{ "nbformat": 4, "nbformat_minor": 0, "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": "1004_Burger Equation.ipynb", "provenance": [], "include_colab_link": true } }, "cells": [ { "cell_type": "markdown", "metadata": { "id": "view-in-github", "colab_type": "text" }, "source": [ "\"Open" ] }, { "cell_type": "markdown", "metadata": { "id": "iEq4oJCtDpqu" }, "source": [ "# Burger 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 Lax-Freidrich numerical method on the the Burger Equation.\n", "## The Burger Differential Equation\n", "Consider the one-dimensional non-linear Burger Equation:\n", "\\begin{equation} \\frac{\\partial u}{\\partial t} +u\\frac{\\partial u}{\\partial x}=0,\\end{equation}\n", "with the initial conditions\n", "\\begin{equation} u(x,0)=1-\\cos(x), \\ \\ 0 \\leq x \\leq 2\\pi. \\end{equation}\n", "and wrap around boundary conditions.\n", "\n", "This notebook will implement the Lax-Friedrich method to appoximate the solution of the Burger Equation.\n", "The Lax-Fredrich method was designed by Peter Lax (https://en.wikipedia.org/wiki/Peter_Lax) and Kurt Otto Friedrichs (https://en.wikipedia.org/wiki/Kurt_Otto_Friedrichs).\n" ] }, { "cell_type": "code", "metadata": { "id": "vSXHp7t7Dpqy" }, "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": "WEitQFCwDpqz" }, "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": "1VcBEOoRDpqz", "outputId": "d0fbf6d2-e037-4acc-fe44-be1ac803ff5d", "colab": { "base_uri": "https://localhost:8080/", "height": 324 } }, "source": [ "N=10\n", "Nt=10\n", "h=2*np.pi/N\n", "k=1/Nt\n", "r=k/(h*h)\n", "time_steps=10\n", "time=np.arange(0,(time_steps+.5)*k,k)\n", "x=np.arange(0,2*np.pi+h/2,h)\n", "\n", "\n", "X, Y = np.meshgrid(x, time)\n", "\n", "fig = plt.figure()\n", "plt.plot(X,Y,'ro');\n", "plt.plot(x,0*x,'bo',label='Initial Condition');\n", "plt.xlim((-h,2*np.pi+h))\n", "plt.ylim((-k,max(time)+k))\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 $\\Omega_h$ ',fontsize=24,y=1.08)\n", "plt.show();" ], "execution_count": 2, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "id": "9wV3-ueRDpq0" }, "source": [ "## Initial Conditions\n", "\n", "The discrete initial conditions is,\n", "\\begin{equation} w[0,j]=1-\\cos(x[j]), \\ \\ 0 \\leq x[j] \\leq \\pi, \\end{equation}\n", "The Figure below plots values of $w[0,j]$ for the inital (blue) conditions for $t[0]=0.