{
"cells": [
{
"cell_type": "markdown",
"metadata": {
"colab_type": "text",
"id": "view-in-github"
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"
"
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{
"cell_type": "markdown",
"metadata": {
"id": "xyThqXAkOEHv"
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"source": [
"# 1st vs 2nd order Taylor methods\n",
"\n",
"## Intial Value Poblem\n",
"The general form of the population growth differential equation\n",
"\\begin{equation} y^{'}=t-y, \\ \\ (0 \\leq t \\leq 4), \\end{equation}\n",
"with the initial condition\n",
"\\begin{equation}x(0)=1, \\end{equation}\n",
"For N=4\n",
"with the analytic (exact) solution\n",
"\\begin{equation} y= 2e^{-t}+t+1. \\end{equation}\n",
"\n",
"## Taylor Solution\n",
"\n",
"\\begin{equation} f(t,y)=t-y, \\end{equation}\n",
"differentiate with respect to $t$,\n",
"\\begin{equation} f'(t,y)=1-y'=1-t+y, \\end{equation}\n",
"This gives the first order Taylor,\n",
"\\begin{equation}T^1(t_i,w,i)=f(t_i,w_i)=t_i-w_i, \\end{equation}\n",
"and the second order Taylor,\n",
"\\begin{equation}\n",
"T^2(t_i,w,i)=f(t_i,w_i)+\\frac{h}{2}f'(t_i,w_i)=t_i-w_i+\\frac{h}{2}(1-t_i+w_i).\\end{equation}\n",
"\n",
"The first order Taylor difference equation, which is identical to the Euler method, is\n",
"\n",
"\\begin{equation}\n",
"w_{i+1}=w_i+h(t_i-w_i). \\end{equation}\n",
"The second order Taylor difference equation is\n",
"\\begin{equation}\n",
"w_{i+1}=w_i+h(t_i-w_i+\\frac{h}{2}(1-t_i+w_i)). \\end{equation}"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true,
"id": "ZQvUtvmZOEHy"
},
"outputs": [],
"source": [
"import numpy as np\n",
"import math \n",
"\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt # side-stepping mpl backend\n",
"import matplotlib.gridspec as gridspec # subplots\n",
"import warnings\n",
"\n",
"warnings.filterwarnings(\"ignore\")\n"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true,
"id": "BzW5RnluOEHz"
},
"outputs": [],
"source": [
"def Second_order_taylor(N,IC):\n",
" x_end=4\n",
" x_start=0\n",
" \n",
" INTITIAL_CONDITION=IC\n",
" h=x_end/(N)\n",
" N=N+1;\n",
" Numerical_Solution=np.zeros(N)\n",
" Numerical_Solution_first=np.zeros(N)\n",
" t=np.zeros(N)\n",
" Analytic_Solution=np.zeros(N)\n",
" Upper_bound=np.zeros(N)\n",
" \n",
" t[0]=x_start\n",
" Numerical_Solution[0]=INTITIAL_CONDITION\n",
" Numerical_Solution_first[0]=INTITIAL_CONDITION\n",
" Analytic_Solution[0]=INTITIAL_CONDITION\n",
" for i in range (1,N):\n",
" Numerical_Solution_first[i]=Numerical_Solution_first[i-1]+h*(t[i-1]-Numerical_Solution_first[i-1])\n",
" Numerical_Solution[i]=Numerical_Solution[i-1]+h*(t[i-1]-Numerical_Solution[i-1]+h/2*(1-t[i-1]+Numerical_Solution[i-1]))\n",
" t[i]=t[i-1]+h\n",
" Analytic_Solution[i]=2*math.exp(-t[i])+t[i]-1\n",
" \n",
"\n",
" fig = plt.figure(figsize=(10,4))\n",
" # --- left hand plot\n",
" ax = fig.add_subplot(1,3,1)\n",
" plt.plot(t,Numerical_Solution,color='blue',label='Second Order')\n",
" plt.plot(t,Numerical_Solution_first,color='red',label='First Order')\n",
" plt.legend(loc='best')\n",
" plt.title('Numerical Solution h=%s'%(h))\n",
"\n",
" # --- right hand plot\n",
" ax = fig.add_subplot(1,3,2)\n",
" plt.plot(t,Analytic_Solution,color='blue')\n",
" plt.title('Analytic Solution')\n",
"\n",
" #ax.legend(loc='best')\n",
" ax = fig.add_subplot(1,3,3)\n",
" plt.plot(t,np.abs(Analytic_Solution-Numerical_Solution),color='blue',label='Second Order Error')\n",
" plt.plot(t,np.abs(Analytic_Solution-Numerical_Solution_first),color='red',label='First Order Error')\n",
" plt.title('Error')\n",
" plt.legend(loc='best')\n",
" # --- title, explanatory text and save\n",
" \n",
" \n",
" # --- title, explanatory text and save\n",
" fig.suptitle(r\"$y'=y-t$\", fontsize=20)\n",
" plt.tight_layout()\n",
" plt.subplots_adjust(top=0.85) "
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 302
},
"id": "qCELqgOtOEH0",
"outputId": "eec370ed-8c88-41e8-e4eb-8aa508f8fc8f"
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"outputs": [
{
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"Second_order_taylor(40,1)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true,
"id": "dmnDk7IuOEH1"
},
"outputs": [],
"source": []
}
],
"metadata": {
"colab": {
"include_colab_link": true,
"name": "202_Taylor Method Error Example.ipynb",
"provenance": []
},
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.11"
}
},
"nbformat": 4,
"nbformat_minor": 1
}