{
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"display_name": "Python 3",
"language": "python",
"name": "python3"
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"name": "ipython",
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"file_extension": ".py",
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"name": "python",
"nbconvert_exporter": "python",
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"colab": {
"name": "901_Poisson Equation-Laplacian.ipynb",
"provenance": [],
"include_colab_link": true
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"cells": [
{
"cell_type": "markdown",
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"id": "view-in-github",
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"source": [
""
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "7eUsSZNzDlgu"
},
"source": [
"# Finite Difference Methods for the Laplacian Equation\n",
"#### John S Butler john.s.butler@tudublin.ie [Course Notes](https://johnsbutler.netlify.com/files/Teaching/Numerical_Analysis_for_Differential_Equations.pdf) [Github](https://github.com/john-s-butler-dit/Numerical-Analysis-Python)\n",
"## Overview\n",
"\n",
"This notebook will focus on numerically approximating a homogenous second order Poisson Equation which is the Laplacian Equation.\n",
"## The Differential Equation\n",
"The general two dimensional Poisson Equation is of the form:\n",
"\\begin{equation} \\frac{\\partial^2 u}{\\partial y^2} + \\frac{\\partial^2 u}{\\partial x^2}=f(x,y), \\ \\ \\ (x,y) \\in \\Omega=(0,1)\\times (0,1),\\end{equation}\n",
"with boundary conditions\n",
"\\begin{equation}U(x,y) = g(x,y), \\ \\ \\ (x,y)\\in\\delta\\Omega\\text{ - boundary}. \\end{equation}\n",
"## Homogenous Poisson Equation\n",
"This notebook will implement a finite difference scheme to approximate the homogenous form of the Poisson Equation $f(x,y)=0$:\n",
"\\begin{equation} \\frac{\\partial^2 u}{\\partial y^2} + \\frac{\\partial^2 u}{\\partial x^2}=0.\\end{equation}\n",
"with the Boundary Conditions:\n",
"\\begin{equation} u(x,0)=\\sin(2\\pi x), \\ \\ \\ \\ \\ 0 \\leq x \\leq 1, \\text{ lower},\\end{equation}\n",
"\\begin{equation}u(x,1)=\\sin(2\\pi x), \\ \\ \\ \\ \\ 0 \\leq x \\leq 1, \\text{ upper},\\end{equation}\n",
"\\begin{equation} u(0,y)=2\\sin(2\\pi y), \\ \\ \\ \\ \\ 0 \\leq y \\leq 1, \\text{ left},\\end{equation}\n",
"\\begin{equation} u(1,y)=2\\sin(2\\pi y), \\ \\ \\ \\ \\ 0 \\leq y \\leq 1, \\text{ right}.\\end{equation}\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "j7I3FVCgDlgx"
},
"source": [
"# LIBRARY\n",
"# vector manipulation\n",
"import numpy as np\n",
"# math functions\n",
"import math \n",
"\n",
"# THIS IS FOR PLOTTING\n",
"%matplotlib inline\n",
"import matplotlib.pyplot as plt # side-stepping mpl backend\n",
"import warnings\n",
"warnings.filterwarnings(\"ignore\")\n",
"from IPython.display import HTML\n",
"from mpl_toolkits.mplot3d import axes3d\n",
"import matplotlib.pyplot as plt\n"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "sbJvPuBUDlgy"
},
"source": [
"## Discete Grid\n",
"The region $\\Omega=(0,1)\\times(0,1)$ is discretised into a uniform mesh $\\Omega_h$. In the $x$ and $y$ directions into $N$ steps giving a stepsize of\n",
"\\begin{equation} h=\\frac{1-0}{N},\\end{equation}\n",
"resulting in \n",