$" ] }, { "cell_type": "code", "metadata": { "id": "dxcTEFs7Dpq1", "outputId": "7c58e516-9d43-47bf-a203-443f5ec2d80a", "colab": { "base_uri": "https://localhost:8080/", "height": 304 } }, "source": [ "w=np.zeros((time_steps+1,N+1))\n", "b=np.zeros(N-1)\n", "# Initial Condition\n", "for j in range (0,N+1):\n", " w[0,j]=1-np.cos(x[j])\n", " \n", "\n", "fig = plt.figure(figsize=(8,4))\n", "plt.plot(x,w[0,:],'o:',label='Initial Condition')\n", "plt.xlim([-0.1,max(x)+h])\n", "plt.title('Intitial Condition',fontsize=24)\n", "plt.xlabel('x')\n", "plt.ylabel('w')\n", "plt.legend(loc='best')\n", "plt.show()\n", "ipos = np.zeros(N+1)\n", "ineg = np.zeros(N+1)\n", "for i in range(0,N+1):\n", " ipos[i] = i+1\n", " ineg[i] = i-1\n", "\n", "ipos[N] = 0\n", "ineg[0] = N\n" ], "execution_count": 3, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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Hfm/9okWLuO+++1i2bBlr1qzhzTff3Gv9tGnTyMjIYPHixTz++ON7rUtPT2fmzJksXLiQuXPncsstt9Qn36YsXbqU8ePHN7luxowZLF68mPfff5+XXnqJqVOnsnHjxmZjLC8v55vf/Cb//Oc/WbBgAZs27fsF+IQTTuD888/n3nvvZfHixRxxxBH168rLy7nqqqt46qmnWLJkCdXV1TzwwAP163v37s3ChQu5/vrr+cUvfrH/J7IVolmDPxH4KnCamS0Ofs41s+vMrO7r1LPAGmA18AfgBgB3LwZ+CswPfu4KykSklZ7KX89d/1zG9j2VAHz5uIEc0++Q+vUXjs3hzVtP45NpX+DNW0+r7z0/oFdXHroyj6P7Rra9f+5qTv9/r7GrvKrjT0I61MadTSfs4j3t99pPmDCB3NxckpKSGDNmDGvXrm31vu7O7bffzqhRozjjjDMoLCxsc3P7G2+8wWWXXUZycjKHHXYYEydOZP78+c3GuGLFCoYMGcLQoUMxM6644ooDeryVK1cyZMgQjjrqKACuvPJK5s2bV7/+4osvBmD8+PEH9Jy0JGq3ybn7G0CL/fo98tXr282sexh4OAqhicSlgu2l3DFrKTefcRRjBmTxrVMO5+snDKZnty4HddyrTxrC6AE9OCQ9MoLWI29+Qt7gXozI6dEeYUsHe+pbn6//OzU5aa/l/lkZTXbAzAn6ZvTq1mWv7ftkph/w46elfdb/Izk5merq6lbv+/jjj1NUVMSCBQtITU1l8ODBLd4bPnz48Prm8Y6Ksa3qHrM9H09j0Yt0Yu5OcVBDz+rahXXbStkYfEBnde1Cn0MO/AO4sQG9unLR2FwAdldUc9/LHzH7/Q0HfVyJPVPPHrZP34yM1GSmnj2sQ+NITU2lqmrfVoOdO3fSp08fUlNTmTt3Lp9+2uxMqQCcdtppVFRUMH369PqyDz74gNdff52TTz6Zp556ipqaGoqKipg3bx4TJkxo9lhHH300a9eu5eOPPwbgiSeeaHK7zMxMSkpK9ikfNmwYa9euZfXq1QD85S9/YeLEiS3Gf7CU4EU6sav/nM91jy0AoHtaCi/fMpFzRvaL2uN1T0th3n+dyrcnHQnA0sKdXHj/m3xctDtqjykdp6m+GXdfPLLDBz+69tprGTVqVH0nuzqXX345+fn5jBw5kkcffZSjjz66xeOYGTNnzuSll17iiCOOYPjw4dx222307duXiy66iFGjRjF69GhOO+007rnnHvr27dvssdLT05k+fTpf+MIXGDduHH369GlyuylTpnDvvfcyduzY+i8Ddfv/6U9/4tJLL2XkyJEkJSXt1fkvGqylDgqdTV5enufn54cdhkjUlFfV8NzSjVwwOoekJOMfiwuprnEuHpcTymhlr39UxLTnVvDktZ8jMz2VzbvK6dWtC6nJqjvEiuXLl3PMMceEHYa0g6ZeSzNb4O55TW2vyWZEOpEXlm3me0+9z2GZ6ZxwZG8uGBPusLInD83m5KGfjT9x85OLqayp5Znr9z8wiYhElxK8SAyrqK7h1y99xLC+mVwwJodzR/TlsGs/x4QhvcIObR/uzjUnD6G8qrZ++fF31/HF0f3pkdH6KS5FpH0owYvEoPKqGtJTk+mSnMTrH22luta5YEwOKclJHH/4oWGH1yQz4/RjDqtfXrx+B3fMWkp6ajKXjM8NMTJxd00408m15XK6LpSJxJg/zFvDab94lfKqGsyMp6//PLef2/muoY4d2JNnv3syF4zpD8Ds9zdw+8wllFZG/5Yj+Ux6ejrbtm1rU4KQ2FA3H3x6+oHdFaMavEgMWLhuO0dkd6dHRiojcnoweUQ/KmtqSU9NJi0lef8HiFHH9v9sYJ31xaV8WLiz/jasXeVV9ffWS/Tk5uZSUFCAJuPq3NLT08nNPbCWMPWiFwnZJ1v3cOovXuUHk4/m+klH7H+HTqym1klOMiqqa5h4z6tcmpfLLWd17D3WIvGkpV70aqIXCcHzSzfxyJufADCkdzd+d/k4vvb5QSFHFX3JSZHrwLW1cPnxAznhiN5ApDY/d8UWNSOLtCM10YtEyaxFhdw7ZyUbdpTRPyuD/zzzKC4KOpu98OEmVm4u4WufH0xSknFuFAeniUUZXZL5zulD65efzi/grn8t47mbTq4fL7/x8zf17GEdPuCKSGemBC8SBXXTbtbNzFW4o4zv//19issqufqkw7nz/OF0T0shKUk9mwGu+NwghmR3q0/uNz+5iH8v2UhVTaRGXzdtKaAkL9JKaqIXiYJ756zcZ9pNBx58bQ0APTJS65urBbqkJHHqsMjQn+7Oc0s31Sf3OmVVNdw7Z2UY4Yl0SkrwIlGwoYkZuSAyt7q0zMyorK5tcl1zz6uI7EsJXiQK+gfTa7a2XPam50/k4CnBi0RBrEy72Vnp+RM5eFFL8Gb2sJltMbOlzayfamaLg5+lZlZjZr2CdWvNbEmwTje2S6dRXVPLTU8uYkCvrjEx7WZn1dy0pQN6ddWtdCKtFLWBbszsFGA38Ki7j9jPtl8EvufupwXLa4E8d996II+pgW4kbBt2lDFl+jt89/ShGn+9nc1fW8ylv3+bey4ZxX/kDQg7HJGYEMp0se4+z8wGt3Lzy4AnohWLSEfpn5XBC987hfTUzju8bKzKG9STuy8eWT+2vYi0LPRr8GbWFZgMPNOg2IEXzGyBmV27n/2vNbN8M8vXWMsSlsXrd/CrF1dRW+tK7lFiZlw2YSBpKcmUV9WoR73IfoSe4IEvAm+6e3GDspPcfRxwDvDtoLm/Se4+3d3z3D0vOzs72rGKNOn5pZt4ZmEBJeWaKa0jXP/YAr728HtU1TR9O52IxMZIdlNo1Dzv7oXB7y1mNhOYAMwLITaRVvnB5GFce8rh9Oiq2dE6wnUTj2BnWRWpybFQRxGJTaH+d5hZD2Ai8I8GZd3MLLPub+AsoMme+CJhcnceePVjNu4sw8zo1a1L2CEljOMPP5SzhvcFYOtuDR4k0pRo3ib3BPA2MMzMCszsajO7zsyua7DZRcAL7r6nQdlhwBtm9j7wHvBvd38+WnGKtFXB9jLun7uaGQsLww4lYS1ev4NT7pnL80s3hR2KSMzRfPAiB2F9cSk5WRmaNCYkFdU1/Ozfy/n2qUfS55D0sMMR6XCaD16kHRVsL+X5pRsBGNCrq5J7iNJSkvnJBSPoc0g67k5ppTo5itRRghc5QPfPXc1/Pf0BO0orww5FGrj1mSVc/Ug+1epZLwLERi96kU7lx+cP54rPDSKrqzrVxZIJQ3oxoFeGpuEVCSjBi7TSy8s3c+KRvUlPTWZ4/x5hhyONfKnB0MDVNbWk6BY6SXD6DxBphfXFpVz7lwXcP3d12KHIfqzeUsJZv5rHonXbww5FJFSqwYu0woBeXfnz1ycwflDPsEOR/Ti0Wxq9M9NISVL9RRKbErxIC0rKqyjYXsYx/Q7hpKG9ww5HWqFnty787Vufr192d8x0XV4Sj77iirTgZ88u5z9+/7Z6zHdSD772MbfPXKI55CUhqQYv0oLvnzmMiUdlq8d8J7Wnoppd5dVU1zqpyarFS2JRghdpwsdFuzm8dzeyM9OYPKJf2OFIG918xlGYoSZ6SUhqohdpZH1xKef95g1++4p6zHd2SUmGmbF1dwXf+ks+64tLww5JpMMowYs0ktszg6lnD2PKcQPCDkXaya6yKhat28FHW0rCDkWkw2iyGZFAdU0tu8qrNe1rnCqvqiE9NTnsMETalSabEWmFe+as5Iu/fYOdpVVhhyJRUJfc567Ywh/f+CTkaESiT53sRALnj+5PZloKPbqmhh2KRNGsxYWsKdrDVz83iC4pquNI/FKCl4S3p6KabmkpjMjpwYgcjTEf76ZdPApAyV3iXtTe4Wb2sJltMbOlzayfZGY7zWxx8POjBusmm9lKM1ttZrdGK0aRLSXlnPnL13j83U/DDkU6SEaXZDK6JFNZXcuvXlzFrnJdkpH4FM2vsI8Ak/ezzevuPib4uQvAzJKB+4FzgGOBy8zs2CjGKQksMy2VE4/szbiBGmM+0SzfuIv7567mpWWbww5FJCqi1kTv7vPMbHAbdp0ArHb3NQBm9iRwAbCs/aKTROfu1NQ6GV2SuffS0WGHIyEYPSCLV26ZxMBDu4YdikhUhH0R6vNm9r6ZPWdmw4OyHGB9g20KgrImmdm1ZpZvZvlFRUXRjFXiyF/e+ZQp099R82yCq0vuq7eUMHfFlpCjEWlfYSb4hcAgdx8N/BaY1ZaDuPt0d89z97zs7Ox2DVDiV69uXejbI53uXdTPVOCn/1rOj2YvpbK6NuxQRNpNaJ9u7r6rwd/PmtnvzKw3UAg0HEIsNygTOWh1U4eeN6o/543qH3Y4EiPuvXQUVTWunvUSV0J7N5tZXwtmgDCzCUEs24D5wFAzG2JmXYApwOyw4pT4UVZZw5Tp7/DKCnWqkr31yUwnJysDd+f5pRupqlFNXjq/aN4m9wTwNjDMzArM7Gozu87Mrgs2uQRYambvA78BpnhENXAjMAdYDvzN3T+MVpySOEoqqiivqsHQzGLStIXrtnPdYwv5e35B2KGIHDSNRS8JpbbWSUpSgpfmzV2xhYlHZet9Ip2CxqKXhPbqyi3cNmMJFdU1+tCW/Tr16D4kJRk7S6tYsWnX/ncQiVFK8BL3Ptywi/fX76CmNn5aqyT6bnxiIdf8OV8966XTUhO9JARNFSoHasWmXewuryZvcK+wQxFplproJeHU1jo/nv0hH20uAVBylwN2dN9D6pP76i0lxFNlSBKDErzEpcIdZfzrg428s2Zb2KFIJ7dw3XbOvu91nlmo4Tikc9EwXhKXBvTqykvfP4UeGZrbXQ7OmNwsbjnrKM4efljYoYgcENXgJa6s2LSLR99ei7uT1bULwVhKIm2WlGTcMOlIMtNTqa6pZdvuirBDEmkVJXiJK399dx33z13NrrLqsEOROHTTU4u54o/vqWe9dApqope48uMvDufaUw6nR1c1zUv7u3R8Lpt3lWvMeukUlOAlLjzx3jrOGdGXrK5dyO2p+b0lOiYN61P/956Karql6SNUYpfendJpzVpUyL1zVrJhRxkOvLayiN9/dXzYYUkCWLZhF5f+/i3SU5Mp3lNJ/6wMpp49jAvH5oQdmkg9tTNJpzRrUSG3zVhCYZDcAV5dtYVZi3Qrk0Tf0sKdlFfVsm1PJU7ktszbZizR+09iihK8dEr3zllJWVXNXmXlVbXcO2dlSBFJIvn1yx9R02jgm7KqGr3/JKYowUuntGFH2QGVi7Qnvf+kM1CCl06pf1bGAZWLtCe9/6QziFqCN7OHzWyLmS1tZv3lZvaBmS0xs7fMbHSDdWuD8sVmptljZC8V1TX855lHkdFofPmM1GSmnj0spKgkkUw9e5jefxLzolmDfwSY3ML6T4CJ7j4S+CkwvdH6U919THOz5Eji+n8vrOKv89fx0wuGk5OVgQE5WRncffFI9WKWDnHh2BzuvnjkXu+/m884kuQkjZwosSNqt8m5+zwzG9zC+rcaLL4D5EYrFokvR/fNxIBL8gZwSd6AsMORBHXh2Jy9vlB++/GFPPLWp5x57GGavVBiQqzcB3818FyDZQdeMDMHHnT3xrX7emZ2LXAtwMCBA6MapMSGi8fpu6DEnh+fPxzQ1MQSO0LvZGdmpxJJ8D9oUHySu48DzgG+bWanNLe/u0939zx3z8vOzo5ytBKmh15fw78/2Bh2GCJNys5MIzszDXdn3bbSsMMRCTfBm9ko4CHgAnevn7jb3QuD31uAmcCEcCKUWFFT6zy7ZCMvL98cdigiLbp/7mom/3oehbplTkIWWhO9mQ0EZgBfdfdVDcq7AUnuXhL8fRZwV0hhSoxITjL+9q3PU6FZvCTGXTQul7SUZA7LTAs7FElwUUvwZvYEMAnobWYFwJ1AKoC7/x74EXAo8Ltgzu7qoMf8YcDMoCwF+Ku7Px+tOCX2vbV6K2MH9iSjSzIpyaFfVRJpUU5WBt885XAA3J3gs0ykw0WzF/1l+1l/DXBNE+VrgNH77iGJqKikgqsemc9XJgys78Qk0hl8ULCDH85cykNX5nHYIelhhyMJKFZ60Ys0KTszjUe+fhxD+2SGHYrIAclMT6WqpoKIFLMAABvsSURBVJaikgoleAmFErzErNLKarp2SeGEI3qHHYrIARvSuxvP3XSymuglNLqgKTHp0217OHHaK7zw4aawQxFpMzOjuqaWh15fw9bdFWGHIwlGCV5iUkZqMicPzWZkbo+wQxE5KOuKS7nn+ZWaK146nHmjOY07s7y8PM/P19w0IhJbVm8p4Yjs7mqul3ZnZguam7NFNXiJKRt2lHHL395Xc6bElSP7ZGJmFJVUsLO0KuxwJEEowUtMWbRuBy+v2ExZZU3YoYi0qz0V1Zzz69e5+7nlYYciCUK96CWmfGFUPyYOy6Z7mt6aEl+6paXwX2cPY9ygnmGHIglCn6ISE7aUlLO+uJTxg3opuUvc+o/jPpveWKPcSbSpiV5iwm9e/ogrHnqP7Xsqww5FJKrcnZ/880PunP1h2KFInFNVSWLCbeccw+Th/ejZrUvYoYhElZmRkhSpuasWL9GkBC+hKq2sJi0lmW5pKZw0VCPWSWK4/dxjlNgl6tREL6G6fcYSLn/oHWpq42c8BpH9qUvuq7eU8Jd3Pg05GolXqsFLqE45KpttuytJTlJtRhLPo29/yr8/2MgFY/pzSHpq2OFInNFIdiIiISkpr6K8qpbszLSwQ5FOSiPZScyZ9twK/v3BxrDDEAlVZnoq2ZlpuDsrN5WEHY7EmagmeDN72My2mNnSZtabmf3GzFab2QdmNq7BuivN7KPg58poxikdq7yqhrc/3soHhTvCDkUkJvz5rbWc+5vXWbVZSV7aT6uuwZvZY8BrwOvuvuIAjv8I8H/Ao82sPwcYGvwcDzwAHG9mvYA7gTzAgQVmNtvdtx/AY0uMSk9N5pnrT6Amji4PiRyMi8bmAnBEdveQI5F40toa/B+BfsBvzWyNmT1jZjftbyd