{ "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": "1003_Wave Equation-Lax-Wendroff.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": "qGjwMD__DpX6" }, "source": [ "# Lax-Wendroff Method\n", "## The Differential Equation\n", "Condsider the one-dimensional hyperbolic Wave Equation:\n", "\\begin{equation} \\frac{\\partial u}{\\partial t} +a\\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-Wendroff method to appoximate the solution of the Wave Equation.\n", "The Lax-Wendroff method was designed by Peter Lax (https://en.wikipedia.org/wiki/Peter_Lax) and Burton Wendroff (https://en.wikipedia.org/wiki/Burton_Wendroff)." ] }, { "cell_type": "code", "metadata": { "id": "hMf3yx1gDpX9" }, "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": "X8BPk_9-DpX-" }, "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": { "colab": { "base_uri": "https://localhost:8080/", "height": 324 }, "id": "_0zDHUkHDpX-", "outputId": "e932faf2-721e-4205-f549-8fd686a91877" }, "source": [ "N=20\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": "VCxPHqajDpX_" }, "source": [ "## Initial Conditions\n", "\n", "The discrete initial conditions is,\n", "\\begin{equation} w[i,0]=1-\\cos(x[i]), \\ \\ 0 \\leq x[i] \\leq \\pi, \\end{equation}\n", "The Figure below plots values of $w[i,0]$ for the inital (blue) conditions for $t[0]=0.$" ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 304 }, "id": "698f-0bQDpYA", "outputId": "f05fd129-f49e-4973-f3bc-66a4097fc409" }, "source": [ "w=np.zeros((N+1,time_steps+1))\n", "b=np.zeros(N-1)\n", "# Initial Condition\n", "for i in range (0,N+1):\n", " w[i,0]=1-np.cos(x[i])\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)" ], "execution_count": 3, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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f5q9LCgAYnNuRX04ZzYRhsZqvrh0yueGMQfTqnFW9zUlj8pgxeSR5OdkYkJeTzYzJI5k0Jo/+3dpz2rHdq5d99KZT+fGkkUDsyumXL37Ec+9vrp7/w3kf8PrH2xOeRKR+V933Bn9dErsDWl4Z5ar73uCpZbHPxF11tLm48x8fALBzfxlX3fcGL66MfSncurfxz9YvW7aMu+++m5UrV7J27VoWLlx4yPyZM2eSnZ3N8uXLefTRRw+Zl5WVxVNPPcU777zDggUL+Pa3v13vLaL333+fk08+Oe68OXPmsHz5ct59911efPFFpk2bxqZNm+qMsaSkhK9+9as8/fTTLF26lM2bNx+2zdNPP53LLruMWbNmsXz5cgYPHlw9r6SkhOuvv54nnniCFStWUFFRwb333ls9v0ePHrzzzjt87Wtf42c/+9mRD2QDJLIV/RnAl4AVZrY8KPseMADA3X8HPANcAqwGDgA3BPN2mtmPgMXBene6u+r+ROoxa37+YSfn8krnwYWf8J8XDScrI8LjU09jSK9OAKSlGZePPnJL+Elj8hrUYj6nfSY57TOBWIvfRdM/y4GyCgB2F5fzj/c2MaBbe/7w+id1NtxTy/xw1dXmYuf+8mbbx/jx4+nXrx8Ao0ePZt26dZx55pkNWtfd+d73vserr75KWloahYWFbNmyhd69ezc6jtdff52rr76aSCRCr169OOecc1i8eDGdO3eOG2PHjh0ZNGgQQ4YMAeDaa69l9uzZDd5ffn4+gwYNYujQoQBcd9113HPPPXzrW98CYPLkyQCcfPLJh9QOHI2EJXh3fx2ot12/x756fb2OeQ8ADyQgNJGUtLGoOG55SXm0+vXJx3RrqXDITE8jMz2W8LtkZ7D4+5+lIur86B8r4y5fV/zSvJ74t89Uv86IpB0y3Tcnm8I470NeTjYA3TpkHrJ8z05Zhy17JO3atat+HYlEqKioaPC6jz76KNu2bWPp0qVkZGQwcODAep8NP/HEE6urx1sqxqaq2mdz7k990Yu0ctv2lrK/tIK+wUm4trrKW5qZkRFJqzOeHh3bxS2XljNt4rA621y0pIyMDMrLD6812L17Nz179iQjI4MFCxawfn2dI6UCcN5551FaWnrIlfZ7773Ha6+9xllnncUTTzxBZWUl27Zt49VXX2X8+PF1bmv48OGsW7eONWvWAPDYY4/FXa5Tp07s3bv3sPJhw4axbt06Vq9eDcAf//hHzjnnnHrjP1pK8CKt2O7ici66+1Vmzc9PmpPzkcSL04C+OUrwYauvzUVLmjp1KieddFJ1I7sq11xzDUuWLGHkyJE88sgjDB8+vN7tmBlPPfUUL774IoMHD+bEE0/ktttuo3fv3nz+85/npJNOYtSoUZx33nncdddd9Vb1Z2VlMXv2bD73uc8xduxYevbsGXe5KVOmMGvWLMaMGVP9ZaBq/QcffJArr7ySkSNHkpaWdkjjv0SwVHqGddy4cb5kyZKwwxBJuLKKKJnpse/nj7yxjtMHd+e4np2Yu6yQWfPz2VhUTN+cbKZNHJaU97Vrx3nLeYOZeGIfunXIZNveUjbvLmFkvy5hh5kSPvzwQ44//viww5BmEO+9NLOl7j4u3vIabEaklVmybiffeGwZj9w4niG9OvHlzwysntfQBnFhqy/O/30+n6ff3cii6Z+lS/uGj5wlIodSghdpZQb26MDQXp1Stn/x2y4+nokjelcn9617SujZufGNuUTaOt2DF2kFnv9gM9P/9h7uTo+O7Xj4xvEc1/PI3X+2Rl3aZ3DusNj9zbfW7uDMny5gQf7WkKNq3VLpVmxb1ZT3UAlepBVYv+MAKwp3s6ck8Y/rJJNhvTtx3enHcOqg2ON9lVElqsbKyspix44dSvKtWNV48FlZjavJUiM7kST1/AebyWmfyfhB3aiMOlF3MiJt9zt5RWWUq3//JhNP7M1NZx0bdjitRnl5OQUFBY0eS1ySS1ZWFv369SMj49B2KWpkJ9LKlFVEmfHsKob07Mj4Qd2IpBmR+vuNSnmlFVH65mST20mP0zVGRkYGgwYNCjsMCYGu4EWSyKI12xk/sBvpkTQ27DxAr85Z1Y/DyaGefncj63fs5+ZzBpPehms2pG3TFbxIEqr9LPiV4/px94sf8+NJI7j2tGPo36192CEmtTfW7uDDTXv42oTjgMOPZ7L2ASDSUnQFLxKCqhHVag66kp0R4YqT8/ivS0/UVXsD7S+toEO7dP6y+FO+P/d9yisPns+yMyKh9MIm0pLqu4LXWUQkBPFGfisur+SlVduU3BuhQ7tYJeRPnll1SHKHgyPUibRVOpOIhKCukdM0olrT7C6OP5ypjqe0ZUrwIi3M3enWITPuvGQZ+a21SfaR9ETCoAQv0sL+vnwjO/aXkVmr5XcyjvzWWsQboS4rPU3HU9q0hLWiN7MHgEuBre4+Is78aUDVWIDpwPFArrvvNLN1wF6gEqioqwGBSGt02ai+ZETSKKuo5GfPf6RW382g6rhVtaLvk5PFf04czuWj+1JaUUm79MgRtiCSehLWit7Mzgb2AY/ES/C1lv0X4N/d/bxgeh0wzt23N2afakUvyewvSzZw4Qm9yGkfv3pemt+dT6/k4617+cN1p6jxoqSkUFrRu/urwM4GLn418FiiYhEJ24adB7h97vs88PonYYfSpgzv04lhvTqREWnbvQBK25TQ5+DNbCDwj/qu4M2sPVAAHOfuO4OyT4BdgAP3ufvsetafCkwFGDBgwMnr169vtvhFmtP7hbsZ3ruTel0Lya79ZXTOziCSpmQvqSPZn4P/F2BhVXIPnOnuY4GLga8H1f1xuftsdx/n7uNyc3MTHatIo8xdVlg91OmIvC5K7iHZX1rB5HsX8cN5H4QdikiLSYauaqdQq3re3QuD31vN7ClgPPBqCLGJNFll1Hlw4SfktM9kwtBczHTlGJYO7dL513H9OWVg17BDEWkxoSZ4M+sCnANcW6OsA5Dm7nuD1xcCd4YUokiTRdKMR75yKulppuSeBL42YXD161Wb9zCsVye9L5LSElZfaGaPAW8Aw8yswMy+YmY3m9nNNRb7PPC8u++vUdYLeN3M3gXeBv7P3Z9LVJwizW3h6u1876kVVEadLtkZ1d2pSnJY9ukuLvnla/xlyYawQxFJqISdedz96gYs8xDwUK2ytcCoxEQlknjLNxSxdN0u9pVW0CU7I+xwpJZR/XL43iXHc+lJfcMORSShNJqcSDNx9+oq3+KySrIz1blKsiuriLJozXYmDOsZdigiTZLsrehFWr1Vm/dw6a9fZ9322N0mJffW4f7X13LDQ4v5aMvesEMRaXa6OSjSDCoqnahDmhpttSo3njGIIT07MbRXp7BDEWl2qqIXOQol5ZVkBYOcRKNOmjpRabU+2rKXgl0HOG94r7BDEWkwVdGLJMDWPSVMvPtVnlj8KYCSeys345kPuWPeB5RVRMMORaRZqIpepIk6Z2cwpn8Ow3t3DjsUaQa/uGo0e4orNCiNpAwleJFG2n2gnHYZaWRlRLh7ypiww5FmktM+s3qkvz+8/gljB+QwZoB6vpPWSwlepAHmLiusHms8PWIcl9uRZ249Sz2hpaB9pRU8vGgdL36Yxac7itlYVEzfnGymTRxWPe68SGuguiiRI5i7rJDb5qygsKgYB8ornTXb9vP35RvDDk0SoGO7dG46axDLPy2qfs8Li4q5bc4K5i4rDDs8kQZTghc5glnz8ykurzykrKwyyqz5+SFFJIl23ytrKS4/tLFdcXml3nNpVZTgRY5gY1Fxo8ql9dN7LqlACV7kCPrmZDeqXFo/veeSCpTgRepxoKyC71w4lOyMQ7uezc6IMG3isJCikkSbNnHYYe95ZiSNi0f0DikikcZTghepQ1lFlGvuf4vlG4qYMXkkeTnZGJCXk82MySPVojqFTRqTd8h73jcni15d2vFe4W5SqfdPSW16TE6kDpE04+whuQzt1YnPndRHCb2NmTQm75D3fOueEjpnZ+jRSGk1lOBF4nB3ImnGv18wNOxQJEn07JwFxGp2Xli5hc+d1CfkiETql7AqejN7wMy2mtn7dcyfYGa7zWx58PODGvMuMrN8M1ttZtMTFaNIPOu27+ey3ywkf7OGEJXD/fmt9Xz9z++womB32KGI1CuRV/APAb8BHqlnmdfc/dKaBWYWAe4BLgAKgMVmNs/dVyYqUJGadheXU14ZpUM7jekuh7vmtGM4rmcnRvbrEnYoIvVK2BW8u78K7GzCquOB1e6+1t3LgMeBy5s1OJF6jOqfwzPfPIt+XduHHYokoYxIGmcO6QHEansOlFWEHJFIfGG3ov+Mmb1rZs+a2YlBWR6wocYyBUFZXGY21cyWmNmSbdu2JTJWSXF/X17I/a+txV3jusuR7dpfxmW/eZ2Zz64KOxSRuMJM8O8Ax7j7KODXwNymbMTdZ7v7OHcfl5ub26wBStvycv42nl+5hcqoHoOSI+vaIZPbLz2BfztncNihiMQVWit6d99T4/UzZvZbM+sBFAL9ayzaLygTSaif/+so9pVWkB4Ju2JLWot/HXfwVLX7QDld2meEGI3IoUI7k5lZbwseKDWz8UEsO4DFwBAzG2RmmcAUYF5YcUpqc3fuf20tO/aVYmZ0ytIJWhpv5rOruPye19lbUh52KCLVEnYFb2aPAROAHmZWANwBZAC4+++AK4CvmVkFUAxM8VgXURVmdgswH4gAD7j7B4mKU9q2tdv3c9f8fNzhq2cfG3Y40kp99vieZEaM9pnqWkSSh6VSt4vjxo3zJUuWhB2GtDKrt+5jUI8ORNSwTppBNKpGmtJyzGypu4+LN083G6VN2lNSzhtrdgBwXM+OSu7SLNZu28dFv3yVZZ/uCjsUESV4aZt+9eLHXPfA22zZUxJ2KJJCundoR6esDD2JIUlBN4ykTfqPC4dyxpAe9Ar6FxdpDl3aZ/DkzZ/RgDSSFHQFL23KpzsOUF4ZpX1mOucO6xl2OJKCzAx354HXP2H2q2vCDkfaMCV4aTMOlFUwZfYbTPvru2GHIm3Asg1FLF2/S+PHS2hURS9tRvvMdL578XCO7dEx7FAkxZkZs644iXbpaaqul9DoCl7ahH2lsQFBLh+dp1HApEVkZUQwM3btL+N/n89XwztpcUrwkvLeWLODM3/6Eu/o0SUJwasfb+O+V9ayolDjx0vLUhW9pLx+XbM5Z2guw3p1CjsUaYMuH53H2AFd6d9Nww9Ly9IVvKSsqsZN/bu155dTxtChnb7PSjiqkvui1dvZWFQccjTSVuiMJyln7rJCZs3Pp7ComPaZEX58+Qgmn9wv7LCkjdtTUs4ND71NmqVRUl5J35xspk0cxqQxeWGHJilKCV5Sytxlhdw2ZwXF5ZUAHCir5Ptz3yctzXQilVC99OFWwKo/m4VFxdw2ZwWAPpuSEKqil5Qya35+9Qm0SnF5JbPm54cUkUjMrPn5lFZEDynTZ1MSSQleUkpd9zd131PCps+mtDQleEkpvTq3i1veNye7hSMROVRdn0F9NiVREpbgzewBM9tqZu/XMf8aM3vPzFaY2SIzG1Vj3rqgfLmZaYB3abDpFx9PVsahH+vsjAjTJg4LKSKRmGkTh5GdETmkLDsjwrcvGBpSRJLqEnkF/xBwUT3zPwHOcfeRwI+A2bXmn+vuo+sayF6kpmjUef6DzVw+ui8zJ59EXk42BuTlZDNj8kg1YpLQTRqTx4zJIw/5bH759GP41Usfs1XDFksCJKwVvbu/amYD65m/qMbkm4CeY5Ime+b9Tdzy52U8dMMpTBqTp4QuSan2Z3PNtn28t2