"\\begin{equation}x[i]=0+ih, \\ \\ \\ i=0,1,...,N,$\\end{equation}\n",
"and \n",
"\\begin{equation}x[j]=0+jh, \\ \\ \\ j=0,1,...,N,\\end{equation}\n",
"The Figure below shows the discrete grid points for $N=10$, the known boundary conditions (green), and the unknown values (red) of the Poisson Equation."
]
},
{
"cell_type": "code",
"metadata": {
"id": "GtoksvGnDlgz",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 324
},
"outputId": "d7b42e84-b374-4585-d1c7-dd1e4c6e9f41"
},
"source": [
"N=10\n",
"h=1/N\n",
"x=np.arange(0,1.0001,h)\n",
"y=np.arange(0,1.0001,h)\n",
"X, Y = np.meshgrid(x, y)\n",
"fig = plt.figure()\n",
"plt.plot(x[1],y[1],'ro',label='unknown');\n",
"plt.plot(X,Y,'ro');\n",
"plt.plot(np.ones(N+1),y,'go',label='Boundary Condition');\n",
"plt.plot(np.zeros(N+1),y,'go');\n",
"plt.plot(x,np.zeros(N+1),'go');\n",
"plt.plot(x, np.ones(N+1),'go');\n",
"plt.xlim((-0.1,1.1))\n",
"plt.ylim((-0.1,1.1))\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"plt.gca().set_aspect('equal', adjustable='box')\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n",
"plt.title(r'Discrete Grid $\\Omega_h,$ h= %s'%(h),fontsize=24,y=1.08)\n",
"plt.show();"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
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gnyaY+MTIuOIsnj0R+ff7kTZdkH+/H4tnT2QcD8fxYk5uxXFrmSZyW6LWbJ4FMKqB268EUGBPpQBmm05o4hMjMfvA26hLAyBAXRow+8DbMf9zLp49EaU7ZqOiTR1UgIo2dSjdMTvmDwvGSUwcL+bkVhy3lmkiE0RVE/NAIvkA3lTVfmFumwtgmaq+YF/fAGCEqlY2FLOkpETj7WfjnybWP2UIXwCofTD61yT/fj8q2tSdNj+vxoctj9UyjsfieDEnt+K4tUw7ichKVS2J685EDl7ZZ5MLYJvj+nZ73mlEpFREykWkvLq6Ou4HrJPY5keytfXpHxINzWec5MbxYk5uxXFrmSYywSvFJmqqOk9VS1S1JDs7/m61vghf9CLNj6T7IV9M8xknuXG8mJNbcdxapolM8Eqx2QGgm+N6V3ueMaXtLgNC/wnVnh+Dh3qWIvNE/XmZJ6z5jOO9OF7Mya04bi3TRCZ4pdgsATDePiptKID9je2vaapZ9/4FZW0vgy8AQK3t2mVtL8Ose/8SU5ybymZhXm4Z8mp8ELW2s8/LLcNNZbMYx4NxvJiTW3HcWqaJTEjIAQIi8gKAEQA6AvgawDQALQBAVeeIiAD4X1hHrB0GcKuqNrrnvykHCBBR43iAALnFn4gHUdUbG7ldAfx7InIhIqLE88pmNCIiasZYbIiIyDgWGyIiMo7FhoiIjGOxISIi41hsiIjIOBYbIiIyjsWGiIiMY7EhIiLjWGyIiMi4lC42rrUZXrwYyM8H0tKsy8WLGcfLcbyYk0tx3GydTeQqVT1jp8GDB2u8Fs0q08wpUEw/NWVOgS6aVRZjoEWqmZmqwKkpM9Oazzjei+PFnFyK49oy7QCgXD3wv87pzJ8S1hbahKac9dm1NsP5+UBFxenz8/KALVsYx2txvJiTS3HcbJ0dxLM+k1tSttikTRdomHa5okBgegyvSVqa9V30tEACBAKM47U4XszJpTiuLdP1UmCxIXek7D4b19oMd+8e23zGSW4cN2N5LI6brbOJ3Jayxca1NsMPPQRkZoYEyrTmM4734ngxJ5fiuNk6m8h1yd5p1JSpKQcIqFo7VPPu86lMg+bd54t/R+qiRap5eaoi1mU8O60ZJ3FxvJiTS3FcW6Zt4AECnFyaUnafDRE1jvtsyC0puxmNiIgSh8WGiIiMY7EhIiLjWGyIiMg4FhsiIjKOxYaIiIxjsSEiIuNYbIiIyDgWGyIiMi4hxUZERonIBhHZJCKTw9zeXUT+JiKrRORTEbkqEXkREVFiGC82IuID8DSAKwEUAbhRRIpChv0EwMuqOhDAWACzTOcFsFNnysbxYk7s1EnNnemTrwEYBmCp4/oDAB4IGTMXwH85xn8YTWx26mQcdup0hGGnTk4enoyfiFNErgMwSlUn2NfHARiiqnc5xuQA+DOA9gBaAxipqisbi81OnYzDTp2OMOzUSR7mlQMEbgTwrKp2BXAVgOdEJGxuIlIqIuUiUl5dXR33A25tffo/ZUPzIwfaGtt8xkluHDdjeSyOa8s0kQGJKDY7AHRzXO9qz3P6AYCXAUBV/w4gA0DHcMFUdZ6qlqhqSXZ2dtxJsVNnisZxM5bH4rBTJ3lZIorNCgAFItJDRNJhHQCwJGTMVgCXAYCI9IVVbOJfbYkCO3WmaBwv5sROnZQKErFjCNamsY0ANgOYYs+bAWC0/XcRgA8ArAbwCYAroonLTp2MEzev5cROnZya+cROnUQUEQ8QILd45QABIiJqxlhsiIjIOBYbIiIyjsWGiIiMY7EhIiLjWGyIiMg4FhsiIjKOxYaIiIxjsSEiIuNYbIiIyLiULjbs1JmicbyYEzt1UnOX7JOzNWVip07GYadORxh26uTk4SllT8TJTp0pGseLObFTJ6WAlC02adMFKqfPFwUC02N4TdLSrO+ipwUSIBBgHK/F8WJOLsVxbZmulwKLDbkjZffZsFNnisZxM5bH4rBTJ3lZyhYbdupM0ThezImdOikVJHunUVMmdupknLh5LSd26uTUzKeU3WdDRI3jPhtyS8puRiMiosRhsSEiIuNYbIiIyDgWGyIiMo7FhoiIjGOxISIi41hsiIjIOBYbIiIyjsWGiIiMS0ixEZFRIrJBRDaJyOQIY24QkXUislZEnk9EXkRElBjGi42I+AA8DeBKAEUAbhSRopAxBQAeADBcVYsB/IfpvAB26kzZOF7MiZ06qbkzffI1AMMALHVcfwDAAyFjHgUwIdbY7NTJOOzU6QjDTp2cPDwZPxGniFwHYJSqTrCvjwMwRFXvcox5HcBGAMMB+ABMV9U/NRabnToZh506HWHYqZM8zJ/sBGx+AAUARgDoCuBdEemvqvtCB4pIKYBSAOgeT+Ms29bWp/9TNjQ/cqCtsc1nnOTGcTOWx+K4tkwTGZCIAwR2AOjmuN7Vnue0HcASVT2hql/BWsspCBdMVeepaomqlmRnZ8edFDt1pmgcN2N5LA47dZKXJWLNZgWAAhHpAavIjAXw/ZAxrwO4EcCvRaQjgEIAX5pM6qGepSjdMRuHW5yaF3enztJS4PBhR6A4uzUyjvk4XszJpTiuLdONWLly5Tl+v/8ZAP3An0+QJQBgTW1t7YTBgwd/E26A8WKjqrUicheApbD2xyxQ1bUiMgPWzscl9m1XiMg6AHUA7lfV3SbzuqlsFjAbmPLlPGxtXYfuh3x4qGepNT+mQDdZl1OmWJs9une3PiSC8xnHW3G8mJNLcVxbphvh9/uf6dy5c9/s7Oy9aWlpZ273RXJNIBCQ6urqoqqqqmcAjA43hp06iSiicAcIrF69+sv+/fuz0FA9gUBAPvvss/YDBgzoGe52rgITUazSWGgolL1MRKwpLDZE1OzNnDnz7PHjx8d/+Co1GYsNEZk1Z04HdOnSH2lpg9GlS3/MmdMh2SlR4rHYEJE5c+Z0wKRJeaisTIcqUFmZjkmT8ppacDZs2JBeUFBQHLw+derUTvfee2+XCy64oHdZWVlu//79++bn5/f705/+1Cb0vi+++GK78847r09lZaX/2muvzb/lllu6DRw4sE/Xrl37//rXv24PAIFAAHfccUfXgoKC4sLCwqL58+e3B4Bx48Z1X7x4cTsAuPzyy8+9/vrr8wHgqaeeOvvuu+/O3bBhQ3rPnj2Lx44dm9erV6/i4cOHF9TU1EhTnmtzwWJDRObMmJGLo0frf84cPZqGGTNyTT1kbW2tfPbZZ58/8sgj22bMmNHFedvChQvPeuyxxzq/9dZbX+Tk5NQCwNdff92ivLx8/e9///svpk2blhsc99lnn7X6/PPP17799tsbp06d2rWioqLFRRdddPDdd9/NAoCqqqr0jRs3ZgDA+++/nzVixIiDALB169aMH/7wh99s2rRpbbt27eoWLlzY3tRzPZOw2BCROVVV6THNd8H111+/FwAuvPDCQ9u3bz/5OB988EHW448/3vmtt976Ijs7++RpFUaPHr3P5/Nh8ODBR3fv3t0CAN57772sG264YY/f70e3bt1qhwwZUvP+++9nXn755TXLly9vs3LlyozCwsIjHTt2PFFRUdFi5cqVrb/1rW/VAEBubu6xCy+88AgADBw48PCWLVtamnquZxIWGyIyp3Pn4zHNj5Lf79dAIHDy+lHH2lNGRobaY1BXV3dyE1ZeXt6xQ4cO+dasWZPhjBUcD1gnJm5Ijx49Thw4cMD3xhtvtLvooosODh8+vGbhwoXtW7duHWjfvn0AANLT008G8fl8Wltby81oYLEhIpOmTt2BjIxAvXkZGQFMnRp6yqqYdO3atXbPnj3+qqoq35EjR2Tp0qXtorjP8VdeeWXzrbfe2qO8vDyjobEXX3zxwVdffbVDbW0tdu7c6f/HP/7R5qKLLjoEAIMGDTo0d+7cc0aOHFkzYsSImqeffrrzkCFDapryfFKBV07ESUTN0Z137gFg7bupqkpH587HMXXqjpPz49SyZUv90Y9+VHn++ef37dSp04levXodjeZ+AwcOPLpw4cIvx4wZc+6SJUs2RRo3bty4fR9++GGbvn37FouIPvjgg9u7d+9eCwD//M//XPPee++17dev37Fjx44d379/v+/iiy8+2JTnkwp4BgEiiijCGQS2DBgwYFeyciLvWr16dccBAwbkh7stpTejsVNnisbxYk7s1EnNXEyb0UTkbgCLVHWvoXwSZvHsidYZcu2j8Cva1KF0x2xgNmI7ceHixfXP2FtRYV0HYjuRIuMkJo4Xc3IpjmvLNJEBMW1GE5H/htUi4GMAC2C1e07adjh26mQcdup0hElQp05uRqNIXNuMpqo/gdXU7FcAbgHwhYj8TETObWqSicZOnSkax81YHovDTp3kZTHvs7HXZKrsqRZAewCvisijLudmFDt1pmgcN2N5LA47dZKXxVRsROQeEVkJ4FEAHwDor6plAAYDuNZAfsY81LMUmSfqz4u7U2dmZkigOLs1Mo75OF7MyaU4ri3TRAbEumbTAcD3VPXbqvqKqp4AAFUNAPgX17Mz6KayWZiXW4a8Gh9Ere3a83LL4uvUOW+etX1dxLqcNy++bo2MYz6OF3NyKY5ry/QZwOfzDe7Tp09R7969i4qKivq+9dZbrU0/Zm5ubv/KykrXf5t47NgxmThxYm5eXl6/oqKivuedd16fl19+ua0bsTMzMwcCwJYtW1qMGjWqJwB8+OGHrV566aWTP4JdvHhxux//+Med3Xi8hvB3NkQUkRsHCMxZMafDjHdn5FbVVKV3btP5+NSLp+648/ym/agzMzNz4OHDh1cBwG9/+9u2Dz/8cM6KFSs2NCVmY3Jzc/uXl5d/HjyBZ2Nqa2vh9zdemyZOnJhbVVXVYvHixRWtWrXSbdu2+ZcuXZo1YcKEJh/163ydgmbOnHl2eXl564ULF8axw7Nh/J0NESXFnBVzOkz686S8yprKdIWisqYyfdKfJ+XNWeFeT5v9+/f72rVrVwtEbg3w5ptvZl166aW9gvcZP35895kzZ54NWEVk0qRJXYqKivoWFhYWrVq1KgMAqqqqfMOHDy/o1atX8ZgxY/KcX8xHjhx5bnFxcd9evXoV/+IXv+gYnJ+ZmTnw9ttv79q7d++iyZMn54wcOfLkwVOvvfZa28svv7zewVQHDx5Me/7557OfeeaZra1atVIA6NatW22w0MydO7dDYWFhUUFBQXFZWVmu83Huvvvu3N69excNGDCgz7Zt2/wAsH79+vTzzjuvT2FhYdEPf/jDk2e8DrZkOHr0qPz85z/v8sYbb7Tv06dP0fz589s7G8tt2LAhfejQoYWFhYVFw4YNK/ziiy/SASBSK4ZYsNgQkTEz3p2Re7S2fouBo7VH02a827QWA8eOHUvr06dPUY8ePYrvueeevGnTplUCkVsDNBavY8eOtevWrfv8tttuq3744Yc7AcDkyZO7DBs2rGbTpk1rv