{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Example: Solving Ordinary Differential Equations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook we will use Python to solve differential equations numerically." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Import the required modules\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "# This makes the plots appear inside the notebook\n", "%matplotlib inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### First-order equations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's try a first-order ordinary differential equation (ODE), say:\n", "$$\\quad \n", "\\frac{dy}{dx} + y = x, \\quad \\quad y(0) = 1.\n", "$$\n", "This has a closed-form solution\n", "$$\\quad\n", "y = x - 1 + 2e^{-x}\n", "$$\n", "(Exercise: Show this, by first finding the integrating factor.)\n", "\n", "We are going to solve this numerically.\n", "\n", "First, let's import the \"scipy\" module and look at the help file for the relevant function, \"integrate.odeint\"," ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from scipy.integrate import odeint\n", "# ?odeint # Uncomment to view the help file for this function\n", "\n", "# Define a function which calculates the derivative\n", "def dy_dx(y, x):\n", " return x - y\n", "\n", "xs = np.linspace(0,5,100)\n", "y0 = 1.0\n", "ys = odeint(dy_dx, y0, xs)\n", "ys = np.array(ys).flatten()" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYMAAAEPCAYAAACgFqixAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(xs, ys)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Compare the numerical solution with the analytical solution by showing both on the same plot" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEACAYAAACj0I2EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nisT/A276rkQFDGnsAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y_exact = xs - 1 + 2*np.exp(-xs)\n", "y_difference = ys - y_exact\n", "plt.plot(xs, ys, xs, y_exact, \"+\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now take a look at the difference between the two series:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY0AAAEZCAYAAABrUHmEAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz\nAAALEgAACxIB0t1+/AAAIABJREFUeJzt3XeYVOX5xvHvQxNksSERFEEEO1GwYE0EGxhbCipgbyE/\nEzX2EhNWo7FrNLYkKiqJYEtQk5gogTWKYCyoASFYaQI2QJQO7++PZyY7O2w5MzszZ8r9ua69dufM\n2TPvDMvc83YLISAiIhJFi7gLICIipUOhISIikSk0REQkMoWGiIhEptAQEZHIFBoiIhKZQkOKipkd\nYGbT4y5HPpjZUjPbppnXGGlmVzdw3zAz+3tzrh+nUi9/pTDN05AkM/sI+AawBjAgAA+GEM6Ns1xS\ny8xGAnNCCL9o5nVOAc4MIXwrNyXL+PG7Ax8CrUII6+Iog2SnVdwFkKISgCNCCBOaOtHMWoYQ1jZ1\nLNNrlKMifZ7JDwX5ubhZiybCIPn4lq8ySH6oeUrS1fuf2MxOMbOXzOxWM/sMGNHAMTOzK83sIzNb\nYGYPmtlGiWt0N7N1Zna6mc0C/lnP4xxoZnNSbn9oZhea2VtmtsjMRptZm0bK+KKZ3WRmX5jZ+2Y2\nKO1aB6XcHmFmo9LKdqqZzTazz81suJntmXjsL8zsN2mPd7qZvZM491kz65Zy3zozO9vMZgIzU45t\nm/i5rZndknidFpnZv8xsg8R9j5nZ/MTxGjPbual/tNTnn1aG4WY2M1H+OxPHdwTuAfZNNJl9kTje\nxsxuNrNZice/O1mmxP2XmNnHZjbXzM5Iez4jE+f/1cyWAv3N7Dtm9oaZLUlcc0RKcV9IfF9sZl+a\n2d71lH8/M/t34nV4xcz2Tblvgpldnfj7+9LM/m5mm0V5naR5FBqSib2B9/AmrGsbOHYacDJwILAt\n0AG4M+063wZ2BAY28Djpn4CPBQ4DegC7Aac2UsZ+wHSgI3ATcH/jT2m9x+oH9AKOB34NXAEcBPQG\njjOzbwGY2THAZcB3gU7Ai8DotGsdk7he8k0/9bFuAfoC+wCbAZcAyU/mfwN64q/pG8Afm3gOjT2f\nI4A98NftODM7LIQwA/gRMCmE0CGEkHyzvSHx3HdNfN8K+EXi+Q4Cfpp4LXoB/et5rKHAL0MIHYCX\ngK+Ak0IIGyfK8SMzOzpx7rcT3zcKIWwUQngltfxmtinwF/zfoCNwG/DXxPHUxzsFf/03AC6K+iJJ\n9hQakm5s4lPposT3M1LumxdCuDuEsC6EsLKBY8OAW0MIs0IIy4DLgSFmlvxbC8CIEMLylGs05fYQ\nwsIQwmLgGaBPI+fOCiE8ELyz7iGgi5l9I+LjBODqEMKqEMI44GtgdAjh8xDCx3gw9E2cOxy4LoQw\nM9EMcz3Qx8y2Trner0IIi1OepwGYmeHhem4IYUFwk0MIqwFCCA+GEJYlbl8N7GZmHSI+h3TXhRCW\nhhDmABNo/LU7Czg/hLAkhPB14jkNTdx3LDAyhDAjhLACqK7n958KIUxOPIdVIYR/hRCmJW5PBcbg\nHyZSNdQ8dQQwM4TwSOJvawwwAzgq5ZyRIYT3E6/vY008N8kR9WlIumMa6dOYE+HYlsCslNuz8L+z\nLVKOzc2wTAtTfl4GdGnk3AXJH0IIy/39mSrgk4iPlXre8rTHXp64FkB34HYzuyVxO9lGvxW1r0lD\nz3Nz/JPxB+l3JML1V8DgxHkh8bU5sDTic0iV/tpV1XeSmXUCNgReT7xm4B8qkze2BF5N+ZU5rP+G\nX+dvwcz64cHTG2iT+Ho8YrnT/45I3N4q5faClJ8bfG6SW6ppSLrGOibr6zhNP/Yx/oaa1B1YTd03\nr7iG7H2NvzEmdW7GteYAw0MImyW+Ng0hVCU/aSc09Dw/A1bgTVDphuGfpg8KIWwCbIP/m+S6wzi9\nbJ/hb7y7pDynTRJNSwDzga4p53er5xrptx8BxgJbJZ7Lb6l9Hk39DXyMP/dU3YB5Tfye5JlCQ3Jt\nNHC+mW1jZlV4P8eYlJE0cY6WeRNvKmtlZnvin+ZTZVK2e4Erkp3UZraxmaVfr16JprORwK1m1sXM\nWpjZPokO/g7ASmCRmbUHriM/IbsQ6GpmrVPK9Hvg14laB2a2lZkdljj/MeA0M9vRzDYErozwGFXA\nohDC6kStY1jKfZ/ifTj1BSd4v852ZjbEzFqa2fHATnjzpMSopELDfOLXPWb2ezN7Ke7ylKlnEqNR\nkl9PZvj7DwCjgH8B7+OfXlPneWT6BtjcN8zU3/853on7BTCC9TuYm/rk/L/bIYSxeNPLGDNbDLwN\nDGrkd9OPXQT8B2/y+TxxLQMeBmbjn6inAi838LyiaOz5jAemAQvMLNkkdxk+qGFy4jk9B2wPEEL4\nO3AH3i8yE5iU+J3G+qXOBn5pZkvwkHn0fwUJYTn+gWJiou+sX52ChvAFcCT+On2W+H5ECGFRA89N\nCqQkJ/clRq58I4Tw+7jLIlKJEsN2/wNsoMl5lSWWmoaZ3W9mC83s7bTjg8xsRmJc+aWNXGIY3l4q\nIgViZt9NzOXYFB+e+7QCo/LE1Tw1krQx+olRI3cmju8CDE18msHMTjKfQNYlMaRxcWJIoIgUznB8\ndNm7+OCGs+MtjsQhliG3IYSXzNeeSdUPeDeEMAvAzMbgk6NmhBBG4e3kmFk1HjoiUkAhhMPjLoPE\nr5jmaaSObwcf494v/aQQQnWhCiQiInUVU2jkhJmVXs++iEgRCCE0Oey8mIbczsMn7yR1JcuJPCEE\nfYXAiBEjYi9DsXzptdBrodei8a+o4gyN9FmurwK9zFcbbQMMAZ6OpWQiIlKvuIbcPoJPWtrefBnq\n04LvN3AOPqFoGj6LOKsd3Kqrq6mpqclZeUVEylVNTQ3V1dWRzy/JyX2NMbNQbs8pWzU1NfTv3z/u\nYhQFvRa19FrU0mtRy8wIEfo0FBoiIhI5NIqpI1xERIpcWYaG+jRERKJRn4aap0REMqbmKRERyTmF\nhoiIRFaWoaE+DRGRaNSnoT4NEZGMqU9DRERyTqEhIiKRKTRERCSysgwNdYSLiESjjnB1hIuIZEwd\n4SIiknMKDRERiUyhISIikSk0isjIkXDkkXDAAdC7N1x0UdwlEhGpq1XcBciH6upq+vfvX1I7cq1d\nC5deCr/+NWy9NSxbBmecATffHHfJRKSc1dTUZDTaVKOnisRLL8FPfgJvvum3Q4AttoDXX/cQERHJ\nJ42eKjFjx8Ixx9TeNoN994VJk+Irk4hIOoVGEQgBnnqqbmiAh8bLL8dTJhGR+ig0isD06bByJfTt\nW/f4fvuppiEixUWhUQSeegqOPtqbpFLtuSdMnQorVsRTLhGRdAqNIlBf0xTAhhvCTjt5Z7iISDEo\ny9AopQUL58+HmTPhwAPrv1+d4SKST1qwsMSG3P72t/DCC/DII/XfP3o0PP44/OlPhS2XiFQWDbkt\nEQ01TSUlaxollIMiUsYUGjGaMcMn9Q0a1PA53bv791mzClMmEZHGKDRi8sIL3o/xm9/Axhs3fJ4m\n+YlIMVFoxOAPf4Bjj/V+jFNOafr8/fbTJD8RKQ5luWBhMQoB/vUvuP9+/z5hAuyyS7Tf3XdfGDMm\nv+UTEYlCo6fy7PPP4d574YEHoF07OO00OPVU6Ngx+jVWrPDzP/3U526IiOSaRk/FbPZs+OlPYbvt\n4IMP4NFH4T//gQsvzCwwANq29etMm5afsoqIRKXmqRx59VX45z992Y9p03y00xlneFBstVXzr7/b\nbvDWW7DXXs2/lohItsoyNAq5CdMrr0B1NbzzDgweDIcc4jWMnXfObVPSrrvC22/n7noiIqBNmArW\np7FqlY+AmjIFrrgCTj8d2rTJ3+ONGwe//KUP1RURybWofRplWdMohF//2pczf/dd2GCD/D/ebrt5\nTSOE9VfDFREpFNU0sjBvnr+JT5rkHdSF0qWLN4d161a4xxSRyqDRU3l0ySXwwx8WNjCgtjNcRCQu\nCo0Mvfiif/3sZ4V/7Cid4ePGwbJlhSmPiFSesg6NCRPgww9zd701a+AnP4GbboL27XN33agaq2mE\nAFddBYceCvfcU9hyiUjlKOvQePtt3zL1rLPgo4+af73HH/fFBY87rvnXykZDNY116+Dcc2HsWHjm\nGbj9dg84EZFcK+vQOO883xXvG9+APfaAn/+8edcbNw6OPz6+0Us77uiTBlObn9asgRNP9EmENTVw\n5JGwzTbwxBPxlFFyIwRf0PLzz+MuiUhdZR0a4Et2XHut713x+OPw0EPZX+vFF+GAA3JXtky1bg07\n7OCzzpNGjfIg+fvfa5dYv/BCuOUWbdxUqlas8A8CF1wAhx8OS5fGXSKRWmUfGkmdOvmn74su8k/l\nmVqwwBcM7N0792XLRHK+BsDatXDDDT7pr23b2nOOOgqWLPGQk9KycCEMGOA1yA8+8BryUUfB8uVx\nl0zEVUxogL/h33qrL/fx5ZeZ/e7Eib6vRcuW+SlbVLvuWtsZPnas1y4GDKh7TosWcP75XtuQ0jFr\nFuy9Nwwc6Evhb7gh3HWXr102eLCvQiASt4oKDYCTToL+/eHMMzNrvnnxRfjWt/JWrMhSZ4Zfdx1c\nfnn9fSynnOKTD2fOLHwZJXNr1sAJJ8CPfuRrmSX/TVu0gAcf9A8rV14ZZwlFXFmGRnV1daMLcN1+\nO0yenNlS48UWGsn5GEcfXf95G24Iw4fDNdcUtnySnWuv9SbGSy5Z/77WrX3ZmpEjVduQ3KupqaG6\nujry+RW7jMhpp3lTwI9+1PQ1v/wSttzSR7IUYp2ppnTpAptt5m8wjW0Xu3QpfPOb3sRxxBGFK59k\nZuJE+MEP4PXXG19G/8ADfQXl732vcGWTyqFlRJpwwAHw0kvRzp00yTskiyEwwGsbX30Fw4Y1fl6H\nDv7pdPhw+OKLwpRNMrNkiY+U+u1vm9535ZRTmjf6TyQXKjo0Jk6Mdm6xNE0lDR4MN97ozRZNGTDA\nP5mee27+yyXRheATMQcMgEGD4Jhjmv6dwYN9Ls6nn+a9eCINqtjmqRB80t+UKdC1a+PnHnig75kx\ncGCOCllgX38Nffp40Khpo7DWrfOtfidMgM6dvZmzVSu4806//8or4fvf9w7vKE46yVc5OO+8/JVZ\nKlPU5qmKDQ2A734Xhg71Wd4NWbnSJwh+/DFstFGOChmDiRN9vP/RR8PBB8NBB+VmG1px69Z5H1KH\nDrUBMH48XHyxj3w6+WT47DP/O1qyxN/8jzgi89UFxo3zvqw33sj9c5DKpk2YIkj2azQWGq+/7rOw\nSzkwAPbfH/79b3j+eXjqKe9Q3XZbf/MaMsRrXZKZMWO8FvHee/D++x4OK1b4h4wOHTxIrrvOd3jM\n1dIzAwZ489Tbb/ucHZFCq+iaxuTJ8H//501UDbnhBpg/34c8lpO1a+Gf/4SHH4a//MWb3m67zZtP\npHFLlsCPf+wfKKqr/UNFz54eFKtXe43is8/8eD62AL7iCq8Ba/Km5JKapyJYtco/Fc6b13BN4uij\nfdTKD36Qw0IWmaVLvb/j3nvh+ut9v3NtKeu1huuvhz//2T/V77WXD3e+9FIP2Vtu8fkwhfbf//oE\n1Y8/1r+T5I6G3EbQpo0PpZ08ueFz3n0XdtqpcGWKQ4cOvn7VuHG+F8ehh+ZmKflSNn587VL0d93l\nb9LTp/vPt97qr1McgQFeg2nRAmbPjufxpbJVdE0DfPRKixZw9dXr3xeCv6GWeid4Jtas8TfFm27y\nIBk+vLI+za5e7cOT//Y3+M1vGp5xH7ejjvIaoUbDSa6ophHR/vs3PMlvyRIPlEoJDPDhoJdcAi+8\n4BMDDz0U5syJu1SF8eWXvh/J7Nm+/HyxBgbA7rtrBJXEo+JDY9994dVX/RNmujlzYOutC1+mYrDz\nzj5M98AD4dvfLr+mkBdf9FrUH//oNcm5c30C57bb+uiyDh3iLmHjdt/dO+JFCq3iQ2OTTfyN4s03\n179v7tymJ/6Vs1atfLfD887zeR3z5sVdotxYvNiXYNl8c3jySV+fa4cdfDmPu+/2513skqFRZq3L\nUgJK4L9H/u2/v3+q3