{
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"metadata": {
"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": "3.7.9"
},
"colab": {
"name": "802_Heat Equation- BTCS.ipynb",
"provenance": [],
"include_colab_link": true
}
},
"cells": [
{
"cell_type": "markdown",
"metadata": {
"id": "view-in-github",
"colab_type": "text"
},
"source": [
"
"
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "ZEh-LSv_vsxt"
},
"source": [
"# The Implicit Backward Time Centered Space (BTCS) Difference Equation for the Heat 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",
"This notebook will implement the implicit Backward Time Centered Space (FTCS) Difference method for the Heat Equation.\n",
"## The Heat Equation\n",
"The Heat Equation is the first order in time ($t$) and second order in space ($x$) Partial Differential Equation: \n",
"\\begin{equation} \\frac{\\partial u}{\\partial t} = \\frac{\\partial^2 u}{\\partial x^2},\\end{equation}\n",
"the equation describes heat transfer on a domain\n",
"\\begin{equation} \\Omega = \\{ t \\geq, 0\\leq x \\leq 1\\}. \\end{equation}\n",
"with an initial condition at time $t=0$ for all $x$ and boundary condition on the left ($x=0$) and right side ($x=1$).\n",
"\n",
"## Backward Time Centered Space (BTCS) Difference method\n",
"This notebook will illustrate the Backward Time Centered Space (BTCS) Difference method for the Heat Equation with the __initial conditions__ \n",
"\\begin{equation} u(x,0)=2x, \\ \\ 0 \\leq x \\leq \\frac{1}{2}, \\end{equation}\n",
"\\begin{equation}u(x,0)=2(1-x), \\ \\ \\frac{1}{2} \\leq x \\leq 1, \\end{equation}\n",
"and __boundary condition__\n",
"\\begin{equation} u(0,t)=0, u(1,t)=0. \\end{equation}\n"
]
},
{
"cell_type": "code",
"metadata": {
"id": "IxC0J02Mvsxv"
},
"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\")"
],
"execution_count": 1,
"outputs": []
},
{
"cell_type": "markdown",
"metadata": {
"id": "CfCSpPH0vsx2"
},
"source": [
"## Discete Grid\n",
"The region $\\Omega$ is discretised into a uniform mesh $\\Omega_h$. In the space $x$ direction 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 into $N_t$ steps in the time $t$ direction giving a stepsize of \n",
"\\begin{equation}k=\\frac{1-0}{N_t}\\end{equation}\n",
"resulting in \n",
"\\begin{equation}t[i]=0+ik, \\ \\ \\ k=0,...,K.\\end{equation}\n",
"The Figure below shows the discrete grid points for $N=10$ and $Nt=100$, the known boundary conditions (green), initial conditions (blue) and the unknown values (red) of the Heat Equation."
]
},
{
"cell_type": "code",
"metadata": {
"id": "n-22KZbuvsx3",
"outputId": "5a59be6a-492b-43e2-d46b-70ebfeea033e",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 324
}
},
"source": [
"N=10\n",
"Nt=100\n",
"h=1/N\n",
"k=1/Nt\n",
"r=k/(h*h)\n",
"time_steps=15\n",
"time=np.arange(0,(time_steps+.5)*k,k)\n",
"x=np.arange(0,1.0001,h)\n",
"X, Y = np.meshgrid(x, time)\n",
"fig = plt.figure()\n",
"plt.plot(X,Y,'ro');\n",
"plt.plot(x,0*x,'bo',label='Initial Condition');\n",
"plt.plot(np.ones(time_steps+1),time,'go',label='Boundary Condition');\n",
"plt.plot(x,0*x,'bo');\n",
"plt.plot(0*time,time,'go');\n",
"plt.xlim((-0.02,1.02))\n",
"plt.xlabel('x')\n",
"plt.ylabel('time (ms)')\n",
"plt.legend(loc='center left', bbox_to_anchor=(1, 0.5))\n",