/vd7+6rrKw8eQbpxYsXb1m7du3nn3zyybq5c+d2qqqq8gHAkSNH0oYMGXJow4YN6x599NHKzZs3Z+zcudMPAAsWLDj71ltvrbdGuG7dupY5OTnHO3ToUP/8cbA2fU2fPj132bJlG9etW7d21apVrZ977rmzgo8zbNiwmg0bNqwbNmxYzS9/+ctsAJg4cWL3CRMmVG/cuHFdTk7OidCYGRkZ+sADD+y8+uqr965fv37d7bffXm/tqaysrPtNN920e+PGjevGjBmzu6ysrFvwtnCtGGLBYkNExlTVhG8lEGl+tFq2bBlYv379uq+++mrta6+99sWtt97aIxAIRGwN0Fi873//+3sB4IILLji8bdu2lgCwfPnyrNtuu203AIwdO3Z/27ZtTx5D/sgjj3Tq3bt30eDBg/tWVVW1WLt2bQYA+Hw+3HLLLXsBIC0tDTfccMPu+fPnd9i1a5fv448/bnP99dfvj/Y5vv/++62HDh16sEuXLrUtWrTAmDFj9rzzzjttAKBFixY6duzY/QAwePDgQxUVFekA8PHHH7e5/fbb9wDAHXfcsTvaxwpatWpV69LS0j0AUFZWtmflypUnm8+Fa8UQC56Ik4iM6dym8/HKmsrTCkvnNk1rMeA0cuTIQ3v37vU3tPO+RYsW9VoSHDt2rN5p/x1tCRptCfDmm29mvfPOOyA+hakAAA9ySURBVFnl5eXrs7KyAhdccEHvI0eOpAFAenp6wLmfpqysbPd3vvOdXhkZGXr11VfvbdGi/md0UVHRscrKyvQ9e/akhVu7icTv92taWlrwbzhzTktLM7IjPpZWDOFwzYaIjJl68dQdGf76LQYy/BmBqRc3rcWA06pVqzICgQA6depUG6k1wLnnnnts06ZNrY4cOSK7du3yvf/++40e7TV06NCDzz777NkA8PLLL7c9cOCADwD27dvna9euXV1WVlZg1apVGatXr454JFx+fv6JTp06nXj88cdzSktLTzuoIisrKzB27NhdpaWl3Y8ePSoAsHPnTv+CBQvaX3TRRYc++uijrMrKSn9tbS1eeeWVDiNGjGiwlcGgQYNq5s+f3wEA5s+ff3a4MW3btq2rqakJ+9k/cODAQ88880x7wNpfVFJS4lrrBBYbIjLmzvPv3PPkFU9W5LTJOS4Q5LTJOf7kFU9WNPVotOA+mz59+hSNHTu25+zZs7f4/X6MGzduX3Fx8ZG+ffsWjxgxojDYGqBXr14nrr766r19+vQpvuaaa3oWFxcfbuwxHn744Z0ffPBBm169ehX/7ne/a5+Tk3McAK699tr9tbW10rNnz+L7778/d8CAAYcaijN27NjdOTk5xwcNGhS2DcJTTz21o2PHjrWFhYXFBQUFxaNGjerVrl27ury8vBPTpk3bcckllxT27du3eMCAAYduvvnmfQ091qxZs7bOmzfvnMLCwqIdO3aE3dR15ZVXHty4cWOr4AECztvmzJmz9bnnnutYWFhY9MILL5w9a9asbQ2/StHjoc9EFBHPjdZ048eP7z5w4MDDkyZNavavWUOHPnOfDRGRIcXFxX1btWoVmDt3rmtrCGcqFhsiIkPWrl37ebJz8IqE7LMRkVEiskFENonI5AbGXSsiKiIlkcYQEdGZx3ixEREfgKcBXAmgCMCNIlIUZlwWgHsAfGQ6pyB26kzROF7M6czq1BkIBAINHh5MqcdeJiIevp2INZsLAGxS1S9V9TiAFwFcE2bcTwE8AiDsERtuC3Y1rGhTB5VTXQ1j/ucMdlmsqABUT3VZjPXDgnESE8eLObkUx7VlunFrqqur27HgUFAgEJDq6up2ANZEGmP8aDQRuQ7AKFWdYF8fB2CIqt7lGDMIwBRVvVZElgG4T1UbPcyMnToZh506HWES1Klz5cqV5/j9/mcA9AN/PkGWAIA1tbW1EwYPHvxNuAFJP0BARNIAPAGr82c040sBlAJA93gaZ9nYqTNF47gZy2NxEtWp0/4wGe1qUGr2EvGtZAeAbo7rXe15QVmwviEtE5EtAIYCWBLpIAFVnaeqJapakp2dHXdS7NSZonHcjOWxOOzUSV6WiGKzAkCBiPQQkXQAYwEsCd6oqvtVtaOq5qtqPoDlAEZHsxmtKdipM0XjeDEnduqkVKCqxicAVwHYCGAzrH0zADADVlEJHbsMQEk0cQcPHqxNsWhWmebd51OZBs27z6eLZpXFGWiRal6eqoh1uWgR43g5jhdzcimOa8u0DUC5JuAzglPzn3i6GiKKKNwBAkTx4JEkRERkHIsNEREZx2JDRETGsdgQEZFxLDZERGQciw0RERnHYkNERMax2BARkXEsNkREZByLDRERGZfSxYadOlM0jhdzOrM6dRLFLtknZ2vK1JQTcS6aVaaZU6CYfmrKnILYT1y4aJFqZqaq1WPRmjIzYz+RIuMkJo4Xc3IpjmvLtAN4Ik5OLk0peyJOdupM0ThezOkM69RJFI+ULTZp0wUapoO6KBCYHsNrkpZmfRc9LZAAgQDjeC2OF3NyKY5ry3S9FFhsyB0pu8+GnTpTNI6bsTwWh506yctSttiwU2eKxvFiTuzUSakg2TuNmjKxUyfjxM1rObFTJ6dmPqXsPhsiahz32ZBbUnYzGhERJQ6LDRERGcdiQ0RExrHYEBGRcSw2RERkHIsNEREZx2JDRETGsdgQEZFxLDZERGQciw0RERmXkGIjIqNEZIOIbBKRyWFuv1dE1onIpyLytojkJSIvdupM0ThezImdOqm5M33yNQA+AJsB9ASQDmA1gKKQMZcCyLT/LgPwUjSx2amTcdip0xGGnTo5eXgyfiJOERkGYLqqftu+/oBd5H4eYfxAAP+rqsMbi81OnYzDTp2OMOzUSR6WiM1ouQC2Oa5vt+dF8gMAf4x0o4iUiki5iJRXV1fHndTW1qf/UzY0P3KgrbHNZ5zkxnEzlsfiuLZMExngqQMERORmACUAHos0RlXnqWqJqpZkZ2fH/Vjs1JmicdyM5bE47NRJXpaIYrMDQDfH9a72vHpEZCSAKQBGq+ox00mxU2eKxvFiTuzUSanA9E4hAH4AXwLogVMHCBSHjBkI6yCCglhis1Mn48TNazmxUyenZj4lpFOniFwF4ClYR6YtUNWHRGSGvSAvEZG/AOgPoNK+y1ZVHd1YXHbqJDKLBwiQW/yJeBBV/QOAP4TMm+r4e2Qi8iAiouTw1AECRETUPLHYEBGRcSw2RERkHIsNEREZx2JDRETGsdgQEZFxLDZERGQciw0RERnHYkNERMax2BARkXEpXWxca6E7cSLg9wMi1uVEtpf2dBwv5sS20NTcJftMoE2ZPNEWuqxM67XzDU5lbC/tyThezIltoTmlwJSQsz6b4om20H4/UBemE6LPB9SyvbTn4ngxJ7aFphSQssUmbbpA5fT5okBgegyviYQJEhTLa5uWFn68CBAIMI5bcbyYk0txXFum66XAYkPuSNl9Nq610PVFGB9pfsSEvNViuNnGcTOWx+KwLTR5WcoWG9da6JZGGB9pfsSEvNViuNnG8WJObAtNqSDZO42aMnmmLXRZmarPpwpYl7EeHHAyIW+1GG62cbyYE9tCc2rmU8rusyGixnGfDbklZTejERFR4rDYEBGRcSw2RERkHIsNEREZx2JDRETGsdgQEZFxLDZERGQciw0RERnHYkNERMYlpNiIyCgR2SAim0RkcpjbW4rIS/btH4lIfiLyIiKixDBebETEB+BpAFcCKAJwo4gUhQz7AYC9qtoLwJMAHjGdFwBMfGIk/NMEMl3gnyaY+MTIuOK41R2RcRITx4s5uRXHrWWayG2JWLO5AMAmVf1SVY8DeBHANSFjrgHwG/vvVwFcJtJQo5imm/jESMw+8Dbq0gAIUJcGzD7wdsz/nItnT0TpjtmoaFMHFaCiTR1Kd8yO+cOCcRITx4s5uRXHrWWayATjJ+IUkesAjFLVCfb1cQCGqOpdjjFr7DHb7eub7TG7GordlBNx+qeJ9U8ZwhcAah+M/jVxqzsi4yQmjhdzciuOW8u0E0/ESW454w4QEJFSESkXkfLq6uq449RFWG+KND+Sra3DtIRuYD7jJDeOF3NyK45byzSRCYkoNjsAdHNc72rPCztGRPwA2gHYHS6Yqs5T1RJVLcnOzo47KV+EL3qR5kfiVndExklMHC/m5FYct5ZpIhMSUWxWACgQkR4ikg5gLIAlIWOWAPg3++/rAPxVDW/fK213GRD6CGrPj4Fb3REZJzFxvJiTW3HcWqaJjEhEhzYAVwHYCGAzgCn2vBkARtt/ZwB4BcAmAP8A0DOauE3t1Fn2+GXqmwrFNKhvKrTs8cviiuNWd0TGSUwcL+bkVhy3lukgsFMnJ5cmduokooh4gAC55Yw7QICIiM48LDZERGQciw0RERnHYkNERMax2BARkXEsNkREZByLDRERGcdiQ0RExrHYEBGRcSw2RERkHIsNEREZx2JDRETGsdgQEZFxZ/RZn0WkGkCFC6E6AmiwBXWCMZ+GeS0fwHs5uZVPnqrG36WQyHZGFxu3iEi5l06jznwa5rV8AO/l5LV8iLgZjYiIjGOxISIi41hsLPOSnUAI5tMwr+UDeC8nr+VDKY77bIiIyDiu2RARkXEpU2xEZJSIbBCRTSIyOcztLUXkJfv2j0Qk3wM53Ssi60TkUxF5W0TykpmPY9y1IqIiYvRop2jyEZEb7NdorYg8n8x8RKS7iPxNRFbZ79lVhvNZICLfiMiaCLeLiMy08/1URAaZzIeoQara7CcAPgCbAfQEkA5gNYCikDETAcyx/x4L4CUP5HQpgEz77zKTOUWTjz0uC8C7AJYDKEny61MAYBWA9vb1c5KczzwAZfbfRQC2GF6GLgYwCMCaCLdfBeCPAATAUAAfmcyHE6eGplRZs7kAwCZV/VJVjwN4EcA1IWOuAfAb++9XAVwmIpLMnFT1b6p62L66HEDXZOZj+ymARwAcNZhLtPncDuBpVd0LAKr6TZLzUQBt7b/bAdhpMB+o6rsA9jQw5BoAC9WyHMBZIpJjMieiSFKl2OQC2Oa4vt2eF3aMqtYC2A/g7CTn5PQDWN9Sk5aPvRmmm6r+n8E8os4HQCGAQhH5QESWi8ioJOczHcDNIrIdwB8A3G0wn2jEuowRGeNPdgLUOBG5GUAJgEuSmEMagCcA3JKsHMLww9qUNgLWWt+7ItJfVfclKZ8bATyrqo+LyDAAz4lIP1UNJCkfIs9IlTWbHQC6Oa53teeFHSMiflibQXYnOSeIyEgAUwCMVtVjScwnC0A/AMtEZAusfQBLDB4kEM3rsx3AElU9oapfAdgIq/gkK58fAHgZAFT17wAyYJ2jLFmiWsaIEiFVis0KAAUi0kNE0mEdALAkZMwSAP9m/30dgL+qqskfITWak4gMBDAXVqExuT+i0XxUdb+qdlTVfFXNh7UPabSqlicjH9vrsNZqICIdYW1W+zKJ+WwFcJmdT19YxabaUD7RWAJgvH1U2lAA+1W1Mon5UApLic1oqlorIncBWArrqKIFqrpWRGYAKFfVJQB+BWuzxyZYO13HeiCnxwC0AfCKfazCVlUdncR8EibKfJYCuEJE1gGoA3C/qhpZG40ynx8BmC8ik2AdLHCLyS8sIvICrGLb0d5PNA1ACzvfObD2G10FYBOAwwBuNZULUWN4BgEiIjIuVTajERFRErHYEBGRcSw2RERkHIsNEREZx2JDRETGsdgQEZFxLDZERGQciw0ZJyLn2/1UMkSktd17pl+y8yKixOGPOikhROS/YZ2+pRWA7ar68ySnREQJxGJDCWGfT2wFrD44F6pqXZJTIqIE4mY0SpSzYZ3nLQvWGg4RpRCu2VBCiMgSWN0tewDIUdW7kpwSESVQSpz1mZJLRMYDOKGqz4uID8CHIvItVf1rsnMjosTgmg0RERnHfTZERGQciw0RERnHYkNERMax2BARkXEsNkREZByLDRERGcdiQ0RExrHYEBGRcf8fB4/7ZAPjdI4AAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "gxFX1vHDDlg0"
},
"source": [
"## Boundary Conditions\n",
"\n",
"The discrete boundary conditions are \n",
"\\begin{equation} w_{i0}=w[i,0]=\\sin(2\\pi x[i]), \\text{ for } i=0,...,10, \\text{ upper},\\end{equation}\n",
"\n",
"\\begin{equation} w_{iN}=w[i,N]=\\sin(2\\pi x[i]), \\text{ for } i=0,...,10, \\text{ lower},\\end{equation}\n",
"\n",
"\\begin{equation} w_{0j}=w[0,j]=2\\sin(2\\pi y[j]), \\text{ for } j=0,...,10, \\text{ left},\\end{equation}\n",
"\\begin{equation} w_{Nj}=w[N,j]=2\\sin(2\\pi y[j]), \\text{ for } i=0,...,10,\\text{ right}. \\end{equation}\n",
"\n",
"The Figure below plots the boundary values of $w[i,j]$."
