{ "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": "1002_Wave Equation-Lax-Friedrich.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": "VuInPUo3DovT" }, "source": [ "# Wave Equation\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-Friedrich method to appoximate the solution of the Wave 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)." ] }, { "cell_type": "code", "metadata": { "id": "L6ezJqg2DovW" }, "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": "APbAdGHeDovX" }, "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": "RFLnCJ26DovX", "outputId": "ad3bba82-dc14-4256-a7f2-42effff00b53", "colab": { "base_uri": "https://localhost:8080/", "height": 324 } }, "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "id": "Ne7lTi8hDovZ" }, "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 $t[0]=0.$\n", "## 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": "Uh7dZmoPDovZ", "outputId": "73416538-8258-4908-8d8b-1e627aa98bfe", "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 (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)\n", "for i in range(0,N+1): \n", " ineg[i] = i-1\n", " ipos[i] = i+1\n", "\n", "\n", "ipos[N] = 0\n", "ineg[0] = N\n" ], "execution_count": 4, "outputs": [ { "output_type": "display_data", "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAfgAAAEfCAYAAACtadRFAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAAgAElEQVR4nO3deXxU9b3/8dcnk4SENSxhCyCILCrIIqJ1Raui1quU6hWrrUst1/5qa+9tucXWW3ttb6HS29rFWql1a63aWqTYq6JW3MAFEBRFooAgCfsS1uzz+f0xJyGESUhCJmcyeT8fjzwy53u2T85MzmfO93zP92vujoiIiKSWtLADEBERkeanBC8iIpKClOBFRERSkBK8iIhIClKCFxERSUFK8CIiIilICV7kKJmZBz8Dm7j+umD9Cc0Y0w+DbT7UXNtMBXUdazO7Pih/uYnbnRCsv64ZwhRpFkrw0uqZ2UNHc3KuZ7sTgkQ5qYnrjw7Wv74542pJZjbOzO42s+Vmtt3Mys1sh5m9aWZ3mdmIsGNMtCD5/9DMRocdi0hjKMGL1G0CcAdwpASfH/yU1yofHax//RHWXxOsf6DRESaImXUys8eBxcCtwCggB9gDdAFOBaYBK4LlWrvdxN6DT+PMu57Y+1hfgj8QrL+m2SMTaaL0sAMQae3cffhRrv/Z5oqlOZhZJ+A1Ykm9Avg98ADwjrtHzSwNOBG4EvgmcBUwJaRwm4W7PwU8dRTrvw0c1edApLkpwYtIbbOJJfcS4HJ3f77mTHePAiuIXb3/Evhjy4coIkeiKnpJaWb2cnB//nozyw7upeabWbGZbTWzx81sSK11BpqZE6uWBbiuRkO6wxrU1VUGPBhMnhNn/Qk1lq2zkZ2ZnW1mvzSzt8xso5mVBXE/Z2ZXNM9ROmR/J3Pwavz22sm9NnffAXyujm2NMbM/mdkGMysN7uHPN7Mv1LP/6mNhZt3M7Odm9kmwfqGZ/d7M+hzhb7gmaCOwz8x2mtlLZhY3xhrrHNbIrqoMOCcoerDWe7iuxrJHbGRnZuea2Rwz2xy8j5vN7CkzO6+edao/W2Y2IPj7C4Lj8YmZ/czMOtf3t0nbpSt4aSs6AwuBMUApEAVyiVUvX2Bm49296v5pJbAF6Ah0IHYlu7vW9iqPsL8tQHaw33JgZ635ZUcK2Mw6Aq/UKNoLFAdxTwQmmtlsd/+3I22rEaq2tRO4pyEreJwRq8xsKnAvBy8iiojdw78QuNDM/gRc7+51Hcd+wEPAMcTubzvQF7gJON/Mxrr7rjj7/Q3w9WAySuzYTwDONbNbG/L31FBM7H3sBmQQa39QXGP+toZuyMx+DHw/mHRin6eexNp3TDKzme5+Wz2bGEXsNkk3Yp+DNGAg8G1iXyBPd/fabUCkjdMVvLQV/w10BS4ilrQ7AmcDBcROmjOqFnT3De7eG/hZUPSEu/eu9bOhvp0F61cllEVx1l/UgJijwJPA54Hu7t7Z3bsEf8ctwD5gqpld2bBD0CDnBr9fcPeSpmzAzE7nYHJ/Eujv7l2JJfjbiSW4a4H6EtqvgV3A6e5e9X5dTuyLwsB465rZNRxM7j8jdsy6An2AR4Ky3Ib+He7+RPA+Vr1Xt9Z6D09pyHbMbAoHk/tvgJ5BXLnB3wkw3cyurWczDwHLgZHu3pnY8fgKsS+r44CvNvTvkrZDCV7ainbABe4+390r3T3q7q8B3wrmX2ZmmSHGdxh3P+DuV7r7XHffWaO8yN3vAf5fUPT/4m+hccwsAzgumHz3KDb1I2LnloXAFHcvAHD3fe7+P8DMYLnv1lO9XAqc7+5vBOtWuPs84MfB/ENuT5iZEfsSB/Cwu09z96Jg3S3EWsK/ArQ/ir+r0YK4fhRMPu7u33D37UFcO9z9m8BjwfwfBQ0Y4ykELnH394N1S939AWINIKHW8RABJXhpO55099VxyucRu6Jsx8Hk1lo8Hfw+zcwizbC9bjVe176l0CBm1o2DtQAz6qiC/ymx2x4dgUvq2NTs4P5+bXOD34PMrEON8tHA4Kr91l4puI3wkyOEnwijOfi5+nEdy1R9MRkIjK9jmZ+7e2mc8qrjkfL9EUjjKcFLW7E4XmFw33JrMNm15cJpGDNLN7OvBI3qNgWNqzxo/FV1DzqL5Il9DGDEvjS9Em8Bd98NLA0mx9axnbjvF7Er2So5NV5XbWeLu+fXse4iYo/9taSquLa5+wfxFgjiLay1fG1HOh7J8v5LElEjO2kr9tYzr+pec0ZLBNJQQSO7+cDpNYqLiTXuigbTvYLfHYDtR7nLmlft3epcqn5V97h3u/u+epYrqLV8bXHfL3cvidV6A4e+X1Xb2VjXDt291My2A73riau5VcVVWO9SseORRyOPBwc/uzqXy2F0BS+SvP6LWHLfDlwH9HL39u7eM2j8lVdjWYu3gcYIajOqbmOMOsrNtTvK9VNNVtgBSNujBC+SvKpax3/D3R9x96215veqvUIzWBD8vsDMmpKUqh4dyzaz+lqs96u1/NGq2k7fuhYIGlH2aKb9NVRVXP2PsFxzHw8RJXiRelRVgzf16vho16866S+rY/75TdxufWYHv7vRwNb5VqPOnFisVc/FnxtnccysC3ByMPlOE2KMp2o7vcxsaB3LnE7TqrKP5n2siquDmcVtQBfEm1dreZGjpgQvUrc9we+cepdK3PpVneuMrD0juD///drlR8vdlwB/CSb/x8wuqG95M+sO/F+N9XdysBbgu3U89vVdYlXW+4BnjjromOUcvL3w3ThxGjC9ids+mvexZlzfq2OZHwa/1wFvN2EfInEpwYvUrarV85lWqzvbRq5/gpmd2oT1Xwh+/9zMzqm6UjazU4B/At2bsM2G+CqxvuazgGfM7B4zG1uVrC1mhJn9N7HR0y6utf5/EbvqHQs8bmb9gvU6mtn3OJhoZ7r7HppB8BjcD4PJG83sp2aWE+y3F7Fe4M6jaSP2Vb2Pk4Pah8bGdXswebmZ/Tr4UoSZdTezXwFXB/NvD/r5F2kWSvAidXuZWALrBuRbrA/4dcFPv/pXBXf/GHiVWLXwmxYbR71q/dMasP/biTWw6x/EcsDM9hG7yhsJfLEpf1QD4t4DnEmsF7p0YlX1S4EyM9tBrJvdFcAPiHXF+3Ct9RcF60SJtSP41Mx2EuuF7n+IVXU/ysEOb5or7kc52L3ufwLbg/1uItbRzXdo2j3uPxL7m88MtlkYvIevNzCuJ4j93RDrgXBrENdW4BtB+cwgfpFmowQvUoegVflniZ3gC4k9a3xM8NPQe7mTgd8CnxDr2KVq/SM2YHP3tcQ6PvkTsWQQIZYkHwVOOdJAMEfD3fe4+5XB/n9NLKHvIZbQ9wBvEkvQx7v79XHWvw84BfgzsQTbkdgthxeAK9392nr6oT+auG8h1g3uW8R6wzNiz+Nf6u6/auI2VwEXAM8R+xt6E3sPj/glr8Y2bif2Wfo7sS9tHYEdxDpaOv8I/dCLNInFGSdCREREWjldwYuIiKQgJXgREZEUpAQvIiKSgpTgRUREUlBKDVDQo0cPHzhwYNhhiIiItIilS5dud/e43UKnVIIfOHAgS5YsCTsMERGRFmFm6+uapyp6ERGRFKQELyIikoKU4EVERFJQSt2DFxGRQ5WXl1NQUEBJSUnYochRyMrKol+/fmRkZDR4HSV4EZEUVlBQQKdOnRg4cCDBgITSyrg7O3bsoKCggEGDBjV4vYRV0ZtZfzNbYGYrzewDM7s1zjJmZr8ys9Vm9p6Zja0x7zoz+zj4uS5RcYpI/eYuK+SMmS8xaPr/ccbMl5i7rDDskKQRSkpK6N69u5J7K2ZmdO/evdG1MIm8gq8Avu3u75hZJ2Cpmb3g7itrLHMxMCT4ORW4FzjVzLoBdwDjAA/WnefuuxIYr4jUMndZIbfNWUFxeWzgt8KiYm6bswKASWPywgxNGkHJvfVrynuYsCt4d9/k7u8Er/cCHwK1zwiXA494zJtAjpn1ASYCL7j7ziCpvwBclKhYRSS+nz63qjq5Vykur2TW/PyQIhKRhmqRVvRmNhAYQ2yM5prygA01pguCsrrK4217qpktMbMl27Zta66QRdqkjUXFlFVEAfjL4g1s2h2/SnBjUTH5m/eyavMeNOS0HEnHjh2PuMxNN93EypWxCt6f/OQnh8w7/fTTm7yPzZs3M2XKFAYPHszJJ5/MJZdcwkcffdSAqOv38ssvc+mllwIwb948Zs6cCcDcuXOr/w6AH/zgB7z44otHvb+mSHiCN7OOwN+Ab7n7nubevrvPdvdx7j4uNzdub30iEkdl1Plg42527S8D4KVVWzh95kusKCwC4KT+XejULv5dvL452fz6pY+54cHF1VWHr3y0jSXrdrZM8JIwYbW5uP/++znhhBOAwxP8okWLmrRNd+fzn/88EyZMYM2aNSxdupQZM2awZcuWo463pssuu4zp06cDhyf4O++8k/PPP79Z99dQCU3wZpZBLLk/6u5z4ixSCPSvMd0vKKurXETqUd/JubwyysLV21mzbR8Aa7ft43O/ep0XPoyd7Mb078od/3IC/bq2B2B47878aNIIsjMih+wjOyPCtInD+O5Fw/nFVaOry+96bhW/ePHgldEf31zPwtXbGx2nhKeqzUVhUTHOwTYXzfX+vPzyy0yYMIErrriC4cOHc80111TXAE2YMIElS5Ywffp0iouLGT16NNdccw1w8Op83759fPazn2Xs2LGMHDmSv//97/Xub8GCBWRkZHDzzTdXl40aNYqzzjoLd2fatGmMGDGCkSNH8sQTTxwxxueee47hw4czduxY5sw5mNIeeughbrnlFhYtWsS8efOYNm0ao0ePZs2aNVx//fU8+eSTAPzzn/9kzJgxjBw5khtvvJHS0lIg1s36HXfcUf13rVq1qjkOd0Jb0RvwB+BDd/95HYvNA74ctKY/Ddjt7puA+cCFZtbVzLoCFwZlIlKHeCfnaU++y13PxU4WlVHn+gff5q9LCgAYnNuRX04ZzYRhsZqvrh0yueGMQfTqnFW9zUlj8pgxeSR5OdkYkJeTzYzJI5k0Jo/+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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "markdown", "metadata": { "id": "lGsOLqw7Dova" }, "source": [ "## Lax-Friedrichs Method\n", "The Lax-Friedrichs Method of the Wave Equation is,\n", "\\begin{equation}\n", "\\frac{w_{ij+1}-\\frac{w_{ij+1}+w_{ij-1}}{2}}{k}+a\\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}-\\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": "NIdHa0PeDovb" }, "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[int(ipos[i]),j]+w[int(ineg[i]),j])/2-lamba/2*(w[int(ipos[i]),j]-w[int(ineg[i]),j])\n", " " ], "execution_count": 5, "outputs": [] }, { "cell_type": "markdown", "metadata": { "id": "UWRbQmWNDovc" }, "source": [ "## Results" ] }, { "cell_type": "code", "metadata": { "id": "h_Q6wkoXDovd", "outputId": "c225361c-0a32-4df5-f60e-01c886a4bda2", "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", "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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" } } ] }, { "cell_type": "code", "metadata": { "id": "9TG4FTg_Dove" }, "source": [ "" ], "execution_count": 6, "outputs": [] }, { "cell_type": "code", "metadata": { "id": "7Bx6v_7CDove" }, "source": [ "" ], "execution_count": null, "outputs": [] } ] }