"plt.title(r'Discrete Grid $\\Omega_h,$ h= %s, k=%s'%(h,k),fontsize=24,y=1.08)\n",
"plt.show();"
],
"execution_count": 2,
"outputs": [
{
"output_type": "display_data",
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "P56aUMtTvsx8"
},
"source": [
"## Discrete Initial and Boundary Conditions\n",
"\n",
"The discrete initial conditions are \n",
"\\begin{equation} w[i,0]=2x[i], \\ \\ 0 \\leq x[i] \\leq \\frac{1}{2} \\end{equation}\n",
"\\begin{equation} w[i,0]=2(1-x[i]), \\ \\ \\frac{1}{2} \\leq x[i] \\leq 1 \\end{equation}\n",
"and the discete boundary conditions are \n",
"\\begin{equation} w[0,j]=0, w[10,j]=0,\\end{equation}\n",
"where $w[i,j]$ is the numerical approximation of $U(x[i],t[j])$.\n",
"\n",
"The Figure below plots values of $w[i,0]$ for the inital (blue) and boundary (red) conditions for $t[0]=0.$"
]
},
{
"cell_type": "code",
"metadata": {
"id": "JoQfiuyNvsx9",
"outputId": "1b737fee-15ca-4359-e6c6-790eb7b8c175",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 304
}
},
"source": [
"w=np.zeros((N+1,time_steps+1))\n",
"b=np.zeros(N-1)\n",
"# Initial Condition\n",
"for i in range (1,N):\n",
" w[i,0]=2*x[i]\n",
" if x[i]>0.5:\n",
" w[i,0]=2*(1-x[i])\n",
" \n",
"\n",
"# Boundary Condition\n",
"for k in range (0,time_steps):\n",
" w[0,k]=0\n",
" w[N,k]=0\n",
"\n",
"fig = plt.figure(figsize=(8,4))\n",
"plt.plot(x,w[:,0],'o:',label='Initial Condition')\n",
"plt.plot(x[[0,N]],w[[0,N],0],'go',label='Boundary Condition t[0]=0')\n",
"#plt.plot(x[N],w[N,0],'go')\n",
"plt.xlim([-0.1,1.1])\n",
"plt.ylim([-0.1,1.1])\n",
"plt.title('Intitial and Boundary Condition',fontsize=24)\n",
"plt.xlabel('x')\n",
"plt.ylabel('w')\n",
"plt.legend(loc='best')\n",
"plt.show()"
],
"execution_count": 3,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
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"## The Implicit Backward Time Centered Space (BTCS) Difference Equation\n",
"\n",
"\n",
"\n",
"The implicit Backward Time Centered Space (BTCS) difference equation of the Heat Equation is derived by discretising \n",
"\\begin{equation} \\frac{\\partial u_{ij+1}}{\\partial t} = \\frac{\\partial^2 u_{ij+1}}{\\partial x^2},\\end{equation}\n",
"around $(x_i,t_{j+1})$ giving the difference equation\n",
"\\begin{equation}\n",
"\\frac{w_{ij+1}-w_{ij}}{k}=\\frac{w_{i+1j+1}-2w_{ij+1}+w_{i-1j+1}}{h^2}\n",
"\\end{equation}\n",
"Rearranging the equation we get\n",
"\\begin{equation}\n",
"-rw_{i-1j+1}+(1+2r)w_{ij+1}-rw_{i+1j+1}=w_{ij}\n",
"\\end{equation}\n",
"for $i=1,...9$ where $r=\\frac{k}{h^2}$.\n",
"\n",
"This gives the formula for the unknown term $w_{ij+1}$ at the $(ij+1)$ mesh points\n",
"in terms of $x[i]$ along the jth time row.\n",
"\n",
"Hence we can calculate the unknown pivotal values of $w$ along the first row of $j=1$ in terms of the known boundary conditions.\n",
"\n",
"This can be written in matrix form \n",
"\\begin{equation} A\\mathbf{w}_{j+1}=\\mathbf{w}_{j} +\\mathbf{b}_{j+1} \\end{equation}\n",
"for which $A$ is a $9\\times9$ matrix:\n",
"\\begin{equation}\n",
"\\left(\\begin{array}{cccc cccc}\n",
"1+2r&-r& 0&0&0 &0&0&0\\\\\n",
"-r&1+2r&-r&0&0&0 &0&0&0\\\\\n",
"0&-r&1+2r &-r&0&0& 0&0&0\\\\\n",
"0&0&-r&1+2r &-r&0&0& 0&0\\\\\n",
"0&0&0&-r&1+2r &-r&0&0& 0\\\\\n",
"0&0&0&0&-r&1+2r &-r&0&0\\\\\n",
