkWFOGifmpfFhTjzvUj6g4GRkAABgWwQdAABgW0FPPPHEE1YX4W1BQUHq27evgoP9rnPXqDEvjQ9z0jgxL40Pc9J4BZiLvU4LAADAR9C6AgAAtkXQAQAAtkXQAQAAtkXQAQAAtuXzQWfmzJkKCAjQmDFj3MuMMZo6daoSExMVERGhzMxM7dq1q952VVVVevDBB9WiRQs1bdpUw4cPV1lZWb0xR48e1ciRIxUVFaWYmBj94he/0LFjx7yyX76ouLhYP/vZz9SiRQtFRESoS5cuWrdunXs98+J9TqdTjz32mFJSUhQREaErrrhCTz/9dL3fimFePOvTTz/VrbfeqlatWikgIEALFy6st96bx7+oqEgDBw5UZGSk4uLiNGHCBNXV1Xlmxxu5881LbW2tJk2apC5duqhJkyZq1aqV7r33Xn311Vf1HoN58RHGh+Xm5prk5GSTlpZmHn74YffymTNnmujoaLNw4UKTn59vBg8ebFJSUszJkyfdYx544AGTlJRksrOzzbp168y1115r+vTpU+/x+/fvb9LT080XX3xhPvvsM3PllVeaESNGeG3/fMnRo0dN27ZtzX333WfWrFlj9u7da5YuXWp2797tHsO8eN+0adNMixYtzEcffWQKCwvNggULTNOmTc3s2bPdY5gXz1q8eLF59NFHzbvvvmskmffee6/eem8d/7q6OpOammoyMzPNxo0bzeLFi01sbKyZMmWKZw9AI3W+eSkvLzeZmZlm3rx5ZseOHSYnJ8f06tXL9OjRo95jMC++wWeDTmVlpWnfvr1ZtmyZueGGG9xBx+VymYSEBDNr1iz32PLychMWFmb+8Y9/uO+HhISYBQsWuMds377dSDI5OTnGGGO2bdtmJJm1a9e6x/zrX/8yAQEBpri42Bu76FMmTZpkrr/++nOuZ16sMXDgQPPzn/+83rJhw4aZkSNHGmOYF2/77huqN4//4sWLTWBgoCktLXWPmTNnjomKijLV1dWe2WEfcbYA+l25ublGktm/f78xhnnxJT7bunrwwQc1cOBAZWZm1lteWFio0tLSesujo6PVu3dv5eTkSJLWr1+v2traemM6duyoNm3auMfk5OQoJiZGPXv2dI/JzMxUYGCg1qxZ48ld80kffPCBevbsqTvuuENxcXHq1q2bXn/9dfd65sUaffr0UXZ2tnbu3ClJys/P1+rVqzVgwABJzIvVvHn8c3Jy1KVLF8XHx7vH9OvXTw6HQ1u3bvXoftpBRUWFAgICFBMTI4l58SU++RWO//znP7VhwwatXbv2e+tKS0slqd4/mjP3z6wrLS1VaGio+x/sucbExcXVWx8cHKzmzZu7x+Abe/fu1Zw5c5SVlaVHHnlEa9eu1W9+8xuFhoZq1KhRzItFJk+eLIfDoY4dOyooKEhOp1PTpk3TyJEjJfF6sZo3j39paelZn+fbdeDsqqqqNGnSJI0YMcL9o53Mi+/wuaBz4MABPfzww1q2bJnCw8OtLgenuVwu9ezZU9OnT5ckdevWTVu2bNHcuXM1atQoi6vzX/Pnz9dbb72lv//97+rcubPy8vI0ZswYtWrVinkBLkBtba3uvPNOGWM0Z84cq8vBJfC51tX69et18OBBde/eXcHBwQoODtYnn3yiF198UcHBwe4k/N0z38vKypSQkCBJSkhIUE1NjcrLy8875uDBg/XW19XV6ejRo+4x+EZiYqI6depUb9nVV1+toqIiSXIfM+bFuyZMmKBJkybp7rvvVpcuXXTPPfdo7NixmjFjhiTmxWrePP4JCQlnfZ5v14H6zoSc/fv3a9myZe5PcyTmxZf4XNC56aabtHnzZuXl5blvPXv21MiRI5WXl6d27dopISFB2dnZ7m0cDofWrFmjjIwMSVKPHj0UEhJSb0xBQYGKiorcYzIyMlReXq7169e7x6xYsUIul0u9e/f20t76juuuu04FBQX1lu3cuVNt27aVJKWkpDAvFjhx4sT3fmQwKChILpdLEvNiNW8e/4yMDG3evLneG++ZN+/v/icF34ScXbt2afny5WrRokW99cyLD7H6bOiG8O2rrow5dblmTEyMef/9982mTZvMkCFDznq5Zps2bcyKFSvMunXrTEZGhsnIyKj3uP379zfdunUza9asMatXrzbt27fnctlzyM3NNcHBwWbatGlm165d5q233jKRkZHmb3/7m3sM8+J9o0aNMpdffrn78vJ3333XxMbGmokTJ7rHMC+eVVlZaTZu3Gg2btxoJJnnn3/ebNy40X31jreO/5nLmG+55RaTl5dnlixZYlq2bOm3lzGfb15qamrM4MGDTevWrU1eXp4pKSlx3759JRTz4htsGXRcLpd57LHHTHx8vAkLCzM33XSTKSgoqLfNyZMnza9//Wtz2WWXmcjISDN06FBTUlJSb8yRI0fMiBEjTNOmTU1UVJQZPXq0qays9Mo++aIPP/zQpKammrCwMNOxY0fz2muv1VvPvHifw+EwDz/8sGnTpo0JDw837dq1M48++mi9P9bMi2etXLnSSPrebdSoUcYY7x7/ffv2mQEDBpiIiAgTGxtrxo0bZ2praz26/43V+ealsLDwrOskmZUrV7ofg3nxDQHGfOsrUgEAAGzE587RAQAAuFAEHQAAYFsEHQAAYFsEHQAAYFsEHQAAYFsEHQAAYFsEHQAAYFsEHQAAYFsEHQAAYFsEHQC20bdvX40ZM8bqMgA0IgQdAABgW/zWFQBbuO+++/Tmm2/WW1ZYWKjk5GRrCgLQKBB0ANhCRUWFBgwYoNTUVD311FOSpJYtWyooKMjiygBYKdjqAgCgIURHRys0NFSRkZFKSEiwuhwAjQTn6AAAANsi6AAAANsi6ACwjdDQUDmdTqvLANCIEHQA2EZycrLWrFmjffv26fDhw3K5XFaXBMBiBB0AtjF+/HgFBQWpU6dOatmypYqKiqwuCYDFuLwcAADYFp/oAAAA2yLoAAAA2yLoAAAA2yLoAAAA2yLoAAAA2yLoAAAA2yLoAAAA2yLoAAAA2yLoAAAA2yLoAAAA2yLoAAAA2/o/M0uK46NTV7AAAAAASUVORK5CYII=", "text/plain": [ - "PyPlot.Figure(PyObject )" + "PyPlot.Figure(PyObject )" ] }, "metadata": {}, "output_type": "display_data" - }, + } + ], + "source": [ + "plot(RK2[1],RK2[2])\n", + "title(\"método de runge-kutta con x''=-2x con 10^4 oscilaciones\")\n", + "xlabel(\"t\")\n", + "ylabel(\"x evaluada en t\")\n", + "show()" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": { + "collapsed": false + }, + "outputs": [ { "data": { + "image/png": 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", "text/plain": [ - "1-element Array{Any,1}:\n", - " PyObject " + "PyPlot.Figure(PyObject )" ] }, - "execution_count": 8, "metadata": {}, - "output_type": "execute_result" + "output_type": "display_data" } ], "source": [ - "plot(t,x)" + "#energía con el método de runge-kutta\n", + "Errort=[]\n", + "Errorx=[]\n", + "for i in 2:length(RK2[1])-1\n", + " if (RK2[2][i]>RK2[2][i-1] && RK2[2][i]>RK2[2][i+1])\n", + " push!(Errort,RK2[1][i])\n", + " push!(Errorx,RK2[2][i])\n", + " end\n", + "end\n", + "plot(Errort,Errorx)\n", + "show()" ] }, {