3nwcUt7DJBcCjHvEOkGVm/YCzgRfdvThI6i8Ck1sZq8SwOR9uoqyyhpTkJNJSksMORyQm9OiaylUnDiE5yajVHSXSTlqV4N19LvC/wH8DfyBSs76+HR4/B1jfYLkgKGuufB9mdq2Z5ZtZflFRUTuEJNGyblsp1z+2gN+/9nHYoYjEpGUbdnHWffP4SE310g5a20T/MtANeBt4HTjO3bdEM7DWcvfpwHSI9KIPORxpwcBDu/LENz/HiJweYYciEpP6HJJGZnoKpZpNUdpBa5voPwAqgRHAKGCEmWW0w+MXAgMaLOcGZc2VSye1sywyB/bxhx9KN00mI9Kk3t3TmHH9CYwekBV2KBIHWttE/z13PwW4GNgG/Alojy7Qs4GvBb3pPwfsdPeNwBzgLDPraWY9gbOCMumE3l+/gxPufpl5q3QJRWR/zIzqmloefO1j1m7dE3Y40om1ton+RuBkYDywFniYSFP9/vZ7ApgE9DazAiI941MB3P33wLPAucBqoBT4erCu2Mx+CswPDnWXu7fUWU9iWN8e6Zw3qr9qJSKtVLynkv+bu5ryqlpuOmNo2OFIJ9WqkezM7D+JJPQF7l4d9ajaSCPZiUi8KNheSk5WhialkRYd9Eh27v4Ld383lpO7xJ7lG3fxnScWUaw53kUOWG7PrpgZW0rK2bSzPOxwpBPSULUSNcs27GLB2mJU/xBpm8rqWi66/y3umNXkYKAiLVJ3ZomaL43P5Quj+pGeqgFtRNqiS0oS/33esQw9TCPcyYFTgpd2t6ZoN8V7Kskb3EvJXeQgTR7Rt/7vmlrX1MrSamqil3b3q5c+4puP5lNaqS4bIu3lZ88u54bHFxBPU3xLdKkGL+1u2sUjWbW5hK5d9PYSaS99MtOoqqmlptZJSVYtXvZPn8DSbnaWVtE9PYVuaSmMHdgz7HBE4so1Jx8edgjSyaiJXtqFu3PDXxfw9UfmqwlRJIpWbS7hty9/FHYY0gkowUu7uXT8AC4c018Dc4hE0fNLN/Hwm5+wpUT3xkvLWjWSXWehkexEJN5VVteyq7yK3t3Twg5FYsBBj2Qn0hx355a/vc+zSzaGHYpIQuiSkkTv7mm4OwvXbQ87HIlhSvByUHaVV7N6SwkbNZSmSId6ZmEhF//uLeav1Txc0jT1opeD0iMjlWeuP0HX3UU62Hmj+lFZXcs43bEizVANXtrs7/nrKausISU5SaNriXSw9NRkvnL8QJKTIvPHizSmBC9tsrRwJ1Of/oCn5q8LOxSRhLZ6Swmn//I13vtETfWyNzXRS5uMyOnBM9efwKjcHmGHIpLQ+mdlMOjQbmpFk31ENcGb2WTg10Ay8JC7T2u0/lfAqcFiV6CPu2cF62qAJcG6de5+fjRjldYrKqkgOzON8YN07U8kbF27pPDoNyaEHYbEoKg10ZtZMnA/cA5wLHCZmR3bcBt3/567j3H3McBvgRkNVpfVrVNyjx1zV27hpJ+/op67IjGmuqaWB179mMXrd4QdisSIaF6DnwCsdvc17l4JPAlc0ML2lwFPRDEeaQfD+x3C5ccPUtO8SIwpq6rh0bfX8pzGpJBANJvoc4D1DZYLgOOb2tDMBgFDgFcaFKebWT5QDUxz91nN7HstcC3AwIED2yFsaUmfQ9L50ReP3f+GItKhMtNTmX3jSfTu3iXsUCRGxEov+inA0+5e06BsUDD83leA+8zsiKZ2dPfp7p7n7nnZ2dkdEWtCemv1Vm54fAE7SivDDkVEmpGdmYaZsaWknDVFu8MOR0IWzQRfCAxosJwblDVlCo2a5929MPi9BngVGNv+IUprfVpcypqiPaSnJocdioi0oLbW+cof3mXq0x9oZscEF80m+vnAUDMbQiSxTyFSG9+LmR0N9ATeblDWEyh19woz6w2cCNwTxVilCbMWFXLvnJVs2FFG/6wMbjlzqBK8SIxLSjLuOn84Szbs5KSfz63//5169jAuHJsTdnjSgaKW4N292sxuBOYQuU3uYXf/0MzuAvLdfXaw6RTgSd/7q+YxwINmVkuklWGauy+LVqyyr1mLCrltxhLKqiJXTQp3lPHDWR+SlJSkDwmRGLelpIL7Xvxor//f22ZE7jrW/2/i0HSx0qQTp71C4Y6yfcpzsjJ489bTQohIRFpL/7+JQ9PFygHb0MSHQ0vlIhI79P8roAQvzejVrelbbfpnZXRwJCJyoJr7P9X/b2JRgpd9fFCwg217KklN3nts64zUZKaePSykqESktaaePYyMRh1iDfji6H7hBCSh0GQzso9RuVn84Wt57Cqr5JcvfqReuCKdTN3/ad1dMH17pNM1NZkTj+wdcmTSkdTJTupt3V1BWWUNA3p1DTsUEWln7o6ZZpyLN+pkJ61y6zNL+I8H36a8qmb/G4tIp1KX3GcsLOA7TyyitjZ+KnfSNDXRS707vnAMq7fs1mA2InFsR2kVW0sqKK2qoXuaUkA8UxO9sHbrHgb37hZ2GCLSAdydWofkJDXXxwM10Uuzlhbu5MxfvcaT760LOxQR6QBmRnKSsaeimu8/tZhVm0vCDkmiRAk+wR3dN5PvnjaUc0bo9