muvuscruaaR6qc/9SGeBx/sy1h07hx3iZrnggu86enaa/32unU+92GLLeIt\nVya6dvVyz5+vYdJSWAoNfHOm5G54qSq9ppHq0ks9OA480EcOHXRQ3CXKzrPP+pIeqbs3tmhRWoEB\nPjgh2a+h0JBCqvjmKfCJWe+/v/5x1TTq+vnP4Ve/gjPO8FE79b1mxWzJEu/HuP9+qKqKuzTNp85w\niUNJhYaZbW1mfzaz+8zs0lxdt1cvXwoinWoadZn5JMfp070pr18/n/y2dm3cJYvm/PN9vadSrSWl\nU2hIHEoqNIBvAo+HEM4E+uTqot26edtw+q5oqmnUr21bX8piyhT4xz/8TXjWrLhL1bjRo31o9Y03\nxl2S3NljD4WGFF4soWFm95vZQjN7O+34IDObYWYzG6hJTAbONLNxwN9zVZ7Wrb1GkToLOgTVNJrS\nrZvPIj/ySK95PPxwcY7mmTnTJ+w99ljxD6XNRI8evgSM9teQQoqrpjESqLM7hZm1AO5MHN8FGGpm\nOybuO8nMbgN+DPwihHAIcGQuC5Ter7F4sa9aWkkT+7LRsqUv//3cc3Dzzb7c/Pz5cZeq1ooVcNxx\nPru9T87qpsXBDPr2VW1DCiuW0AghvAQsSjvcD3g3hDArhLAaGAMckzh/VAjhfOBPwHlmdg/wYS7L\n1LNn3X4N1TIy06cPvPaar9e0224+aS4O69Z54C9a5Fvc/vSnPgdj+PB4ypNv6teQQiumIbdbAakL\nVszFg+R/QgjTgGObulB1dfX/fu7fvz/9+/dv8sF79apb01B/RubatPFP9N/9rk+UmzzZl1sv5GS5\nSy/1RQU32MA/iffs6UvAl+v6Wbvv7qvwimSqpqaGmpqajH8vtgULzaw78EwIYdfE7R8AA0MIP0zc\nPhHoF0LIaHfrTBcsTHrqKfj9731vCYDf/c43LbrvvowvJfjw1uOO8zfrRx+FjTfO/2OuXeu1wxde\ngO23z//jFYMZM3xEWKkNf5biU4oLFs4DuqXc7po4VhCqaeTWxhvDX//qb9777luYtateftl3IKyU\nwADYbjv45BNvjhMphDhDwxJfSa8Cvcysu5m1AYYAT2dz4erq6oyrXdtuCx9+WDvnQH0azdeqFdxx\nhy/j/ctf5v/xnngCBg/O/+MUk5YtvQ+psd0nRRpTU1NTp0m/KbE0T5nZI0B/oCOwEBgRQhhpZocD\nv8bD7P4QwvVZXDur5inwkHj5ZR9KesghvkT4YYdldSlJMX++r5o7e3b+hryuW+f/bs8/X/6bZqW7\n7DLvT6pvTxiRqIq6eSqEMCyEsGUIYYMQQrcQwsjE8WdDCDuEELbLJjCaK3UElWoaudOli+98N2ZM\n/h7jlVe8SazSAgNg0CD4e85mLYk0rpj6NGKX7NdITuxTn0bunHWWDzTIl0psmkrabz/fN1yT/KQQ\nyjI0sunTgNqaRnJiXznNHo7bwIGwYAG89Vburx2C74tRqaHRpg0MGOBNcyKZKok+jXxqTp/GY4/5\n14gRMHSob/kpuVNdDZ99BnfemdvrvvYanHCCDz8t1/kYTbn3Xu+Pe/jhuEsipaqo+zSKVbKmMWeO\n+jPy4fTTfeHAZctye90nnvDVdys1MMD7Nf7xDx8QIJJPCo0UyfWnNEcjP7p1g7339jf5XFm3zmuH\nldo0lbTNNrDZZhp6K/mn0EixySa+/MQbb6imkS9nnpnbJpS//MXfLPv2zd01S5VGUUkhlGVoZNsR\nDl7bqKlRTSNf+vSpf8OrbN10k6+yW8lNU0kKDcmGOsKb0REO3qH6yCPePqyJfbm3fDlsuql/b+4b\n/eTJPmDh3XcLuyhisVq+3JdRmTPHa80imVBHeJZ69vTvap7Kj3btfOe/XKyVdPPNvoWrAsO1awcH\nHOCr+orki0IjTa9e/l3NU/mz5Zbw8cfNu8Z77/lqtqefnpsylYvDD4dnn427FFLOFBppevb03fo0\nsS9/unRp/u5+t97qGytVVeWmTOUi2a9RZq3OUkTKsmJfXV0defOldH36+CQ0yZ/mhsann/p8jxkz\nclemcrHddj5DfNo06N077tJIKch0MyZ1hEvBXXwxbL6577KXqbVr4eijfWHCm2/OfdnKwdlnQ48e\n/jqLRKWOcClazalpXHYZrFgB112X2zKVk8MP19BbyR+FhhRctqHx4IMwdiw8/ji0bp3zYpWNAQN8\nq+Kvvoq7JFKOFBpScNmExsSJvinW00/7DHBpWFWVL9cyfnzcJZFyVJah0ZwZ4ZJ/2Qy5vf56/6rE\nTZayodnhEpVmhKsjvOgtXQqdO3vzSdRZ4Xvt5Uuq7713fstWLqZO9b3ZP/hAS6xINOoIl6LVoYO/\nkS1dGv13PvkEttgif2UqN7vsAmvWwMyZcZdEyo1CQ2KRSb9GCLBwIXTqlN8ylRMzNVFJfig0JBaZ\nhMbSpb6+VPv2+S1TuRk0SEuKSO41GRpm1tLMNI1KciqT0PjkE1+9VTJzyCE+6mz58rhLIuWkydAI\nIawFDihAWaSCbLllZqGh/ozMbbyxh+3cuXGXRMpJ1LWnppjZ08DjwNfJgyGEP+WlVFL2unSJPuxW\nNY3sbb45fP65r0klkgtRQ6Mt8DlwUMqxABRlaDRnwUIpjC5d4K23op27cKFCI1sdO3poiDQk0wUL\nI4VGCOG0bAsUh0wmqkg81KdRGAoNaUryA/ZVV10V6fxIo6fMrKuZ/dnMPkl8