]
},
{
"cell_type": "code",
"metadata": {
"id": "BvX2BqUyDlg1",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 272
},
"outputId": "134c46e7-1464-4fa4-939f-f046dd92e2ce"
},
"source": [
"w=np.zeros((N+1,N+1))\n",
"\n",
"for i in range (0,N):\n",
" w[i,0]=np.sin(2*np.pi*x[i]) #left Boundary\n",
" w[i,N]=np.sin(2*np.pi*x[i]) #Right Boundary\n",
"\n",
"for j in range (0,N):\n",
" w[0,j]=2*np.sin(2*np.pi*y[j]) #Lower Boundary\n",
" w[N,j]=2*np.sin(2*np.pi*y[j]) #Upper Boundary\n",
"\n",
" \n",
"fig = plt.figure()\n",
"ax = fig.add_subplot(111, projection='3d')\n",
"# Plot a basic wireframe.\n",
"ax.plot_wireframe(X, Y, w,color='r', rstride=10, cstride=10)\n",
"ax.set_xlabel('x')\n",
"ax.set_ylabel('y')\n",
"ax.set_zlabel('w')\n",
"plt.title(r'Boundary Values',fontsize=24,y=1.08)\n",
"plt.show()"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "pRbYOUSbDlg2"
},
"source": [
"## Numerical Method\n",
"The Poisson Equation is discretised using \n",
"$\\delta_x^2$ is the central difference approximation of the second derivative in the $x$ direction\n",
"\\begin{equation}\\delta_x^2=\\frac{1}{h^2}(w_{i+1j}-2w_{ij}+w_{i-1j}), \\end{equation}\n",
"and $\\delta_y^2$ is the central difference approximation of the second derivative in the $y$ direction\n",
"\\begin{equation}\\delta_y^2=\\frac{1}{h^2}(w_{ij+1}-2w_{ij}+w_{ij-1}). \\end{equation}\n",
"The gives the Poisson Difference Equation,\n",
"\\begin{equation}-(\\delta_x^2w_{ij}+\\delta_y^2w_{ij})=f_{ij} \\ \\ (x_i,y_j) \\in \\Omega_h, \\end{equation}\n",
"\\begin{equation}w_{ij}=g_{ij} \\ \\ (x_i,y_j) \\in \\partial\\Omega_h, \\end{equation}\n",
"where $w_ij$ is the numerical approximation of $U$ at $x_i$ and $y_j$.\n",
"Expanding the the Poisson Difference Equation gives the five point method,\n",
"\\begin{equation}-(w_{i-1j}+w_{ij-1}-4w_{ij}+w_{ij+1}+w_{i+1j})=h^2f_{ij} \\end{equation}\n",
"for $i=1,...,N-1$ and $j=1,...,N-1$ which can be written\n",
"\n",
"\\begin{equation}\\nabla^2_h w_{ij}=f_{ij}. \\end{equation}\n",
"\n",
"### Matrix form\n",
"This can be written as a system of $(N-1)\\times(N-1)$ equations can be arranged in matrix form\n",
"\\begin{equation} A\\mathbf{w}=\\mathbf{r},\\end{equation}\n",
"where $A$ is an $(N-1)^2\\times(N-1)^2$ matrix made up of the following block tridiagonal structure\n",
"\\begin{equation}\\left(\\begin{array}{ccccccc}\n",
"T&I&0&0&.&.&.\\\\\n",
"I&T&I&0&0&.&.\\\\\n",
".&.&.&.&.&.&.\\\\\n",
".&.&.&0&I&T&I\\\\\n",
".&.&.&.&0&I&T\\\\\n",
"\\end{array}\\right),\n",
"\\end{equation}\n",
"where $I$ denotes an $N-1 \\times N-1$ identity matrix and $T$ is the tridiagonal matrix of the form:\n",
"\\begin{equation} T=\\left(\\begin{array}{ccccccc}\n",
"-4&1&0&0&.&.&.\\\\\n",
"1&-4&1&0&0&.&.\\\\\n",
".&.&.&.&.&.&.\\\\\n",
".&.&.&0&1&-4&1\\\\\n",
".&.&.&.&0&1&-4\\\\\n",
"\\end{array}\\right).\n",
"\\end{equation}\n",
"The plot below shows the matrix $A$ and its inverse $A^{-1}$ as a colourplot."
]
},
{
"cell_type": "code",
"metadata": {
"id": "Cc62bPREDlg3",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 297
},
"outputId": "b8d38d7a-155d-41ff-8b14-a4c419afb3c0"
},
"source": [
"N2=(N-1)*(N-1)\n",
"A=np.zeros((N2,N2))\n",
"## Diagonal \n",
"for i in range (0,N-1):\n",
" for j in range (0,N-1): \n",
" A[i+(N-1)*j,i+(N-1)*j]=-4\n",
"\n",
"# LOWER DIAGONAL \n",
"for i in range (1,N-1):\n",
" for j in range (0,N-1): \n",
" A[i+(N-1)*j,i+(N-1)*j-1]=1 \n",
"# UPPPER DIAGONAL \n",
"for i in range (0,N-2):\n",
" for j in range (0,N-1): \n",
" A[i+(N-1)*j,i+(N-1)*j+1]=1 \n",
"\n",
"# LOWER IDENTITY MATRIX\n",
"for i in range (0,N-1):\n",
" for j in range (1,N-1): \n",
" A[i+(N-1)*j,i+(N-1)*(j-1)]=1 \n",
" \n",
" \n",
"# UPPER IDENTITY MATRIX\n",
"for i in range (0,N-1):\n",
" for j in range (0,N-2): \n",
" A[i+(N-1)*j,i+(N-1)*(j+1)]=1\n",
"Ainv=np.linalg.inv(A) \n",
"fig = plt.figure(figsize=(12,4));\n",
"plt.subplot(121)\n",
"plt.imshow(A,interpolation='none');\n",
"clb=plt.colorbar();\n",
"clb.set_label('Matrix elements values');\n",
"plt.title('Matrix A ',fontsize=24)\n",
"plt.subplot(122)\n",
"plt.imshow(Ainv,interpolation='none');\n",
"clb=plt.colorbar();\n",
"clb.set_label('Matrix elements values');\n",
"plt.title(r'Matrix $A^{-1}$ ',fontsize=24)\n",
"\n",
"fig.tight_layout()\n",
"plt.show();"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "HiMy8hjiDlg4"
},
"source": [
"\n",
"\n",
"The vector $\\mathbf{w}$ is of length $(N-1)\\times(N-1)$ which made up of $N-1$ subvectors $\\mathbf{w}_j$ of length $N-1$ of the form\n",
"\\begin{equation}\\mathbf{w}_j=\\left(\\begin{array}{c}\n",
"w_{1j}\\\\\n",
"w_{2j}\\\\\n",
".\\\\\n",
".\\\\\n",
"w_{N-2j}\\\\\n",
"w_{N-1j}\\\\\n",
"\\end{array}\\right).\n",
"\\end{equation}\n",
"The vector $\\mathbf{r}$ is of length $(N-1)\\times(N-1)$ which made up of $N-1$ subvectors of the form $\\mathbf{r}_j=-h^2\\mathbf{f}_j-\\mathbf{bx}_{j}-\\mathbf{by}_j$, \n",
"where $\\mathbf{bx}_j $ is the vector of left and right boundary conditions \n",
"\\begin{equation}\\mathbf{bx}_j =\\left(\\begin{array}{c}\n",
"w_{0j}\\\\\n",
"0\\\\\n",
".\\\\\n",
".\\\\\n",
"0\\\\\n",
"w_{Nj}\n",
"\\end{array}\\right),\n",
"\\end{equation}\n",
"\n",
"for $j=1,..,N-1$, where $\\mathbf{by}_j$ is the vector of the lower boundary condition for $j=1$,\n",
"\n",
"\\begin{equation}\n",
"\\mathbf{by}_{1} =\\left(\\begin{array}{c}\n",
"w_{10}\\\\\n",
"w_{20}\\\\\n",
".\\\\\n",
".\\\\\n",
"w_{N-20}\\\\\n",
"w_{N-10}\\\\\n",
"\\end{array}\\right),\n",
"\\end{equation}\n",
"upper boundary condition for $j=N-1$\n",
"\n",
"\\begin{equation}\n",
"\\mathbf{by}_{N-1} =\\left(\\begin{array}{c}\n",
"w_{1N}\\\\\n",
"w_{2N}\\\\\n",
".\\\\\n",
".\\\\\n",
"w_{N-2N}\\\\\n",
"w_{N-1N}\\\\\n",
"\\end{array}\\right),\n",
"\\end{equation}\n",
"for $j=2,...,N-2$\n",
"\\begin{equation}\\mathbf{by}_j=0,\\end{equation}\n",
"and \n",
"\\begin{equation}\\mathbf{f}_j =-\\left(\\begin{array}{c}\n",
"0\\\\\n",
"0\\\\\n",
".\\\\\n",
".\\\\\n",
"0\\\\\n",
"0\\\\\n",
"\\end{array}\\right)\n",
"\\end{equation}\n",
"for $j=1,...,N-1$.\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "3Nq1t39uDlg5"
},
"source": [
"r=np.zeros(N2)\n",
"\n",
"# vector r \n",
"for i in range (0,N-1):\n",
" for j in range (0,N-1): \n",
" r[i+(N-1)*j]=-h*h*0 \n",
"# Boundary \n",
"b_bottom_top=np.zeros(N2)\n",
"for i in range (0,N-1):\n",
" b_bottom_top[i]=np.sin(2*np.pi*x[i+1]) #Bottom Boundary\n",
" b_bottom_top[i+(N-1)*(N-2)]=np.sin(2*np.pi*x[i+1])# Top Boundary\n",
" \n",
"b_left_right=np.zeros(N2)\n",
"for j in range (0,N-1):\n",
" b_left_right[(N-1)*j]=2*np.sin(2*np.pi*y[j+1]) # Left Boundary\n",
" b_left_right[N-2+(N-1)*j]=2*np.sin(2*np.pi*y[j+1])# Right Boundary\n",
" \n",
"b=b_left_right+b_bottom_top"
],
"execution_count": null,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "8xD-cC0BDlg5"
},
"source": [
"## Results\n",
"\n",
"To solve the system for $\\mathbf{w}$ invert the matrix $A$\n",
"\\begin{equation} A\\mathbf{w}=\\mathbf{r},\\end{equation}\n",
"such that\n",
"\\begin{equation} \\mathbf{w}=A^{-1}\\mathbf{r}.\\end{equation}\n",
"Lastly, as $\\mathbf{w}$ is in vector it has to be reshaped into grid form to plot.\n",
"\n",
"The figure below shows the numerical approximation of the homogeneous Equation."