"0&0&0&0&0&-r&1+2r &-r&0\\\\\n",
"0&0&0&0&0&0&-r&1+2r&-r\\\\\n",
"0&0&0&0&0&0&0&-r&1+2r\\\\\n",
"\\end{array}\\right)\n",
"\\left(\\begin{array}{c}\n",
"w_{1j+1}\\\\\n",
"w_{2j+1}\\\\\n",
"w_{3j+1}\\\\\n",
"w_{4j+1}\\\\\n",
"w_{5j+1}\\\\\n",
"w_{6j+1}\\\\\n",
"w_{7j+1}\\\\\n",
"w_{8j+1}\\\\\n",
"w_{9j+1}\\\\\n",
"\\end{array}\\right)=\n",
"\\left(\\begin{array}{c}\n",
"w_{1j}\\\\\n",
"w_{2j}\\\\\n",
"w_{3j}\\\\\n",
"w_{4j}\\\\\n",
"w_{5j}\\\\\n",
"w_{6j}\\\\\n",
"w_{7j}\\\\\n",
"w_{8j}\\\\\n",
"w_{9j}\\\\\n",
"\\end{array}\\right)+\n",
"\\left(\\begin{array}{c}\n",
"rw_{0j+1}\\\\\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"0\\\\\n",
"rw_{10j+1}\\\\\n",
"\\end{array}\\right).\n",
"\\end{equation}\n",
"It is assumed that the boundary values $w_{0j+1}$ and $w_{10j+1}$ are known for $j=1,2,...$, and $w_{i0}$ for $i=0,...,10$ is the initial condition.\n",
"The Figure below shows the values of the $9\\times 9$ matrix in colour plot form for $r=\\frac{k}{h^2}$."
]
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"source": [
"A=np.zeros((N-1,N-1))\n",
"for i in range (0,N-1):\n",
" A[i,i]=1+2*r\n",
"\n",
"for i in range (0,N-2): \n",
" A[i+1,i]=-r\n",
" A[i,i+1]=-r\n",
" \n",
"Ainv=np.linalg.inv(A) \n",
"fig = plt.figure(figsize=(12,4));\n",
"plt.subplot(121)\n",
"plt.imshow(A,interpolation='none');\n",
"plt.xticks(np.arange(N-1), np.arange(1,N-0.9,1));\n",
"plt.yticks(np.arange(N-1), np.arange(1,N-0.9,1));\n",
"clb=plt.colorbar();\n",
"clb.set_label('Matrix elements values');\n",
"#clb.set_clim((-1,1));\n",
"plt.title('Matrix A r=%s'%(np.round(r,3)),fontsize=24)\n",
"\n",
"plt.subplot(122)\n",
"plt.imshow(Ainv,interpolation='none');\n",
"plt.xticks(np.arange(N-1), np.arange(1,N-0.9,1));\n",
"plt.yticks(np.arange(N-1), np.arange(1,N-0.9,1));\n",
"clb=plt.colorbar();\n",
"clb.set_label('Matrix elements values');\n",
"#clb.set_clim((-1,1));\n",
"plt.title(r'Matrix $A^{-1}$ r=%s'%(np.round(r,3)),fontsize=24)\n",
"\n",
"fig.tight_layout()\n",
"plt.show();"
],
"execution_count": 4,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
}
}
]
},
{
"cell_type": "markdown",
"metadata": {
"id": "mJKjl_jNvsyC"
},
"source": [
"## Results\n",
"To numerically approximate the solution at $t[1]$ the matrix equation becomes \n",
"\n",
"\n",
"\\begin{equation} \\mathbf{w}_{1}=A^{-1}(\\mathbf{w}_{0} +\\mathbf{b}_{1}) \\end{equation}\n",
"where all the right hand side is known. \n",
"To approximate solution at time $t[2]$ we use the matrix equation\n",
"\\begin{equation} \\mathbf{w}_{2}=A^{-1}(\\mathbf{w}_{1} +\\mathbf{b}_{2}).\n",
"\\end{equation}\n",
"Each set of numerical solutions $w[i,j]$ for all $i$ at the previous time step is used to approximate the solution $w[i,j+1]$. \n",
"The Figure below shows the numerical approximation $w[i,j]$ of the Heat Equation using the FTCS method at $x[i]$ for $i=0,...,10$ and time steps $t[j]$ for $j=1,...,15$. The left plot shows the numerical approximation $w[i,j]$ as a function of $x[i]$ with each color representing the different time steps $t[j]$. The right plot shows the numerical approximation $w[i,j]$ as colour plot as a function of $x[i]$, on the $x[i]$ axis and time $t[j]$ on the $y$ axis. \n",
"The solution is stable for $r>\\frac{1}{2}$ unlike in the explicit method."
