diff --git a/tareas/Carlos/Tarea6.ipynb b/tareas/Carlos/Tarea6.ipynb new file mode 100644 index 0000000..b2bde5d --- /dev/null +++ b/tareas/Carlos/Tarea6.ipynb @@ -0,0 +1,467 @@ +{ + "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": 17, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "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" + ] + }, + { + "data": { + "text/plain": [ + "runge_kutta_4" + ] + }, + "execution_count": 17, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\"\"\"\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,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", + " t[1]=t_0\n", + " x[1]=x_0\n", + " for i in 1:n\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", + " 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=x_0+h*i\n", + " push!(t,n)\n", + " else \n", + " break\n", + " end\n", + " end\n", + " return t,x\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "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": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + ", Any) in module Main at In[14]:1 overwritten at In[18]:1.\n" + ] + } + ], + "source": [ + "f(t,x)=x^2" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(Number[0,13.0,23.0],Number[3,2.9384e18,1.2568e306])" + ] + }, + "execution_count": 19, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "R_K=runge_kutta_4(f,0,3,1000)" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "using PyPlot\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": 6, + "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": 7, + "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": {}, + "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": 8, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "g (generic function with 1 method)" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "g(x,t)=-2x" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "runge_kutta_4_2 (generic function with 5 methods)" + ] + }, + "execution_count": 9, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "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": 10, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(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": 10, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "RK2=runge_kutta_4_2(f,2,0,(10^4)*(2*pi/(sqrt(2))),10)" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "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": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "#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()" + ] + }, + { + "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 +}