{ "metadata": { "name": "", "signature": "sha256:f8e9c4abe9dedb664fd9c2afa606870547ba4b54dff5625511bdd96406909fa3" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## A simple implementation of the Fisher-Kolmogorov\n", "\n", "We will show below a simple method to numerically solve the Fisher-Kolmogorov equation, by using a technique known as the \"method of lines\", which involves discretizing the space domain in equally-spaced intervals and turning the partial differential equation (PDE) into a (large) system of ordinary differential equations (ODEs).\n", "\n", "it is important to remember that methods to solve PDEs are considerably more involved than for ODE, and there is no single method for all equations. Also, depending on the type of PDE, the description of the problem (such as initial conditions, boundary conditions etc.) can be quite different and impose further restrictions." ] }, { "cell_type": "code", "collapsed": false, "input": [ "from numpy import *\n", "from scipy.integrate import odeint\n", "% matplotlib inline\n", "from matplotlib.pyplot import plot, xlabel, ylabel\n", "\n", "# parameters\n", "r = 1.\n", "K = 1.\n", "D = 0.1\n", "\n", "# the size of the spatial domain\n", "# his is actual size, such as \"kilometres\"\n", "L = 50.\n", "# the number of points in the grid\n", "grid_size = 100\n", "# the integration times\n", "t = arange(0, 300, 0.1)\n", "# the grid\n", "dx = L / (grid_size+1)\n", "grid = arange(0, L, dx)[1:-1]\n", "\n", "# the initial condition, consisting of a small \"square\" in the middle\n", "y0 = zeros_like(grid)\n", "y0[grid_size//2 - 2:grid_size//2 + 2] = 0.1\n", "\n", "# let's define the flux\n", "def fkpp(y, t, r, K, D, dx):\n", " # we calculate the spatial second derivative\n", " d2x = -2 * y\n", " d2x[1:-1] += y[2:] + y[:-2]\n", " d2x[0] += y[1]\n", " d2x[-1] += y[-2]\n", " d2x = d2x/dx/dx\n", " # then add the reaction terms\n", " dy = r * y * (1. - y/K) + D * d2x\n", " return dy\n", "\n", "y = odeint(fkpp, y0, t, (r, K, D, dx))" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "code", "collapsed": false, "input": [ "# let us plot the solution\n", "\n", "for i in linspace(t[0], t[-1], 10):\n", " plot(grid, y[int(i),:])\n", "xlabel('space')\n", "ylabel('population density')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 2, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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N8MVW8p9/vhxrCYCnnnqKrtgswcsuu4zi4mLLMdvaFuPziQtFQcF0MjP3caXf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CyLhXxt2WLPJA0OAs0Eme6sbUcHUnTPCnbyFY/HsWfPHsRiseP+3dHRUXRQXiEleMAVLVTUfDXF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\nzmP9wPXkvGlcfByRDros7EJoI2s9SR8cP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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "# now for some real fun! let's animate the solution!\n", "\n", "# THIS WILL NOT WORK IN THE NOTEBOOK\n", "# you have to copy this into an ipython shell and run it there\n", "\n", "def animate(grid, data, skip_frames=1, labelx='x', labely='', labels=[], log=False):\n", " import matplotlib\n", " # this is required. In case of problems, try one of:\n", " # GTK, GTKAgg, TkAgg, WX, WXAgg\n", " matplotlib.use('GtkAgg')\n", " from pylab import plot, legend, xlabel, ylabel, ion, draw, ylim, yscale\n", " import time\n", "\n", " ion()\n", "\n", " nvars = shape(data)[1]//len(grid)\n", " ldata = [ data[:,i*len(grid):(i+1)*len(grid)] for i in range(nvars) ]\n", " lines = []\n", " for d in ldata:\n", " lines.append(plot(grid, d[0])[0])\n", " xlabel(labelx)\n", " ylabel(labely)\n", " if len(labels) == nvars:\n", " legend(labels)\n", " ymin = 0 if data.min() > 0 else floor(data.min())\n", " ylim((ymin, ceil(data.max())))\n", " if log:\n", " yscale('log')\n", " ylim((1e-25, 15))\n", " for l in range(len(lines)):\n", " lines[l].set_ydata(ldata[l][0]) # initial condition\n", " draw()\n", " time.sleep(0.1)\n", " tstart = time.time() # for profiling\n", " for i in range(1, shape(data)[0]//skip_frames):\n", " for l in range(len(lines)):\n", " lines[l].set_ydata(ldata[l][i*skip_frames]) # update the data\n", " draw() # redraw the canvas\n", "\n", " print('FPS:' , shape(data)[0]/(time.time()-tstart))\n", "\n", "animate(grid, y)" ], "language": "python", "metadata": {}, "outputs": [] }, { "cell_type": "code", "collapsed": false, "input": [], "language": "python", "metadata": {}, "outputs": [] } ], "metadata": {} } ] }