]
},
{
"cell_type": "code",
"metadata": {
"id": "H_6PLzn7vsyD",
"outputId": "7f42d345-c079-4f9d-ae2f-a2685fa11dbc",
"colab": {
"base_uri": "https://localhost:8080/",
"height": 487
}
},
"source": [
"fig = plt.figure(figsize=(12,6))\n",
"\n",
"plt.subplot(121)\n",
"for j in range (1,time_steps+1):\n",
" b[0]=r*w[0,j]\n",
" b[N-2]=r*w[N,j]\n",
" w[1:(N),j]=np.dot(Ainv,w[1:(N),j-1]+b)\n",
" plt.plot(x,w[:,j],'o:',label='t[%s]=%s'%(j,time[j]))\n",
"plt.xlabel('x')\n",
"plt.ylabel('w')\n",
"#plt.legend(loc='bottom', bbox_to_anchor=(0.5, -0.1))\n",
"plt.legend(bbox_to_anchor=(-.4, 1), loc=2, borderaxespad=0.)\n",
"\n",
"plt.subplot(122)\n",
"plt.imshow(w.transpose())\n",
"plt.xticks(np.arange(len(x)), x)\n",
"plt.yticks(np.arange(len(time)), time)\n",
"plt.xlabel('x')\n",
"plt.ylabel('time')\n",
"clb=plt.colorbar()\n",
"clb.set_label('Temperature (w)')\n",
"plt.suptitle('Numerical Solution of the Heat Equation r=%s'%(np.round(r,3)),fontsize=24,y=1.08)\n",
"fig.tight_layout()\n",
"plt.show()"
],
"execution_count": 5,
"outputs": [
{
"output_type": "display_data",
"data": {
"image/png": 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\n",
"text/plain": [
""
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"source": [
"## Local Trunction Error\n",
"The local truncation error of the classical implicit difference given by\n",
"\\begin{equation}\n",
"F_{ij+1}(w)=\\frac{w_{ij+1}-w_{ij}}{k}-\\frac{w_{i+1j+1}-2w_{ij+1}+w_{i-1j+1}}{h^2}=0,\n",
"\\end{equation} \n",
"of the heat equation\n",
"\\begin{equation}\n",
"\\frac{\\partial U}{\\partial t} - \\frac{\\partial^2 U}{\\partial x^2}=0,\n",
"\\end{equation}\n",
"is calculated by substituting the exact solution into the difference scheme give the truncation error:\n",
"\\begin{equation}\n",
"T_{ij+1}=F_{ij+1}(U)=\\frac{U_{ij+1}-U_{ij}}{k}-\\frac{U_{i+1j+1}-2U_{ij+1}+U_{i-1j+1}}{h^2}.\n",
"\\end{equation} \n",
"By Taylors expansions we have\n",
"\\begin{eqnarray*}\n",
"U_{i+1j}&=&U((i+1)h,(j+1)k)=U(x_i+h,t_{j+1})\\\\\n",
"&=&U_{ij+1}+h\\left(\\frac{\\partial U}{\\partial x} \\right)_{ij+1}+\\frac{h^2}{2}\\left(\\frac{\\partial^2 U}{\\partial x^2} \\right)_{ij+1}+\\frac{h^3}{6}\\left(\\frac{\\partial^3 U}{\\partial x^3} \\right)_{ij+1} +...\\\\\n",
"U_{i-1j}&=&U((i-1)h,(j+1)k)=U(x_i-h,t_{j+1})\\\\\n",
"&=&U_{ij+1}-h\\left(\\frac{\\partial U}{\\partial x} \\right)_{ij+1}+\\frac{h^2}{2}\\left(\\frac{\\partial^2 U}{\\partial x^2} \\right)_{ij+1}-\\frac{h^3}{6}\\left(\\frac{\\partial^3 U}{\\partial x^3} \\right)_{ij+1} +...\\\\\n",
"U_{ij}&=&U(ih,(j)k)=U(x_i,t_j)\\\\\n",
"&=&U_{ij+1}-k\\left(\\frac{\\partial U}{\\partial t} \\right)_{ij+1}+\\frac{k^2}{2}\\left(\\frac{\\partial^2 U}{\\partial t^2} \\right)_{ij+1}-\\frac{k^3}{6}\\left(\\frac{\\partial^3 U}{\\partial t^3} \\right)_{ij+1} +...\n",
"\\end{eqnarray*}\n",
"\n",
"substituting these into the expression for $T_{ij+1}$ gives\n",
"\n",
"\\begin{eqnarray*}\n",
"T_{ij+1}&=&\\left(\\frac{\\partial U}{\\partial t} - \\frac{\\partial^2 U}{\\partial x^2} \\right)_{ij+1}+\\frac{k}{2}\\left(\\frac{\\partial^2 U}{\\partial t^2} \\right)_{ij+1}\n",