hmRRLK7opq312xj8fodYYciUaIm+gRVXlVDda3rGpxIAiutrKZrF30GdGZqopd93DFrKZc88BYV1eoxL5Ko6pL7onXbuX/u6pCjkfamBJ+gLhyTwyXjc0lLUY95kUQ3+/0NPDV/PSXlVWGHIu1ITfQJpqyyhowuSuoi8pmqmlr2VFST1bXpOSgkdqmJXgD4dNseJt47l+eXbgw7FBGJIanJSWR17UJtrfPgax9TVFIRdkjSDqKa4M1sspmtNLPVZnZrE+uvMrMiM1sc/FzTYN2VZvZR8HNlNONMFD0yUjlucC+O6XdI2KGISAz6tLiUX720ihkLC8IORdpB1JrozSwZWAWcCRQA84HL3H1Zg22uAvLc/cZG+/YC8oE8wIEFwHh3397SY6qJvml1Q1ImaWALEdmPNUW7GdK7m8at7yTCaqKfAKx29zXuXgk8CVzQyn3PBl509+Igqb8ITI5SnHHvt6+s5luPLVCPeRHZr8Ozu2NmbNpZrst5nVw0E3wOsL7BckFQ1tiXzOwDM3vazAYc4L6Y2bVmlm9m+UVFRe0Rd9zpkZFCz66pdElWlwsRaZ175qzgB88sYZd61ndaYY9w8E/gCXevMLNvAX8GTjuQA7j7dGA6RJro2z/EzqtuesirThyiqSJF5IDc+cXhXD/xCA5JTw07FGmjaFbpCoEBDZZzg7J67r7N3eu6az4EjG/tvtKynaVVfPnBd1i4LtJtQcldRA5Ej4xUhh6WCcBrq4o0jXQnFM0EPx8YamZDzKwLMAWY3XADM2s4APr5wPLg7znAWWbW08x6AmcFZdJKxaWVFJdWEk/jHIhIx1tTtJuv/+k9ps9bE3YocoCi1kTv7tVmdiORxJwMPOzuH5rZXUC+u88Gvmtm5wPVQDFwVbBvsZn9lMiXBIC73L04WrHGoyG9uzHn5lM0JaSIHJTDs7vz0JV5nHhk77BDkQOkkezizD8WF7J6y26+d8ZRui1ORNpVeVUNHxftZnj/HmGHIgGNZJdAFny6nXc/KaYmjr64iUhs+OHMpVz+0LvqWd9JhN2LXtrZT84fTnlVLam6JU5E2tnNZwxl8oi+6lnfSSgLxIHK6lp+9I+lbNhRhplpMhkRiYoBvbpy5rGHAZG5LepGyZTYpAQfBz7aUsKMhYX1t8SJiETTJ1v3MPm+13noDfWsj2Vqoo8Dw/v34LWpkzi0e1rYoYhIAhh8aFe+e/pQLhzb5ACjEiNUg+/E8tcW868PNgAouYtIhzEzrp90BH0y03F3tu3W9LKxSAm+E/vD62v4fy+s0iQyIhKau/61jIsfeIsS9ayPOWqi78R+c9lYtu6uJC1FnepEJBznjepP7+5pdE9TOok1qsF3Mu7O4+9+SlllDWkpyeRkZYQdkogksPGDevLtU4/EzCirVGtiLFGC72TeL9jJHbOWMmNRQdihiIjUW19cyhm/fI1ZizQvWKxQm0onM2ZAFjNvOJFRORoqUkRiR98e6eQN7skR2d3DDkUCSvCdxKfb9lBSXs2InB6MGZAVdjgiIntJTU7i11PG1i/X1LomuwqZmug7iTtnf8g3H81Xj3kRiXl/fOMTvvKHd6isrg07lISmGnwnce8lo1m/vVQ95kUk5vXJTCM7M40aDWUbKiX4GLfg02LGDexJdvAPIyIS6744uj/njeqHmeHumKmpPgxqoo9hi9fv4EsPvM3j764LOxQRkQNiZmzbXcEVf3yX+WuLww4nIUU1wZvZZDNbaWarzezWJtZ/38yWmdkHZvaymQ1qsK7GzBYHP7OjGWesGp3bg3u+NIpLxueGHYqIyAFLSU6ieE8VW0s0lG0YzD0610jMLBlYBZwJFADzgcvcfVmDbU4F3nX3UjO7Hpjk7l8O1u129wO63yIvL8/z8/Pb7RzCsrO0iqraWnprfHkR6eTUmz66zGyBu+c1tS6aNfgJwGp3X+PulcCTwAUNN3D3ue5eGiy+A6iqCkx9+n2+9MBb6jEvIp1eXXJ/ZcVm/nvWUqJVqZR9RbOTXQ6wvsFyAXB8C9tfDTzXYDndzPKBamCau89qaiczuxa4FmDgwIEHFXCs+O7pQ/m4aLd6zItI3PiwcBcL122npKKaQ9JTww4nIcREL3ozuwLIAyY2KB7k7oVmdjjwipktcfePG+/r7tOB6RBpou+QgKOkqKSC7Mw0RuT0YIRGqhOROHLjaUfyzVMOJz1VFZeOEs0m+kJgQIPl3KBsL2Z2BvBD4Hx3r++J4e6Fwe81wKvA2Mb7xpPlG3cx8d65/GOxxnEWkfhjZqSnJlNZXctP/7WMtVv3hB1S3ItmDX4+MNTMhhBJ7FOArzTcwMzGAg8Ck919S4PynkCpu1eYWW/gROCeKMYailmLCrl3zko27CijX4908gb15MQje4cdlohI1BTtrmDGwgK276ng3U+2s2FHGf2zMph69jAuHJsTdnhxJWo1eHevBm4E5gDLgb+5+4dmdpeZnR9sdi/QHfh7o9vhjgHyzex9YC6Ra/DLiCOzFhVy24wlFO4ow4ENO8uZv3Y7b3y0NezQRESiJicrg1vOOornlm6u//wr3FHGbTOWaCa6dha12+TC0Jlukztx2isU7ijbpzwnK4M3bz0thIhERDqGPv/aT1i3yUkzPtpcwoYm3txAs+UiIvFCn38dQwm+g81fW8yZv5pHVtembxPpn5XRwRGJiHSs5j7nUpOT+Nmzyzs4mvilBB9l7s5rq4p4adlmAMYN7MkdXziG/zxrGBmNbhfJSE1m6tnDwghTRKTDTD1738+/9NQkThp6KEf2iQxgWlPrLPh0exjhxY2YuA8+3t330ipSk5I449jDSE4yrjn5cAC6paXU96JXL1IRSRR1n3Mtff69uGwz1z22gD9/YwITj8oOK9ROTZ3somDeqiLue2kVj11zPF27pFC4o4zs7ml0SVGDiYhIa5RV1jD7/UIuGT+A5CTj+aWbKK+q4fzR/UnS2Pb11MmuA+yuqKakvAqArl2SqapxNu+KjNuTk5Wh5C4icgAyuiTz5eMG1o9l//f89Tz85ifUTS0fT5XTaFHWaQc7y6o4+eev8Id5awDIG9yL2TeeyJDe3UKOTEQkPvzha3k8dGUeZkZ5VQ3n/uYNnluyMeywYpoSfBtt2FHGs8Gbq0dGKtdNPILTjzmsfr2ZmpBERNpLUpLRJzMdgOI9lfTu3oVe3boAsKu8iq27Ned8Y0rwbfTbV1Yz9e/vs6eiGoBvTTyC0QOyQo5KRCT+9c/K4C9XH8/xhx8KwMNvfMLJP5+rJN+IEnwrrS8u5YbHF/BJMEHCTacPZc73TqFbmm5EEBEJ0xdH9+e/Jg+jd/c0AGYuKmDV5pKQowqfEnwL3L2+hp6emsz8tdvr3zR9e6ST27NrmOGJiAhwRHZ3vn7iEADKq2r46b+W1/eJSmS6Ta4FVz78HumpSTz41cgdCFU1taQm6zuRiEgs276nkqqaWvocks6n2/Zw+8wl/OT84RzZJzPs0NpdS7fJqX25gaqaWuatKqrvLHf6MX32SuhK7iIisa9n0PkOYH1xGeuLy8hMjwwPvrO0iu7pKfW338Uz1eAbePzdT/nhzKX849snqsOciEicqK31+sFxbnh8ARt2lDPzhhPi4m4n1eCbUV5Vw0Ovr2FkbhYTj8rm4rG59O+RwajcHmGHJiIi7aThyHdfHNWf4tLK+uT+z/c3cNrRfeKyw3RCtjlX19QCkJJk/C2/gLc+3gpERk469eg+cfGtTkRE9nXOyH5cfvwgAFZuKuE7TyziqfnrQ44qOqL6lcXMJgO/BpKBh9x9WqP1acCjwHhgG/Bld18brLsNuBqoAb7r7nMO9PFnLSrcZzKDzbvKmbmokH9/92RSkpP493dPqr82IyIiiWNY30yeuf4Eju4b6Xw3b1URr60q4ntnHsVLyzZ3+snAolaDN7Nk4H7gHOBY4DIzO7bRZlcD2939SOBXwM+DfY8FpgDDgcnA74LjtdqsRYXcNmMJhTvKcKBwRxm3zVjCpl3ljBvUk7KqGgAldxGRBDZ+UM/65vmlG3by0vLNzFm6scn8MWtRYbjBHqBoNtFPAFa7+xp3rwSeBC5otM0FwJ+Dv58GTrdI+/gFwJPuXuHunwCrg+O12r1zVtYn8TplVTW88OFmfnbRSLrH4fUWERFpuxsmHcmcm0/hly9+1GT+uHfOypAia5toJvgcoOGFjYKgrMlt3L0a2Akc2sp9ATCza80s38zyi4qK6ss37ChrMqjmykVERNJTk+Mmf3T6TnbuPt3d89w9Lzs7u768f1ZGk9s3Vy4iIgLxkz+imeALgQENlnODsia3MbMUoAeRznat2bdFU88eRkbq3pftM1KTmXr2sAM5jIiIJJh4yR/RTPDzgaFmNsTMuhDpNDe70TazgSuDvy8BXvHIyDuzgSlmlmZmQ4ChwHsH8uAXjs3h7otHkpOVgQE5WRncffHITtcLUkREOla85I+ojmRnZucC9xG5Te5hd/9fM7sLyHf32WaWDvwFGAsUA1PcfU2w7w+BbwDVwM3u/tz+Hq+9x6IXERGJZS2NZKehakVERDqplhJ8p+9kJyIiIvtSghcREYlDSvAiIiJxSAleREQkDsVVJzszKwI+bWJVb2BrB4cTSxL5/BP53EHnn8jnn8jnDolz/oPcPbupFXGV4JtjZvnN9TJMBIl8/ol87qDzT+TzT+RzB50/qIleREQkLinBi4iIxKFESfDTww4gZIl8/ol87qDzT+TzT+RzB51/YlyDFxERSTSJUoMXERFJKErwIiIicSiuE7yZTTazlWa22sxuDTuejmZmD5vZFjNbGnYsHc3MBpjZXDNbZmYfmtlNYcfUkcws3czeM7P3g/P/SdgxdTQzSzazRWb2r7Bj6WhmttbMlpjZYjNLuBm4zCzLzJ42sxVmttzMPh92TGGI22vwZpYMrALOBAqIzE9/mbsvCzWwDmRmpwC7gUfdfUTY8XQkM+sH9HP3hWaWCSwALkyU19/MDOjm7rvNLBV4A7jJ3d8JObQOY2bfB/KAQ9z9vLDj6UhmthbIc/dEGOhlH2b2Z+B1d3/IzLoAXd19R9hxdbR4rsFPAFa7+xp3rwSeBC4IOaYO5e7zgOKw4wiDu29094XB3yXAciAn3Kg6jkfsDhZTg5