PWlm2ttOsqbQKAyF\nhuRa1CG3I4GngS0TX88kjolkJdPQUEd4dhQakmtRQ6NTCGFkCGFN4utBQFOtJGubbupLnC9b1vS5\n6tPInkJDci1qaHxuZicm5my0NLMT8Y5xkayYRa9tqHkqewoNybWooXE6cBywAJgPDAZKqnNcio9C\nI/8UGpJrTY6eMrOWwPdDCEcXoDxSQaKExpo1sGSJv/lJ5hQakmtRZ4QPLUBZpMJECY3PPvNNl1q2\nLEyZyo1Co3A++ABmzIi7FPkXtXlqopndaWbfMrPdk195LVkzaBOm0hAlNNQJ3jwdO3rwSn799a++\n18tBB8Eee8Ctt0Zrev36a6ipgdWr817EBmW6CVPU0OgD7AJcDdyS+CraRQyTM8KluEUJDfVnNM+G\nG/rS8lFGqUl27r4bzjwTnnkG5syBG2/0TbB694YLLqg/tOfNg8svh222gbPPhp49PWi+/LLxx1qz\nBv7wB/jmN6FPHxg50kchNkf//v1zGxpm1gK4J4QwIO3roKZ+V6QxURYtVGg0j5maqPJl5UoPhTvu\n8NWE99nHm1EPPhgeeACmTfNzdtwRRozwMDnjDDjgAH/T//prmDQJ3nkH/vQnePVV6NEDzjvPQyfV\n3LkeTjvsAL//PdxyC9xwAzz2mAfPiBHw6aeFed5NdoSHENaZ2SXAYwUoj1SQKIsWamJf8yVDY+ut\n4y5JaQgBXnsNFi3yT/GrV3utYfvta7fOffZZOPdcP/7yy97vlq5zZ7jrLjj/fK9FLF0K/frBSSfB\n7rvDRhvVnrvnnjB6NMyaBffdBwMHQvfu3tQ1fjwsWACHHgoPPeShkzRwoPej3HabB8qwYXDhhR4+\nSStWwHvvwX//68Fy/PE+TypbkfYIN7Prgc+AR6m7yu0X2T90fmiP8NLxySew886Nt7lfdpn/57ri\nisKVq9wMGABXXumfgKVpjz3mn/Z794YNNvANwF57DVq39jfpBQu8FnHHHXD44fkpw5o18Le/eS3k\n4IM9ZJoaDDJ/Ptx+O/zud7BqVd1r9ejhodKmDUyYABddBOec482XSVH3CI8aGh/WcziEELZt8pcL\nTKFROtatg7Zt4auv/I+5PqefDvvt523Gkp3Bg+G44/xLGrdsGey0E4waBd/+du3xEDwo/vEPr22c\nfbb/7Raj1au9WSypbVsPvqQZM+BnP4NXXvFayWmnwSabRA+NqKvc9mj6LJHMtGjh/RULFkC3bvWf\noz6N5kvuqSFNu/FG75tIDQzwoOjd27+KXevW/tWQHXeEJ5/02tNtt8HVV2f2gaLRjvBEX0by52PT\n7vtV9IcRqV+nTo03Tyk0mk8d4dHMng2/+Y0HRyXYc0/44x9h+nTYaqvov9fU6KkhKT9fnnbfoOgP\nI1K/qiofRdIQdYQ3n0Ijmosv9nb+7t3jLklhde4Mv/hF9PObCg1r4Of6botkrKrK+zTqE4Im9+WC\nQqNpL7wAkyfDJZc0fW6layo0QgM/13dbJGONhcZXX3m/R/v2hS1TuVFoNG7pUh9wcccddUcTSf2a\n6gjfzcy+xGsV7RI/k7hdpGMHpJQ0Fhrqz8gNhUbjzjnHh7Uec0zcJSkNjYZGCEHLxEletW/fcJ+G\n+jNyQ6HRsEcf9VnZb7wRd0lKR9S1p0qKFiwsHY3VNNSfkRtxhMakSb4WUzGbPdtrGY88UtlNoJku\nWBhpcl8p0eS+0nLNNb7MwTXXrH/f734H//63L6sg2Vu71mc2r1hRd5JXPp1wgofG1KkNz8HJt3Xr\n4OSTPcA23dS/OnSoXQpk6lTvy7j00njKV2xyOrlPJF+qqhqep6E+jdxo2RI23tjXUurUKf+PF4Kv\nl3TssTB8uC+HYTGMtbzuOvjoI18naskSf/5Ll9be364dDNLEgYwpNCRWTXWEb1t0C9WUpmQTVSFC\nY8YMX7ri3nthr718SY6TT87/46Z6/nlfLPC113w1ZcmdsuzTkNLRVJ+GOsJzo5D9GhMm+CKJrVv7\nEuEXXeRLxRTK7Nm+kuwjjygw8kGhIbHSkNvCKGRojB/vO9iBr8561lnwk58U5rG//NKbxS68ELQP\nW34oNCRWCo3CKFRorFvn25cOGFB77Oc/9z0npk3L72PPmeN7Teyxh9duJD8UGhIrhUZhFCo0/vMf\nf6zUBfDatvUO8TvvzN/jvv467LsvnHKK92XE0fFeKdQRLrFqKDTWrIHFi31Zb2m+QoXG+PF1axlJ\nP/yhb7h13XW+d0Nz/exnvj1q27Y+nLimxodof+97zb+2NE6hIbFqKDQWLfId+5rarUyi6djRtxLN\ntwkT4MT0WdV1AAANr0lEQVQT1z/epYvvcjdypG9/2hwLFvh+2aNH+w51K1b4nhA77dS860o0Cg2J\nVfv29YfG4sW5+UQqrhAbMa1ZA//6V8OTMc85x0c1nXeeL0SZrcceg6OO0hyLuKhPQ2KVDI30SfxL\nlviENMmN9OaplSvhL3/J7WO88QZsvXXD/VD77OP/ps8+27zHGT0ahg5t3jUkewoNiVWbNt4EtWpV\n3eMKjdxKD42xY32pj1yuuJOcn9EQM69tNKdD/MMP4b334JBDsr+GNI9CQ2JXX7+GQiO30kNj1Cif\n0/DJJ7l7jNT5GQ05/ngf6TRzZnaP8eijMHhw43tgS34pNCR2Co38S4ZGCB4UL70Eu+4K//1v7h5j\nyhTo16/xc9q1847yP/whu8cYPRqGDGn6PMkfhYbETqGRf23b+gq3X38NY8bAkUf6bO1chcaSJX7t\nLl2aPnfIEC9Dpk1j77zjwfetb2VXRskNhYbETqFRGB07+orCo0b5KKYddsi+mSjd++9Dr17RJtXt\ntZePtJoyJbPHGD3am7eaM/JKmq+kXn4z28nMHjWzu8zsB3GXR3JDoVEYHTvCxIkwd65vb7r99rmr\nabz/PvTsGe1cM69tPPpo9OuHoFFTxaKkQgM4HLgjhPBjoMCLLUu+KDQKo2NHuP12GDbMm6p22CF3\nofHee17TiCrTJqq33vLve+yRedkkt2IJDTO738wWmtnbaccHmdkMM5tpZvXtpzUKGGJmNwKbFaSw\nkncKjcLo2NGX3jjpJL/dq5fPEl+9uvnXzjQ0vvlNn6MzeXK0859/3ifzaU2p+MVV0xgJDEw9YGYt\ngDsTx3cBhprZjon7TjKzW4FWIYRzgMuABvZ7k1Kj0CiMjh2hd2/YbTe/vcEGvt/Ehx82/9qZhkay\niWrMmGjnjxunuRnFIpbQCCG8BCxKO9wPeDeEMCuEsBoYAxyTOH9UCOECoI2Z/RZ4CLipkGWW/Klv\nKRGFRu7ts4/vM5H6aT1XTVSZ9GkkHX88PP6472HemJUrfWl17Y9RHIpp7amtgDkpt+fiQfI/IYRZ\nwPCmLlRdXf2/n/v3709//bUVNdU0CqO+LVdzMYJq2TIfldW1a2a/t8MOvjPjiy82HgiTJvkKuVqL\nLLdqamqoqanJ+PeKKTRyJjU0pPhVVcGnn9Y9tmSJ3iQKYfvt4c03m3eNDz6AHj2yW5F4yBAfFdVY\naKhpKj/SP1BfddVVkX6vmEZPzQO6pdzumjgmZa6qyieGpVq8WDWNQshF81RyjkY2hg2DJ57w5c0b\n8s9/KjSKSZyhYYmvpFeBXmbW3czaAEOAp2MpmRRUevPUypXezt2uXXxlqhS5aJ56773M+zOStt4a\n+vaFpxv4n75kCUyd6rvySXGIa8jtI8DLwPZmNtvMTgshrAXOAZ4DpgFjQgjTs7l+dXV1Vm11Eo/0\n0Ej2Z2h4Zf5tuSUsXeqLF2Yr05FT6U49FR58sP77amo8MNq2zf760riampqMmvQt5HJt5CJgZqHc\nnlO5e+45uPlm/w7w7rs+Jv/99+MtV6Xo29e3St1rr+x+/9BDfVRWtpsiff21d6K/8876a1ede67f\nd8kl2V1bojMzQghNflQrpj4NqVAN1TSkMJpqopo6tfHfb06fBviQ6+9/v/6Vb8eN8yVPpHgoNCR2\nCo14NbYG1Rdf+Ozt11+v//5Vq2DePOjevXllOPVUeOihusuKzJsHCxdCnz7Nu7bkVlmGhvo0SotC\nI16NjaBKrkR7zz313//RR9581NxNkQ44AJYvrxtO48b5pk7ZDOWV6DLt0yjb0NCEvtKh0IhXY81T\nU6b4zO0nn4RF6Ws40PymqSQzOOUU7xD/6CM4+2w4//z6JyRKbvXv31+hIaVFoRGv7bf30Fi3bv37\npkyBgQPhO9/x5qN0zRlum+7kk+GBB3wl2002gRkz4KijcnNtyR2FhsSuXTuf3JVcg0ihUVgbbeRf\n8+qZSjtlio+uOvtsuPvu9YOlucNtU22zDYwd67WXX/0KvvGN3FxXcqssQ0N9GqXFzEfQJGeFKzQK\nb5dd4O236x5btsybinbeGfbbz8N9/Pi65+QyNAAOO0zLxxSa+jRQn0YpSm2iUmgU3kEHecdzqrff\nhh13hDZtPNiTtY1UuerTkPioT0NKkkIjXocdVju5MinZNJV0wgk+Qzu5/8batV4T6dGjUKWUYlCW\nq9xK6UldtFChUXh9+/qciLlza5c4Tw+Nqiq4+GLYdVfvrN5nH+jUSWuEVRrVNKQopNc01K5dWC1b\n+szr1Caq9NAAuPxyWLDAw+Orr2q3jpXKUZY1jWSfhvo1Soeap+KXbKI69VTfN3zatNqtYVO1bw9H\nHOFfUvoy3YxJCxZKUTj2WDjuOP/eubN/yk1fvE7ya/Zsb3ZauNADY/Dg3GwFK6Uh6oKFZVnTkNKj\nmkb8unWDjh19J7+pU9dvmhIBhYYUiWRorFoFa9aoczUuySaqhQsVGlI/dYRLUUiGhjZgilcyNOrr\nBBcB1TSkSLRv76GhvcHj1b8/DB3qoa3QkPqUZU1Dy4iUnvSahsSjqgp2393XourUKe7SSCFou1eN\nnipJ990HkybBsGFwzTUwYULcJapc114LkyfDM8/EXRIpJI2ekpKimkbxOOccOPHEuEshxUqhIUVB\noVE8kkuli9SnLPs0pPQoNERKg0JDikJywUKFhkhxU2hIUVBNQ6Q0lGVoaMht6VFoiMRDQ2415LYk\nLV7se0QfcogvXHjccXGXSKSyRB1yW5Y1DSk9yRnh2ktDpLgpNKQotG7tGwEtXKjmKZFiptCQolFV\nBfPmKTREiplCQ4pGVRV88YVCQ6SYKTSkaFRV+XeFhkjxUmhI0aiqglattAGTSDFTaEjRqKrSBkwi\nxa4sQ0OT+0pTMjREpHA0uU+T+0rWCSfA9Onwxhtxl0Sk8mhyn5Qc1TREip9CQ4qGQkOk+Ck0pGgo\nNESKn0JDisYmm8Dmm8ddChFpjDrCpWgsWwarV6u2IRKHqB3hCg0REdHoKRERyT2FhoiIRKbQEBGR\nyBQaIiISmUJDREQiK8vQ0IKFIiLRaMFCDbkVEcmYhtyKiEjOKTRERCQyhYaIiESm0BARkcgUGiIi\nEplCQ0REIlNoiIhIZAoNERGJTKEhIiKRKTRERCQyhYaIiESm0BARkcgUGiIiEplCQ0REIlNoiIhI\nZAoNERGJrGhDw8x6mNl9ZvZYyrENzexBM/utmQ2Ls3wiIpWoaEMjhPBhCOHMtMPfBx4PIQwHjo6h\nWCVFW97W0mtRS69FLb0Wmct7aJjZ/Wa20MzeTjs+yMxmmNlMM7s04uW6AnMSP6/NaUHLkP5D1NJr\nUUuvRS29FpkrRE1jJDAw9YCZtQDuTBzfBRhqZjsm7jvJzG41sy7J01N+dQ4eHOnHRUSkAPIeGiGE\nl4BFaYf7Ae+GEGaFEFYDY4BjEuePCiFcAKw0s3uAPik1kT8Dg83sLuCZfJddRETqshBC/h/ErDvw\nTAhh18TtHwADQwg/TNw+EegXQjg3B4+V/yckIlKGQghNtuC0KkRBCinKkxYRkezENXpqHtAt5XbX\nxDERESlihQoNo27H9atALzPrbmZtgCHA0wUqi4iIZKkQQ24fAV4Gtjez2WZ2WghhLXAO8BwwDRgT\nQpieg8fKZhhv2WlomHMlMrOuZjbezKaZ2X/MrNn9ZqXKzDYws1fMbEritRgRd5niZmYtzOwNM6vo\nD61m9pGZvZX42/h3o+cWoiO8EBLDeGcCBwMf47WZISGEGbEWLAZmdgDwFfBwcvBBpTKzzkDnEMKb\nZlYFvA4cU4l/F+CrKoQQlplZS2AicG4IodE3iXJmZucDewAbhRAqdsKwmX0A7BFCSB/pup6inRGe\nhQaH8VaaBoY5V6QQwoIQwpuJn78CpgNbxVuq+IQQliV+3AAfCFMenxqzYGZdge8A98VdliJgRMyD\ncgqNraidLQ4wlwp+c5D1mdk2QB/glXhLEp9Ec8wUYAHwfAjh1bjLFKPbgIup4OBMEYDnzexVMzur\nsRPLKTREGpRomnoCOC9R46hIIYR1IYS++IjFvc1s57jLFAczOwJYmKiFpg/UqUT7hxB2x2teP040\ncdernEJDw3ilXmbWCg+MUSGEp+IuTzEIIXwJTAAGxV2WmOwPHJ1oyx8NDDCzh2MuU2xCCPMT3z/F\nV97o19C55RQaGsZblz491XoAeCeEcHvcBYmTmW1uZhsnfm4HHApU5ICAEMIVIYRuIYRt8feK8SGE\nk+MuVxwSW05UJX5uDxwGTG3o/LIJjcQw3p+Q42G8pai+Yc5xlykuZrY/cAJwUGI44RtmVqmfrrsA\nE8zsTbxf5x8hhL/FXCaJ3xbAS4m+rsn4kk/PNXRy2Qy5FRGR/CubmoaIiOSfQkNERCJTaIiISGQK\nDRERiUyhISIikSk0REQkMoWGiIhEptAQEZHIFBoieWZmeyY2uGljZu3NbGqlLhQopU8zwkUKwMyu\nBtolvuaEEG6IuUgiWVFoiBSAmbXGF9VcDuwX9B9PSpSap0QKY3OgCugAtI25LCJZU01DpADM7Cl8\n34YewJYhhHNiLpJIVlrFXQCRcmdmJwGrQghjzKwFMNHM+ocQamIumkjGVNMQEZHI1KchIiKRKTRE\nRCQyhYaIiESm0BARkcgUGiIiEplCQ0REIlNoiIhIZAoNERGJ7P8B12btdhdf30wAAAAASUVORK5C\nYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y_diff = np.abs(y_exact - ys)\n", "plt.semilogy(xs, y_diff)\n", "plt.ylabel(\"Error\")\n", "plt.xlabel(\"x\")\n", "plt.title(\"Error in numerical integration\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Exercise: Experiment with the options of \"odeint\" to improve the accuracy of the integration." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Second-order ordinary differential equations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose we have a second-order ODE such as a damped simple harmonic motion equation,\n", "$$\n", "\\quad y'' + 2 y' + 2 y = \\cos(2x), \\quad \\quad y(0) = 0, \\; y'(0) = 0\n", "$$\n", "We can turn this into two first-order equations by defining a new depedent variable. For example,\n", "$$\n", "\\quad z \\equiv y' \\quad \\Rightarrow \\quad z' + 2 z + 2y = \\cos(2x), \\quad z(0)=y(0) = 0.