]
},
{
"cell_type": "code",
"metadata": {
"scrolled": true,
"id": "ZRq1N7S1Dlg5",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 380
},
"outputId": "76a5147a-855c-4754-a139-6985c7d6ec39"
},
"source": [
"C=np.dot(Ainv,r-b)\n",
"w[1:N,1:N]=C.reshape((N-1,N-1))\n",
"\n",
"fig = plt.figure(figsize=(8,6))\n",
"ax = fig.add_subplot(111, projection='3d');\n",
"# Plot a basic wireframe.\n",
"ax.plot_wireframe(X, Y, w,color='r');\n",
"ax.set_xlabel('x');\n",
"ax.set_ylabel('y');\n",
"ax.set_zlabel('w');\n",
"plt.title(r'Numerical Approximation of the Poisson Equation',fontsize=24,y=1.08);\n",
"plt.show();"
],
"execution_count": null,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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""
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"# Consistency and Convergence\n",
"We now ask how well the grid function determined by the five point scheme approximates the exact solution of the Poisson problem.\n",
"## Consistency\n",
"\n",
"### Consitency (Definition)\n",
"Let \n",
"\\begin{equation}\\nabla^2_h(\\varphi)=-(\\varphi_{i-1j}+\\varphi_{ij-1}-4\\varphi_{ij}+\\varphi_{ij+1}+\\varphi_{i+1j})\\end{equation}\n",
"denote the finite difference approximation associated with the grid $\\Omega_h$ having the mesh size $h$, to a partial differential operator \n",
"\\begin{equation}\\nabla^2(\\varphi)=\\frac{\\partial^2 \\varphi}{\\partial x^2}+\\frac{\\partial^2 \\varphi}{\\partial y^2}\\end{equation}\n",
"defined on\n",
"a simply connected, open set $\\Omega \\subset R^2$. For a given function $\\varphi\\in C^{\\infty}(\\Omega)$,\n",
"the truncation error of $\\nabla^2_h$ is\n",
"\\begin{equation}\\tau_{h}(\\mathbf{x})=(\\nabla^2-\\nabla^2_h)\\varphi(\\mathbf{x}) \\end{equation}\n",
"The approximation $\\nabla^2_h$ is consistent with $\\nabla^2$ if\n",
"\\begin{equation} \\lim_{h\\rightarrow 0}\\tau_h(\\mathbf{x})=0,\\end{equation}\n",
"for all $\\mathbf{x} \\in D$ and all $\\varphi \\in C^{\\infty}(\\Omega)$. The approximation is consistent to order $p$ if $\\tau_h(\\mathbf{x})=O(h^p)$.\n",
"\n",
"_In other words a method is consistent with the differential equation it is approximating._\n",
"\n",
"## Proof of Consistency\n",
"The five-point difference analog $\\nabla^2_h$ is consistent to order 2 with $\\nabla^2$.\n",
"\n",
"__Proof__\n",
"\n",
"Pick $\\varphi \\in C^{\\infty}(D)$, and let $(x,y) \\in \\Omega$ be a point such that $(x\\pm h, y),(x,y \\pm h) \\in \\Omega\\bigcup \\partial\\Omega$. By the Taylor Theorem\n",
"\\begin{eqnarray*}\n",
"\\varphi(x\\pm h,y)&=&\\varphi(x,y) \\pm h \\frac{\\partial \\varphi}{\\partial x}(x,y)+\\frac{h^2}{2!}\\frac{\\partial^2 \\varphi}{\\partial x^2}(x,y) \\pm\\frac{h^3}{3!}\\frac{\\partial^3 \\varphi}{\\partial x^3}(x,y)+\\frac{h^4}{4!}\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{\\pm},y)\n",
"\\end{eqnarray*}\n",
"where $\\zeta^{\\pm} \\in (x-h,x+h)$. Adding this pair of equation together and rearranging , we get\n",
"\\begin{equation}\\frac{1}{h^2}[\\varphi(x+h,y)-2\\varphi(x,y)+\\varphi(x-h,y) ] -\\frac{\\partial^2 \\varphi}{\\partial x^2}(x,y)=\\frac{h^2}{4!}\\left[\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{+},y)+\n",
"\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{-},y)\n",
" \\right]\n",
"\\end{equation}\n",
"By the intermediate value theorem\n",
"\\begin{equation}\\left[\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{+},y)+\n",
"\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta^{-},y)\n",
" \\right]\n",
"=2\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta,y),\\end{equation}\n",
"for some $\\zeta \\in (x-h,x+h)$. Therefore,\n",
"\\begin{equation}\\delta_x^2(x,y)\n",
"=\\frac{\\partial^2 \\varphi}{\\partial x^2}(x,y)+\\frac{h^2}{2!}\\frac{\\partial^4 \\varphi}{\\partial x^4}(\\zeta,y)\\end{equation}\n",
"Similar reasoning shows that\n",
"\\begin{equation}\\delta_y^2(x,y)\n",
"=\\frac{\\partial^2 \\varphi}{\\partial y^2}(x,y)+\\frac{h^2}{2!}\\frac{\\partial^4 \\varphi}{\\partial y^4}(x,\\eta)\n",
"\\end{equation}\n",
"for some $\\eta \\in (y-h,y+h)$. We conclude that $\\tau_h(x,y)=(\\nabla-\\nabla_h)\\varphi(x,y)=O(h^2).$\n",
"\n"
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"## Convergence\n",
"### Definition\n",
"Let $\\nabla^2_hw(\\mathbf{x}_j)=f(\\mathbf{x}_j)$ be a finite difference approximation, defined on a grid mesh size $h$, to a PDE $\\nabla^2U(\\mathbf{x})=f(\\mathbf{x})$ on a simply connected set $D \\subset R^n$. Assume that $w(x,y)=U(x,y)$ at all points $(x,y)$ on the boundary $\\partial\\Omega$. The finite difference scheme converges (or is convergent) if\n",