"-\\frac{h^2}{12}\\left(\\frac{\\partial^4 U}{\\partial x^4} \\right)_{ij+1}\\\\\n",
"& &\t+\\frac{k^2}{6}\\left(\\frac{\\partial^3 U}{\\partial t^3} \\right)_{ij+1}\n",
"-\\frac{h^4}{360}\\left(\\frac{\\partial^6 U}{\\partial x^6} \\right)_{ij+1}+ \\cdots .\n",
"\\end{eqnarray*}\n",
"As $U$ is the solution to the differential equation so\n",
"\\begin{equation} \\left(\\frac{\\partial U}{\\partial t} - \\frac{\\partial^2 U}{\\partial x^2} \\right)_{ij+1}=0,\\end{equation} \n",
"\n",
"the principal part of the local truncation error is \n",
"\n",
"\\begin{equation}\n",
"\\frac{k}{2}\\left(\\frac{\\partial^2 U}{\\partial t^2} \\right)_{ij+1}-\\frac{h^2}{12}\\left(\\frac{\\partial^4 U}{\\partial x^4} \\right)_{ij+1}.\n",
"\\end{equation} \n",
"\n",
"\n",
"\n",
"Hence the truncation error is\n",
"\\begin{equation} \n",
"T_{ij}=O(k)+O(h^2).\n",
"\\end{equation} "
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"## Stability Analysis \n",
"\n",
"To investigating the stability of the fully implicit BTCS difference method of the Heat Equation, we will use the von Neumann method.\n",
"The difference equation is:\n",
"\\begin{equation}\\frac{1}{k}(w_{pq+1}-w_{pq})=\\frac{1}{h_x^2}(w_{p-1q+1}-2w_{pq+1}+w_{p+1q+1}),\\end{equation}\n",
"approximating \n",
"\\begin{equation}\\frac{\\partial U}{\\partial t}=\\frac{\\partial^2 U}{\\partial x^2}\\end{equation}\n",
"\n",
"at $(ph,k(q+1))$. Substituting $w_{pq}=e^{i\\beta x}\\xi^{q}$ into the difference equation gives: \n",
"\\begin{equation}e^{i\\beta ph}\\xi^{q+1}-e^{i\\beta ph}\\xi^{q}=r\\{e^{i\\beta (p-1)h}\\xi^{q+1}-2e^{i\\beta ph}\\xi^{q+1}+e^{i\\beta (p+1)h}\\xi^{q+1} \\}\n",
"\\end{equation}\n",
"\n",
"where $r=\\frac{k}{h_x^2}$. Divide across by $e^{i\\beta (p)h}\\xi^{q}$ leads to\n",
"\n",
"\\begin{equation} \\xi-1=r \\xi (e^{i\\beta (-1)h} -2+e^{i\\beta h}), \\end{equation}\n",
"\n",
"\\begin{equation}\\xi-\\xi r (2\\cos(\\beta h)-2)= 1,\\end{equation}\n",
"\n",
"\\begin{equation}\\xi(1+4r\\sin^2(\\beta\\frac{h}{2})) =1.\\end{equation}\n",
"Hence \n",
"\\begin{equation}\\xi=\\frac{1}{(1+4r\\sin^2(\\beta\\frac{h}{2}))} \\leq 1\\end{equation}\n",
"therefore the equation is unconditionally stable as $0 < \\xi \\leq 1$ for all $r$ and all $\\beta$ ."
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"## References\n",
"[1] G D Smith Numerical Solution of Partial Differential Equations: Finite Difference Method Oxford 1992\n",
"\n",
"[2] Butler, J. (2019). John S Butler Numerical Methods for Differential Equations. [online] Maths.dit.ie. Available at: http://www.maths.dit.ie/~johnbutler/Teaching_NumericalMethods.html [Accessed 14 Mar. 2019].\n",
"\n",
"[3] Wikipedia contributors. (2019, February 22). Heat equation. In Wikipedia, The Free Encyclopedia. Available at: https://en.wikipedia.org/w/index.php?title=Heat_equation&oldid=884580138 [Accessed 14 Mar. 2019].\n",
"\n",
"\n"
]
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