\n", "$$\n", "We can solve this system of ODEs using \"odeint\" with lists, as follows:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def dU_dx(U, x):\n", " # Here U is a vector such that y=U[0] and z=U[1]. This function should return [y', z']\n", " return [U[1], -2*U[1] - 2*U[0] + np.cos(2*x)]\n", "U0 = [0, 0]\n", "xs = np.linspace(0, 10, 200)\n", "Us = odeint(dU_dx, U0, xs)\n", "ys = Us[:,0]" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAY4AAAEZCAYAAACAZ8KHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nxOGccy4n/x+gaicl6hS9pgAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(xs,ys)\n", "plt.xlabel(\"x\")\n", "plt.ylabel(\"y\")\n", "plt.title(\"Damped harmonic oscillator\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Predator-Prey Equations" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Also known as Lotka-Volterra equations, the predator-prey equations are a pair of first-order non-linear ordinary differential equations. They represent a simplified model of the change in populations of two species which interact via predation. For example, foxes (predators) and rabbits (prey). Let $x$ and $y$ represent rabbit and fox populations, respectively. Then\n", "\\begin{align}\n", " \\frac{dx}{dt} &= x (a - b y) \\\\\n", " \\frac{dy}{dt} &= -y (c - d x) \n", "\\end{align}\n", "Here $a$, $b$, $c$ and $d$ are parameters, which are assumed to be positive. " ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": false }, "outputs": [], "source": [ "a,b,c,d = 1,1,1,1\n", "\n", "def dP_dt(P, t):\n", " return [P[0]*(a - b*P[1]), -P[1]*(c - d*P[0])]\n", "\n", "ts = np.linspace(0, 12, 100)\n", "P0 = [1.5, 1.0]\n", "Ps = odeint(dP_dt, P0, ts)\n", "prey = Ps[:,0]\n", "predators = Ps[:,1]" ] }, { "cell_type": "code", "execution_count": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYYAAAEPCAYAAABGP2P1AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(ts, prey, \"+\", label=\"Rabbits\")\n", "plt.plot(ts, predators, \"x\", label=\"Foxes\")\n", "plt.xlabel(\"Time\")\n", "plt.ylabel(\"Population\")\n", "plt.legend();" ] }, { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEZCAYAAACNebLAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(prey, predators, \"-\")\n", "plt.xlabel(\"Rabbits\")\n", "plt.ylabel(\"Foxes\")\n", "plt.title(\"Rabbits vs Foxes\");" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The plot above illustrates that the system is periodic. Let's plot a few more curves in the phase space." ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYgAAAEZCAYAAACNebLAAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "ic = np.linspace(1.0, 3.0, 21)\n", "for r in ic:\n", " P0 = [r, 1.0]\n", " Ps = odeint(dP_dt, P0, ts)\n", " plt.plot(Ps[:,0], Ps[:,1], \"-\")\n", "plt.xlabel(\"Rabbits\")\n", "plt.ylabel(\"Foxes\")\n", "plt.title(\"Rabbits vs Foxes\");" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "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": "3.5.1" } }, "nbformat": 4, "nbformat_minor": 0 }