"\\begin{equation} \\max_j|U(\\mathbf{x}_j)-w(\\mathbf{x}_j)| \\rightarrow 0 \\mbox{ as } h \\rightarrow 0.\\end{equation}\n"
]
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"### Theorem (DISCRETE MAXIMUM PRINCIPLE).\n",
"If $\\nabla^2_hV_{ij}\\geq 0$ for all points $(x_i,y_j) \\in \\Omega_h$, then\n",
"\\begin{equation} \\max_{(x_i,y_j)\\in\\Omega_h}V_{ij}\\leq \\max_{(x_i,y_j)\\in\\partial\\Omega_h}V_{ij},\\end{equation}\n",
"If $\\nabla^2_hV_{ij}\\leq 0$ for all points $(x_i,y_j) \\in \\Omega_h$, then\n",
"\\begin{equation} \\min_{(x_i,y_j)\\in\\Omega_h}V_{ij}\\geq \\min_{(x_i,y_j)\\in\\partial\\Omega_h}V_{ij}.\\end{equation}"
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"### Propositions\n",
"1. The zero grid function for which $U_{ij}=0$ for all $(x_i,y_j) \\in \\Omega_h \\bigcup \\partial\\Omega_h$\n",
"is the only solution to the finite difference problem\n",
"\\begin{equation}\\nabla_h^2U_{ij}=0 \\mbox{ for }(x_i,y_j)\\in\\Omega_h,\\end{equation}\n",
"\\begin{equation}U_{ij}=0 \\mbox{ for }(x_i,y_j)\\in\\partial\\Omega_h.\\end{equation}\n",
"\n",
"2. For prescribed grid functions $f_{ij}$ and $g_{ij}$, there exists a unique solution to the problem\n",
"\\begin{equation}\\nabla_h^2U_{ij}=f_{ij} \\mbox{ for }(x_i,y_j)\\in\\Omega_h,\\end{equation}\n",
"\\begin{equation}U_{ij}=g_{ij} \\mbox{ for }(x_i,y_j)\\in\\partial\\Omega_h.\\end{equation}\n"
]
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"### Definition\n",
"For any grid function $V:\\Omega_h\\bigcup\\partial\\Omega_h \\rightarrow R$,\n",
"\\begin{equation}||V||_{\\Omega} =\\max_{(x_i,y_j)\\in\\Omega_h}|V_{ij}|, \\end{equation}\n",
"\\begin{equation}||V||_{\\partial\\Omega} =\\max_{(x_i,y_j)\\in\\partial\\Omega_h}|V_{ij}|. \\end{equation}\n",
"\n",
"### Lemma\n",
"If the grid function $V:\\Omega_h\\bigcup\\partial\\Omega_h\\rightarrow R$ satisfies the boundary condition $V_{ij}=0$ for $(x_i,y_j)\\in \\partial\\Omega_h$, then\n",
"\\begin{equation}||V_||_{\\Omega}\\leq \\frac{1}{8}||\\nabla_h^2V||_{\\Omega}. \\end{equation}"
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"Given these Lemmas and Propositions, we can now prove that the solution to the five point scheme $\\nabla^2_h$ is convergent to the exact solution of the Poisson Equation $\\nabla^2$.\n",
"### Convergence Theorem\n",
"Let $U$ be a solution to the Poisson equation and let $w$ be the grid function\n",
"that satisfies the discrete analog\n",
"\\begin{equation}-\\nabla_h^2w_{ij}=f_{ij} \\ \\ \\mbox{ for } (x_i,y_j)\\in\\Omega_h, \\end{equation}\n",
"\\begin{equation}w_{ij}=g_{ij} \\ \\ \\mbox{ for } (x_i,y_j)\\in\\partial\\Omega_h. \\end{equation}\n",
"Then there exists a positive constant $K$ such that\n",
"\\begin{equation}||U-w||_{\\Omega}\\leq KMh^2, \\end{equation}\n",
"where\n",
"\\begin{equation} M=\\left\\{\n",
"\\left|\\left|\\frac{\\partial^4 U}{\\partial x^4} \\right|\\right|_{\\infty},\n",
"\\left|\\left|\\frac{\\partial^4 U}{\\partial y^4} \\right|\\right|_{\\infty}\n",
" \\right\\}\\end{equation}\n",
" \n",
" __Proof__\n",
" \n",
" The statement of the theorem assumes that $U\\in C^4(\\bar{\\Omega})$. This assumption\n",
"holds if $f$ and $g$ are smooth enough.\n",
"\\begin{proof}\n",
"Following from the proof of the Proposition we have\n",
"\\begin{equation} (\\nabla_h^2-\\nabla^2)U_{ij}=\\frac{h^2}{12}\\left[ \\frac{\\partial^4 U}{\\partial x^4}(\\zeta_i,y_j)+\\frac{\\partial^4 U}{\\partial y^4}(x_i,\\eta_j) \\right],\\end{equation}\n",
"for some $\\zeta \\in (x_{i-1},x_{i+1})$ and $\\eta_j\\in(y_{j-1},y_{j+1})$. Therefore,\n",
"\\begin{equation} -\\nabla_h^2U_{ij}=f_{ij}-\\frac{h^2}{12}\\left[ \\frac{\\partial^4 U}{\\partial x^4}(\\zeta_i,y_j)+\\frac{\\partial^4 U}{\\partial y^4}(x_i,\\eta_j) \\right].\\end{equation}\n",
"If we subtract from this the identity equation $-\\nabla_h^2w_{ij}=f_{ij}$ and note\n",
"that $U-w$ vanishes on $\\partial\\Omega_h$, we find that\n",
"\\begin{equation} \\nabla_h^2(U_{ij}-w_{ij})=\\frac{h^2}{12}\\left[ \\frac{\\partial^4 U}{\\partial x^4}(\\zeta_i,y_j)+\\frac{\\partial^4 U}{\\partial y^4}(x_i,\\eta_j) \\right].\\end{equation}\n",
"It follows that\n",
"\n",
"\\begin{equation} ||U-w||_{\\Omega}\\leq\\frac{1}{8}||\\nabla_h^2(U-w)||_{\\Omega}\\leq KMh^2.\\end{equation}"
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}
]
}