H3YY3vRJqDJXKkoyDB/8PdRxxhue8Aw939pmD6E2AX4MB97l776r7mulOBqQADBgw4ef369c0TvLQq0ajzwodbuPCEXhrcQ0TaDDNbWldNd+iN7MzsXOArwHdrFJ/p7mOBi4Gvm9nZda3v7rPdfZy7j8vNzU1wtJJsyiuj7CkpJy3NmHhibyV3aZUOlFVw59Mr+XTHgbBDkRQSaoI3s5OA+4HL3X1HVbm7Fwa/twJPAePDiVCS3W8XrOGiX7zKzv1lYYci0mRFB8p5cukGXv14W9ihSAoJrSc7MxsAzAG+5O4f1SjvAKS5+zI79R8AAB1lSURBVN7g9YXAnSGFKUnunGG5lFVW0q1DZtihiDRZ35xsXpl2Ll31OZZmlLAEb2aPAROAHmZWANwBZAC4+++AHwDdgd8G1aoVwX2EXsBTQVk68Gd3fy5RcUrrNrp/DqP754QdhshRq0ruH2/Zi5lxXM+OIUckrV0iW9FffYT5NwE3xSlfC4w6fA2Rg2Y+u4qsjDRu/ewQ3XeXlFFeGeW6B97muF6deORG3ZmUo6PBZqTViUadrXtLaJ8ZUXKXlJIRSePXXxzDMd07hB2KpAAleGl10tKMn//raCqjiXvEUyQsJx/TDQB3Z9eBcrUvkSYL/TE5kcZ4aOEnbNodG5wjkqard0ldd8z7gCt+t4iSWqMjijSUruCl1di8u4S75uezc38Z/3Gh+paX1DbxxN7065pNRkTXYdI0Ce3JrqWNGzfOlyzR2DSp7NMdB+jVpR3t0iNHXlhEJMUldU92Ikfi7rxfuBuAAd3bK7lLm7J0/S6uuu8N9pSUhx2KtDJK8JL0Xli5hUt//ToLVm0NOxSRFmcG2/aVasQ5aTRV0UvSK62o5LG3PuXa044hXfcjpQ2qjLoalUpcqqKXVsndKauI0i49wvVnDFJylzYrkmZUVEb5/atr2bGvNOxwpJXQGVOS1qNvfcrl9yzUCU0EWL/zALPm5zN3+cawQ5FWQo/JSdLqm5PF8N6d1NGHCDA4tyPPfussBueqj3ppGCV4SVrnDe/FecN7hR2GSNKoSu5b95QQdejdJSvkiCSZqYpeks5DCz/hicWfkkoNQEWaS1lFlM//dhG3z10RdiiS5HQFL0nF3VmQv432mRH+dVz/sMMRSTqZ6Wn84F9O0HCyckRK8JJUzIwHrz+F4vJKjRQnUoeJJ/aufl1aUanOnyQuVdFL0nju/U3sKSknLc3o0E7fPUWO5Gfz87l69ptUVEbDDkWSUELPomb2AHApsNXdR8SZb8AvgUuAA8D17v5OMO864PZg0R+7+8OJjFXCMXdZIbPm57OxqBgHzh3WgwdvODXssERahaG9O7GioIiz71rApt0l9M3JZtrEYUwakxd2aJIEGnQFb2Z/MrOvmtnwRm7/IeCieuZfDAwJfqYC9wb76wbcAZwKjAfuMLOujdy3JLm5ywq5bc4KCoPkDvDG2p3MXVYYalwirUU06ry9bhcbd5fgQGFRMbfNWaH/IQEaXkX/B6AP8GszW2tmfzOzW4+0kru/CuysZ5HLgUc85k0gx8z6ABOBF9x9p7vvAl6g/i8K0grNmp9Pca2xrkvKo8yanx9SRCKtS7z/oeLySv0PCdDAKnp3X2BmrwKnAOcCNwMnEqtePxp5wIYa0wVBWV3lhzGzqcSu/hkwYMBRhiMtaWNRcaPKReRQ+h+S+jS0iv6fwELgKiAfOMXdG1tdnxDuPtvdx7n7uNzc3LDDkUbom5PdqHIROZT+h6Q+Da2ifw8oA0YAJwEjzKw5PkGFQM2HnfsFZXWVSwr5zoVDyc449PGe7IwI0yYOCykikdZl2sRhh/0PZUSMb553XEgRSTJpUIJ3939397OBycAO4EGgqBn2Pw/4ssWcBux2903AfOBCM+saNK67MCiTFPHc+5uYs6yQ/7r0ePJysjEgLyebGZNHqgWwSANNGpPHjMkjq/+HenZqR3mls7ukPOzQJAk06B68md0CnAWcDKwDHgBea8B6jwETgB5mVkCsZXwGgLv/DniG2CNyq4k9JndDMG+nmf0IWBxs6k53r6+xnrQy+0srKa2IcuW4/nzx1GPCDkek1Zo0Ju+QL8VvrNnB+EHdQoxIkoU1pL9vM/sOsYS+1N0rEh5VE40bN86XLFkSdhjSQO6u3upEEmRfaQWVUadLdkbYoUgCmdlSdx8Xb15Dq+h/5u5vJXNyl9bh/97bxMv5WwGU3EUSpLSikst+/Tp3/P39sEOREKk/UGkx7s4fXl9LRiSNc4bmKsGLJEi79Ag3njmI4b07hR2KhEgJXlqMmfHnr57G3pIKJXeRBLv2tINtW3Q7rG3SYDPSIpau30VZRZSsjAi5ndqFHY5Im3H/a2u5+U9LaUh7K0ktSvCScFv3lvDF37/JzGdXhR2KSJuTZkYkzSit0IhzbU2DWtG3FmpFn7xeWLmFUf260LNzVtihiLQpVed4VdGnpqNuRS/SVAfKYg9eXHBCLyV3kRCYGWbG1j0lzJq/img0dS7qpH5K8JIw7xfu5vSZL7FozfawQxFp8177eDv3v/YJKzftCTsUaSFqRS8Jk9M+g7OG5HJiny5hhyLS5k0em8dnBnfXQDRtiK7gJWH6dW3Pr68eQ5f26klLJGxmVp3cl6zbSXmlGt2lOiV4aXZvrd3BtL++y75SdXwokmw+3LSHK373Bg8vWhd2KJJgqqKXZrdy0x6WfroLtdkVST7H9+nML64axcUj+oQdiiSYHpOThCgprySr1jjVIpJcyiujVEZd/6utmB6TkxbxxpodvF+4G0AnDJEkV1JeyRX3LuKu5/LDDkUSRFX00izcnZ888yGO8/QtZ6pTDZEkl5UR4eyhuRzfp3PYoUiCKMFLszAz/viV8ew6UK7kLtJKfPvCYWGHIAmU0Cp6M7vIzPLNbLWZTY8z/xdmtjz4+cjMimrMq6wxb14i45Sjs277ftydnPaZDOrRIexwRKSR5i4r5M6nV4YdhjSzhF3Bm1kEuAe4ACgAFpvZPHev/hS5+7/XWP4bwJgamyh299GJik+ax/Z9pVx+z0KmnNKf2y45PuxwRKQJPt66lxWFRWocm2ISWUU/Hljt7msBzOxx4HKgrq+JVwN3JDAeSYDuHTL5zsRhnDG4e9ihiEgTfev8odWjzknqSGQVfR6wocZ0QVB2GDM7BhgEvFSjOMvMlpjZm2Y2qa6dmNnUYLkl27Zta464pYEqo46Z8aXTjuHY3I5hhyMiTZQRSSOSZuwrreDRt9Zr7PgUkSyPyU0BnnT3yhplxwTP9n0RuNvMBsdb0d1nu/s4dx+Xm5vbErEKsH7Hfi74+Su88+musEMRkWYy550Cbp/7Ph9s1IA0qSCRVfSFQP8a0/2CsnimAF+vWeDuhcHvtWb2MrH782uaP0xpipLyKF07ZNJbQ8CKpIxrTj2GsQO6MiJPA0SlgkQm+MXAEDMbRCyxTyF2NX4IMxsOdAXeqFHWFTjg7qVm1gM4A7grgbFKA8xdVsis+flsLCqmb0420yYO08hUIikkkmaMyOvC3GWFzHj2Q7buKa3+X580Ju4dVkliCUvw7l5hZrcA84EI8IC7f2BmdwJL3L3q0bcpwON+6E2f44H7zCxK7DbCzJqt76XlzV1WyG1zVlBcHruLUlhUzG1zVgDoH18khcxdVsh3//YepRWx0eb0v956qS96aZAzZr5EYVHxYeV5OdksnH5eCBGJSCLof711UV/0ctQ2xvmHr69cRFon/a+nDiV4aZCuHTLjlusevEhqqet/um+OGtS2NkrwckQl5ZWUV1RSuw+M7IwI0yaqL2uRVDJt4jCya/VmlxExvqN+61sdJXg5oqyMCP/45ln88LITyMvJxojdj5sxeaQa3YikmElj8pgxeeQh/+uzrhjF58f2Uwc4rYwa2Umd3J2l63cxbmC3sEMRkZAtXreTnz67ij9cfwpdsjPCDkcCamQnTfLMis1c8bs3eOUjdQEs0talmbGnpJyd+8vCDkUaSFfwUqfyyihz3ingypP7k6ZBKETavMqoa0CaJKMreGmUPSXlHCirICOSxlWnDFByFxEg1tNdRWWU/30+nyXrdoYdjhyBErwcZtpf3+XK371BRWU07FBEJMkcKK/k78s3siB/a9ihyBEksi96aaW+dNpACnYdID2i738icqjOWRnMu+UMctrH7xtDkocSvFQrq4iSmZ7GmUN6hB2KiCSxquResOsAb67dyRUn9ws5IolHl2gCwPZ9pVzwi1d4+t2NYYciIq3EvS+v4c6nP6DogFrWJyNdwQsQewRmSM9OHJvbIexQRKSV+N4lx/PVs45VdX2SUoIXALp1yOT+6+I+aSEiEleHdul0aBdLI699vI3PHNtdbXeSiN6JNu71j7fztT8tZU9JedihiEgr9e6GIr70h7f589ufhh2K1JDQBG9mF5lZvpmtNrPpceZfb2bbzGx58HNTjXnXmdnHwc91iYyzLft05wHW7ThAup51F5EmGtU/h3u+OJYppwwIOxSpIWE92ZlZBPgIuAAoABYDV7v7yhrLXA+Mc/dbaq3bDVgCjAMcWAqc7O676tunerJrmvLKKBmqVhORZlBcVsne0nJ6dtLwsi0hrJ7sxgOr3X2tu5cBjwOXN3DdicAL7r4zSOovABclKM426b5X1rA46IlKyV1EmoO78+UH3uLmPy4lGk2dbtBbq0Q2sssDNtSYLgBOjbPcF8zsbGJX+//u7hvqWDfuuKRmNhWYCjBggKqHGuJAWQWPvf0pG3Yd4BSNFCcizcTMmHr2YDLT09TFdRIIuxX908Bj7l5qZv8GPAyc15gNuPtsYDbEquibP8TU0z4znXnfOJNMXbmLSDO74IRe1a+LyyrJzoyEGE3blsgzfCHQv8Z0v6CsmrvvcPfSYPJ+4OSGriuNV1pRyZ/eXE9l1OmclUFWhv7xRCQxXli5hbPueolPtu8PO5Q2K5EJfjEwxMwGmVkmMAWYV3MBM+tTY/Iy4MPg9XzgQjPramZdgQuDMjkKz6zYxO1z36++9y4ikign9O3Mqcd2p1NW2BXFbVfCjry7V5jZLcQScwR4wN0/MLM7gSXuPg/4ppldBlQAO4Hrg3V3mtmPiH1JALjT3ZWVjtKk0XkM7N6BMQO6hh2KiKS4vJxs7vniWCDW+M5M9+RbWsIekwuDHpOLb/2O/WSmp9GnS3bYoYhIG3OgrIJv/+Vdzj++F1/QoDTNrr7H5FR3kqLmLitk1vx8NhYVkxFJI6d9Om/cdj4RtWwVkRaUGUljb0kFC1dv4+cvfMTGomL65mQzbeIwJo2J+3CUNBM1o05Bc5cVctucFRQWFeNAWWWUouIKjRQnIi0uPZLGF8bk8ez7W6rPSYVFxdw2ZwVzl6ntdCIpwaegWfPzKS6vPKSsrCLKrPn5IUUkIm3Zz1746LBzUnF5pc5JCaYEn4I2FhU3qlxEJJF0TgqHEnwK6psTvzFdXeUiIomkc1I4lOBTzLsbivjGeYPJrtWJTXZGhGkTh4UUlYi0ZdMmDjvsnJSeZozq1yWkiNoGJfgUsqeknC8/8DZvfbKLGZNHkpeTjRF7HnXG5JFqsSoioZg0Ju+Qc1LfnCxG9+9Cl/aZpNKj2slGz8GnmJfzt3J8n8706qyhGkUkeVVGnTSLDVCjIaubLqzhYqWFfLxlL2+u3QHAhGE9ldxFJOlF0gwzY8e+Ui77zULmvFMQdkgpRwk+Bfz30yv5zyffo7wyGnYoIiKN0qFdOnk52bowSQD1ZJcCfjllNLsOlKuKS0RanayMCPdfd7CGuehAGTntM0OMKHUoI7RSW/aU8Kt/fkw06nTv2I7jenYMOyQRkaPy2sfbOPOnC1iiES+bhRJ8K/X0uxu575U1rN95IOxQRESaxYi+XbhkZG+G9OoUdigpQa3oWyl3p2BXMf27tQ87FBGRZldRGaVgVzEDe3QIO5Skplb0KWJfaQXfenwZhUXFmJmSu4ikrBnPrmLSbxeyfV9p2KG0Wmpk14qs37GfVz7axmWj+5KnLh5FJIVd95mBDOzRgR4d24UdSquV0Cp6M7sI+CUQAe5395m15v8HcBNQAWwDbnT39cG8SmBFsOin7n7ZkfaXqlX07o5ZbBz3vSXldMrKCDkiEZGWs277fiJpqrWMJ5QqejOLAPcAFwMnAFeb2Qm1FlsGjHP3k4AngbtqzCt299HBzxGTe6oqr4zy/x59h78tjXUCoeQuIm1JNOpM/eMSbnlsmbq1baREVtGPB1a7+1oAM3scuBxYWbWAuy+osfybwLUJjKdVqqh09pZUsK+0IuxQRERaXFqa8bMrR5GdEamuyZSGSWSCzwM21JguAE6tZ/mvAM/WmM4ysyXEqu9nuvvceCuZ2VRgKsCAAQOOKuBkEo06le5kZ0Z4+MbxRNL0wRaRtumkfjnVr/++vJBzhuaqM5wGSIpW9GZ2LTAOmFWj+JjgvsIXgbvNbHC8dd19truPc/dxubm5LRBty7jzHyuZ+sgSyiujSu4iIkBhUTHTnnyP372yNuxQWoVEXsEXAv1rTPcLyg5hZucD3wfOcffq5yHcvTD4vdbMXgbGAGsSGG9SGdqrE5npaaQruYuIALGhr//yb5/hxL6dww6lVUhkgl8MDDGzQcQS+xRiV+PVzGwMcB9wkbtvrVHeFTjg7qVm1gM4g0Mb4KWUucsKmTU/n41FxfTqksX0i4bzxVNT53aDiEhzGd0/Vl2/r7SCWx9fxocb97Bpdwl9c7KZNnEYk8bkhRxh8khYgnf3CjO7BZhP7DG5B9z9AzO7E1ji7vOIVcl3BP4aNJ6oehzueOA+M4sSu40w091Xxt1RKzd3WSG3zVlBcXklAJt3l/Ddv70HoA+qiEgd7n7xI/75YfV1IYVFxdw2J/Zktc6dMeqqNmRnzHyJwqLiw8rzcrJZOP28ECISEUl+OnfGqKvaJLYxzge0vnIREdG5syGU4EPWKSv+XZK+6opWRKROdZ0jde48SAk+BOu27+eDjbsBuONfTiAr/dC3ITsjwrSJw8IITUSkVZg2cRjZGZFDyrIzInzngqHc+vgyXv1oW0iRJQ8l+BYWjTo3PbKE2+e+j7vzhZP7M/MLJ5GXk40Ru380Y/JINRIREanHpDF5zJg88rBz5xlDe7By4x427y4JO8TQqZFdCyksKqZP5yzS0ox3NxTRq3MWvbtkhR2WiEjKKa2oJDOShpnxcv5W0sw4e2jqdIRWkxrZhWzNtn2c/7+v8Mc31wMwqn+OkruISIK0Sz/Yb/3vXlnDT59bRTSaOhezDaXx4BOovDJKRiSNY3t04OZzBnPBCb3CDklEpE156Ibx7NhfRlqaUVJeybsbijj12O5hh9UidAWfIM+u2MT5P3+FnfvLMDNuPX+IWneKiLSwrIwIecG598GF67hq9pus3ro35Khahq7gE2Rgjw4c26MD5ZXRsEMRERHghjMGMqBbe47r2QmAbXtLye3ULuSoEkdX8M3o8bc/5e4XPwLg+D6defCG8fTqrHvtIiLJICsjwudO6gPApzsOMGHWAh59a33IUSWOruCb0bsFu9mw8wAVlVHSI/ruJCKSrHI7tePa047h3GE9gdgjzGkpNnqnHpNrpJojv/XNyeKsobncfPZgBvboQEl57NGMVPuQiIikum89vozcTu04sW+XGuf45B+hrr7H5HQF3wi1R34rLCrh8bc3sKmomIdvPJWsWr0qiYhI8quMOjntMynYVcyf3vy0xjm+dY9Qp3rkRpg1P7/6ja/p4637QohGRESaQyTN+OFlJ/JeQdFh5/ji8kpmzc8PKbKjowR/BB9u2sN/PvkuO/aV1jlK0aYidYkoItLabazjXF5YVMzX//xOq+ssRwm+lnXb93PTw0t4d0MRAPtLK3h+5RbW7zyg0YtERFJYXefyzlnplFVEq9tXTfvru3zjsWXV88sqkvNx6IQmeDO7yMzyzWy1mU2PM7+dmT0RzH/LzAbWmHdbUJ5vZhObsv+5ywo5Y+ZLDJr+f5wx8yXmLiusnlf1TWzX/jKuuHdR9byOWems3rqXnfvLABg7oCvv3H4BYwd0rXP0Io38JiLS+tV1jr/z8hH8/ssH27Ed0709g7q3r56efO9Cvvvke9XTW/eWULMBe325KJES1sjOzCLAPcAFQAGw2MzmufvKGot9Bdjl7seZ2RTgp8BVZnYCMAU4EegLvGhmQ9398BvgdTi8QVyssYRHnfteW8u5w3vy3YuG0yU7g+zMCOmR2DezHh3b8fK0c6u3U7NFfFUji9bUwlJERBqmoef4W84bUv3a3bl4RJ/q3vIqKqOcO+tlrjntGL53yfHMXVbId//2HqXBVX5LNtxL2GNyZvYZ4IfuPjGYvg3A3WfUWGZ+sMwbZpYObAZygek1l625XH37rPmY3BkzX6Iwzj3zvJxsLh7Rm5H9unD5aCVmERFpPiXllTy5tIDj+3Ti5GO6cdpPXmTzntLDlsvLyWbh9POOen9hPSaXB2yoMV0AnFrXMu5eYWa7ge5B+Zu11o2bjc1sKjAVYMCAAdXldTWI21hUzO2XntCIP0NERKRhsjIiXHvaMdXTW+Ikd6g7RzWnVt/Izt1nu/s4dx+Xm3twvF81iBMRkbCFmYsSmeALgf41pvsFZXGXCarouwA7GrhuvdQgTkREwhZmLkpkgl8MDDGzQWaWSazR3Lxay8wDrgteXwG85LFGAfOAKUEr+0HAEODtxux80pg8ZkweSV5ONkbsfseMySPVIE5ERFpMmLkooX3Rm9klwN1ABHjA3f/HzO4Elrj7PDPLAv4IjAF2AlPcfW2w7veBG4EK4Fvu/uyR9tcSfdGLiIgki/oa2WmwGRERkVaqvgTf6hvZiYiIyOGU4EVERFKQEryIiEgKUoIXERFJQSnVyM7MtgHr48zqAWxv4XCSlY7FQToWMToOB+lYHKRjEZPsx+EYd8+NNyOlEnxdzGxJXa0M2xodi4N0LGJ0HA7SsThIxyKmNR8HVdGLiIikICV4ERGRFNRWEvzssANIIjoWB+lYxOg4HKRjcZCORUyrPQ5t4h68iIhIW9NWruBFRETaFCV4ERGRFJTyCd7MLjKzfDNbbWbTw44nLGb2gJltNbP3w44lTGbW38wWmNlKM/vAzG4NO6awmFmWmb1tZu8Gx+K/w44pTGYWMbNlZvaPsGMJk5mtM7MVZrbczNr06F1mlmNmT5rZKjP70Mw+E3ZMjZHS9+DNLAJ8BFwAFBAbo/5qd18ZamAhMLOzgX3AI+4+Iux4wmJmfYA+7v6OmXUClgKT2uhnwoAO7r7PzDKA14Fb3f3NkEMLhZn9BzAO6Ozul4YdT1jMbB0wzt2TuXOXFmFmDwOvufv9ZpYJtHf3orDjaqhUv4IfD6x297XuXgY8DlweckyhcPdXgZ1hxxE2d9/k7u8Er/cCHwJ54UYVDo/ZF0xmBD+p+42/HmbWD/gccH/YsUhyMLMuwNnAHwDcvaw1JXdI/QSfB2yoMV1AGz2Zy+HMbCAwBngr3EjCE1RLLwe2Ai+4e1s9FncD/wlEww4kCTjwvJktNbOpYQcTokHANuDB4NbN/WbWIeygGiPVE7xIXGbWEfgb8C133xN2PGFx90p3Hw30A8abWZu7fWNmlwJb3X1p2LEkiTPdfSxwMfD14PZeW5QOjAXudfcxwH6gVbXjSvUEXwj0rzHdLyiTNiy43/w34FF3nxN2PMkgqHpcAFwUdiwhOAO4LLj3/Dhwnpn9KdyQwuPuhcHvrcBTxG51tkUFQEGNWq0niSX8ViPVE/xiYIiZDQoaSEwB5oUck4QoaFj2B+BDd/952PGEycxyzSwneJ1NrDHqqnCjannufpu793P3gcTOES+5+7UhhxUKM+sQND4lqI6+EGiTT964+2Zgg5kNC4o+C7SqxrjpYQeQSO5eYWa3APOBCPCAu38QclihMLPHgAlADzMrAO5w9z+EG1UozgC+BKwI7j0DfM/dnwkxprD0AR4OnjZJA/7i7m36ETGhF/BU7Hsw6cCf3f25cEMK1TeAR4MLxLXADSHH0ygp/ZiciIhIW5XqVfQiIiJtkhK8iIhIClKCFxERSUFK8CIiIilICV5ERCQFKcGLiIikICV4ERGRFKQELyJNYmanmNl7wbjyHYIx5dtcX/YiyUod3YhIk5nZj4EsIJtYv90zQg5JRAJK8CLSZEEXnouBEuB0d68MOSQRCaiKXkSORnegI9CJ2JW8iCQJXcGLSJOZ2TxiQ6wOAvq4+y0hhyQigZQeTU5EEsfMvgyUu/ufgxHpFpnZee7+UtixiYiu4EVERFKS7sGLiIikICV4ERGRFKQELyIikoKU4EVERFKQEryIiEgKUoIXERFJQUrwIiIiKej/A8RyHzzhl74zAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "id": "UuKya1HUDpYC" }, "source": [ "## Boundary Conditions\n", "To account for the wrap-around boundary condtions \n", "\\begin{equation}w_{-1,j}=w_{N,j},\\end{equation}\n", "and\n", "\\begin{equation}w_{N+1,j}=w_{0,j}.\\end{equation}" ] }, { "cell_type": "code", "metadata": { "id": "ZTVwHZ3rDpYD" }, "source": [ "for i in range(0,N+1):\n", " ipos[i] = int(i+1)\n", " ineg[i] = int(i-1)\n", "\n", "ipos[N] = 0\n", "ineg[0] = N" ], "execution_count": 4, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "N7TzYf41DpYE" }, "source": [ "## Lax-Wendroff Method\n", "The Lax-Wendroff method for the Wave Equation is\n", "\\begin{equation}\n", "\\frac{w_{ij+1}-w_{ij}}{k}+a\\big(\\frac{w_{i+1j}-w_{i-1j}}{2h}\\big)-\\frac{a^2k}{2}\\big(\\frac{w_{i+1j}-2w_{ij}+w_{i-1j}}{h^2}\\big)=0\n", "\\end{equation}\n", "Rearranging the equation we get\n", "\\begin{equation}\n", "w_{ij+1}=w_{ij}-\\frac{\\lambda}{2} a(w_{i+1j}-w_{i-1j})+\\frac{\\lambda^2}{2} a^2\\big(\\frac{w_{i+1j}-2w_{ij}+w_{i-1j}}{h^2}\\big)\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": "pn3ktBfEDpYF" }, "source": [ "lamba=k/h\n", "for j in range(0,time_steps):\n", " for i in range (0,N+1):\n", " w[i,j+1]=w[i,j]-lamba/2*(w[int(ipos[i]),j]-w[int(ineg[i]),j])+lamba*lamba/2*(w[int(ipos[i]),j]-2*w[i,j]+w[int(ineg[i]),j])/2\n", " \n", " " ], "execution_count": 5, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "V4E0rgeQDpYG" }, "source": [ "# Results" ] }, { "cell_type": "code", "metadata": { "colab": { "base_uri": "https://localhost:8080/", "height": 487 }, "id": "tdheSuXRDpYG", "outputId": "8250671b-9a67-4dfd-f4d6-f27223eef0b2" }, "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.xticks(np.arange(len(x)), np.round(x,3),rotation=45)\n", "plt.ylabel('w')\n", "\n", "plt.subplot(122)\n", "plt.imshow(w.transpose(), aspect='auto')\n", "plt.xticks(np.arange(len(x)), np.round(x,3),rotation=45)\n", "plt.yticks(np.arange(len(time)), np.round(time,2))\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 Wave Equation'%(np.round(r,3)),fontsize=24,y=1.08)\n", "fig.tight_layout()\n", "plt.show()" ], "execution_count": 6, "outputs": [ { "output_type": "display_data", "data": { "image/png": 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\n", 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