/4/DbfBDPLBb4APBR2LNKxzKwHcArwRwB3r0zE5A7xneBzgPUNlgtIoA94+YyZDQbGAu+GG0nHCpqoFwNbgBfdPZHO/z7gv4DasAMJiQMvmNkCM7s27GA62BCgCPhTcInmITPrFnZQYYjnBC+CmXUHngFudvddYcfTkdy9xt3HALnABDNLiMs0ZnYesMXdF4QdS4hOcvdxwDnAt4PLdYkiBRgHPODuY4E9QML1wYL4TvCFwIAGy7lBmSSI4NrzM8Dj7j4j7HjCEjRPzgUmhx1LBzkROD+4Dv0kcJqZPRZuSB3L3QuD31uAmUQuWSaKAqCgQYvV00QSfsKJ5wQ/HxhqZkOCThZTgNkhxyQdJOhk9kdgubv/Mux4OpqZZZtZVvB3BpHOpivCjapjuPtt7p7r7oOJ/N+/4u5XhBxWhzGzbkHHUoKm6bOAhLmTxt03AevNbFhQdDqQEJ1rG0sJO4BocfdqM7sRmAMkAw+7+4chh9WhzOwJYBLQ28wKgDvd/Y/hRtVhTgS+CiwJrkMD3O7uz4YYU0fqB/w5uJskCfibuyfc7WIJ6jBgZuQ7LinAX939+XBD6nDfAR4PKndrgK+HHE8o4vY2ORERkUQWz030IiIiCUsJXkREJA4pwYuIiMQhJXgREZE4pAQvIiISh5TgRURE4pASvIiISBxSgheRNjGz48zsg2Du+W7BvPMJMd69SGeggW5EpM3M7H+AdCCDyPjfd4cckogElOBFpM2CoUDnA+XACe5eE3JIIhJQE72IHIxDge5AJpGavIjECNXgRaTNzGw2kSlZhwD93P3GkEMSkUDcziYnItFlZl8Dqtz9r8GsdW+Z2Wnu/krYsYmIavAiIiJxSdfgRURE4pASvIiISBxSghcREYlDSvAiIiJxSAleREQkDinBi4iIxCEleBERkTj0/wFXMiPaAvPRNQAAAABJRU5ErkJggg==\n", 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" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "id": "P-a04lCWDpq2" }, "source": [ "## Lax-Friedrichs Method\n", "The Lax-Friedrichs Method of the Burger Equation is,\n", "\\begin{equation}\n", "\\frac{w_{ij+1}-\\frac{w_{ij+1}+w_{ij-1}}{2}}{k}+aw_{ij}\\big(\\frac{w_{i+1j}-w_{i-1j}}{2h}\\big)=0.\n", "\\end{equation}\n", "Rearranging the equation we get\n", "\\begin{equation}\n", "w_{ij+1}=\\frac{w_{ij+1}+w_{ij-1}}{2}-w_{ij}\\frac{\\lambda}{2} a(w_{i+1j}-w_{i-1j}),\n", "\\end{equation}\n", "for $i=0,...10$ where $\\lambda=\\frac{k}{h}$.\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." ] }, { "cell_type": "code", "metadata": { "id": "muPmXOCYDpq3" }, "source": [ "lamba=k/h\n", "for j in range(0,time_steps):\n", " for i in range (0,N+1):\n", " w[j+1,i]=(w[j,int(ipos[i])]+w[j,int(ineg[i])])/2+lamba*w[j,i]/2*(-(w[j,int(ipos[i])]-w[j,int(ineg[i])]))\n", " " ], "execution_count": 4, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "lLbQ2prxDpq3", "outputId": "6d869f0d-a8ca-4b82-b1d8-480d4b9384fb", "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", " plt.plot(x,w[j,:],'o:')\n", "plt.xlabel('x')\n", "plt.ylabel('w')\n", "\n", "plt.subplot(122)\n", "X, T = np.meshgrid(x, time)\n", "z_min, z_max = np.abs(w).min(), np.abs(w).max()\n", "\n", "\n", "plt.pcolormesh( X,T, w, vmin=z_min, vmax=z_max)\n", "\n", "\n", "#plt.imshow(w, aspect='auto')\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 Burger Equation'%(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", 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