{ "cells": [ { "cell_type": "markdown", "id": "37467eca", "metadata": {}, "source": [ "## Les principaux schémas à un pas\n", "\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "1c26ac36", "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import math" ] }, { "cell_type": "code", "execution_count": 2, "id": "cdd0961a", "metadata": {}, "outputs": [], "source": [ "#schéma d'Euler\n", "def euler(f, t0, y0, h, tfin):\n", " t=np.arange(t0,tfin+h,h) # la subdivision, python n'atteint pas la borne superieure :-(\n", " y = np.zeros(len(t)) # initialisation\n", " y[0] = y0\n", " for n in range(len(t)-1):\n", " y[n+1] = y[n] + h*f(t[n], y[n])\n", " return y" ] }, { "cell_type": "code", "execution_count": 3, "id": "3fc14dc9", "metadata": {}, "outputs": [], "source": [ "# definition de la fonction dans l'EDO\n", "def f(t,y):\n", " return y" ] }, { "cell_type": "code", "execution_count": 4, "id": "3b1dc903", "metadata": {}, "outputs": [], "source": [ "#schéma du point-milieu\n", "def runge(f, t0, y0, h, tfin):\n", " t=np.arange(t0,tfin+h,h) # python n'atteint pas la borne superieure :-()\n", " y = np.zeros(len(t))\n", " y[0] = y0\n", " for n in range(len(t)-1):\n", " u = y[n] + (h/2)*f(t[n], y[n])\n", " y[n+1]= y[n]+ h*( f(t[n]+h/2,u) )\n", " return y\n" ] }, { "cell_type": "code", "execution_count": 5, "id": "c9df6170", "metadata": {}, "outputs": [], "source": [ "#schéma de Heun\n", "def heun(f, t0, y0, h, tfin):\n", " t=np.arange(t0,tfin+h,h) # python n'atteint pas la borne superieure :-()\n", " y = np.zeros(len(t))\n", " y[0] = y0\n", " for n in range(len(t)-1):\n", " u2 = y[n] + (h/3)*f(t[n], y[n])\n", " u3 = y[n] + (2*h/3)*f(t[n]+h/3, u2)\n", " y[n+1]= y[n]+ h*( (1/4)*f(t[n],y[n])+ (3/4)*f(t[n]+(2*h)/3,u3) )\n", " return y" ] }, { "cell_type": "code", "execution_count": 6, "id": "8df6f0d0", "metadata": {}, "outputs": [], "source": [ "#schéma de Runge-Kutta 4\n", "def RK4(f, t0, y0, h, tfin):\n", " t=np.arange(t0,tfin+h,h) # python n'atteint pas la borne superieure :-()\n", " y = np.zeros(len(t))\n", " y[0] = y0\n", " for n in range(len(t)-1):\n", " u2 = y[n] + (h/2)*f(t[n], y[n])\n", " u3 = y[n] + (h/2)*f(t[n]+h/2, u2)\n", " u4 = y[n] + h*f(t[n]+h/2, u3)\n", " y[n+1]= y[n]+ h*((1/6)*f(t[n],y[n])+ (2/6)*f(t[n]+h/2,u2) + (2/6)*f(t[n]+h/2,u3) + (1/6)*f(t[n]+h,u4) )\n", " return y" ] }, { "cell_type": "markdown", "id": "012a33cb", "metadata": {}, "source": [ "## Tracé des solutions approchées " ] }, { "cell_type": "code", "execution_count": 7, "id": "ae49c4f7", "metadata": {}, "outputs": [], "source": [ "t0, tfin = 0, 7\n", "y0,h=1, 1\n", "ye=euler(f, t0, y0, h, tfin)\n", "ym=runge(f, t0, y0, h, tfin)\n", "yh=heun(f, t0, y0, h, tfin)\n", "yrk=RK4(f, t0, y0, h, tfin)\n", "t=np.arange(t0,tfin+h,h)\n", "tt=np.arange(t0,tfin+0.01,0.01)\n", "## sol exacte\n", "z=np.exp(tt)" ] }, { "cell_type": "code", "execution_count": 8, "id": "648baa37", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "fig1 = plt.figure(figsize=(10, 8))\n", "plt.plot(t,ye,'-or')\n", "plt.plot(t,ym,'-og')\n", "plt.plot(t,yh,'-ob')\n", "plt.plot(t,yrk,'-om')\n", "plt.plot(tt,z,'-k')\n", "plt.legend(['Euler','Point milieu','Heun','RK4','solution exacte'])\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "c657e06b", "metadata": {}, "source": [ "## Tracé de l'erreur globale en log log " ] }, { "cell_type": "code", "execution_count": 10, "id": "5eb1e42a", "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pas = [1/4, 1/8, 1/16, 1/32, 1/64, 1/128]\n", "err = np.zeros((len(pas), 4))\n", "for i, h in enumerate(pas):\n", " yrk = RK4(f, t0, y0, h, tfin)\n", " yh = heun(f, t0, y0, h, tfin)\n", " yr = runge(f, t0, y0, h, tfin)\n", " ye = euler(f, t0, y0, h, tfin)\n", " t = np.arange(t0, tfin+h, h)\n", " z = np.exp(t)\n", " erreurrk = np.max(np.abs(yrk-z))\n", " erreurh = np.max(np.abs(yh-z))\n", " erreurr = np.max(np.abs(yr-z))\n", " erreure = np.max(np.abs(ye-z))\n", " err[i, :] = np.array([erreure, erreurr, erreurh, erreurrk])\n", "# calcul des pentes avec les droites de régression\n", "pe = np.polyfit(np.log(pas), np.log(err[:, 0]), 1)\n", "pm = np.polyfit(np.log(pas), np.log(err[:, 1]), 1)\n", "ph = np.polyfit(np.log(pas), np.log(err[:, 2]), 1)\n", "prk = np.polyfit(np.log(pas), np.log(err[:, 3]), 1)\n", "plt.loglog(pas, err[:, 0], '-or')\n", "plt.loglog(pas, err[:, 1], '-og')\n", "plt.loglog(pas, err[:, 2], '-ob')\n", "plt.loglog(pas, err[:, 3], '-om')\n", "#plt.loglog(pas, pas, '--or')\n", "plt.loglog(pas, np.power(pas, 2), '--og')\n", "plt.loglog(pas, np.power(pas, 3), '--ob')\n", "plt.loglog(pas, np.power(pas, 4), '--om')\n", "plt.legend([r'Euler pente=%.1f' % (pe[0], ), r'point milieu pente=%.1f' % (pm[0], ), r'Heun pente=%.1f' % (\n", " ph[0], ), r'RK4 pente=%.1f' % (prk[0], ), 'pente 2', '3', '4'], loc='best')\n", "plt.xlabel('log pas')\n", "plt.ylabel('log erreur')\n", "plt.title('convergence comparée RK4, Heun, Point milieu, Euler')\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "2736a8a7", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.12" } }, "nbformat": 4, "nbformat_minor": 5 }