{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## TP 3 Schéma des trapèzes implicites" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy.integrate import solve_ivp # solveur EDO de Python (initial value problem)\n", "from matplotlib import pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "def fun(t, y): \n", " return 3* y - 4*np.exp(-t)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "t0, tfinal = 0, 5\n", "y0 = 1.0" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Code du schéma des trapèzes implicites" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "pas=[];\n", "erreur=[];\n", "h=1;#pas de depart\n", "nbiter=10; #on passe DIX fois dans la boucle\n", "#le dernier pas de temps utilise est 1/2^9 \n", "# la mise à jour du pas s'effectue en effet après le calcul de \n", "# la solution approchee\n", "\n", "# boucle sur les pas de temps de plus en plus petits\n", "for k in range(nbiter):\n", " #initialisation\n", " t=np.arange(t0,tfinal+h,h)\n", " N=len(t)\n", " yapp=np.zeros(N)\n", " y = y0\n", " yapp[0]=y0\n", " # code la methode des trapezes pour le pas h\n", " for n in range(N-1):\n", " y=yapp[n]\n", " #initialisation avec Euler\n", " z=y+h* fun(t[n],y)\n", " # iterations de point fixe\n", " for i in range(3):\n", " z = y + 0.5*h*(fun(t[n],y) + fun(t[n]+h,z))\n", " yapp[n+1]=z\n", " err=np.max(np.abs(yapp-np.exp(-t)));\n", " pas.append(h);\n", " erreur.append(err)\n", " h=h/2 #divise le pas par deux. c'est pour cela que nbiter=10 et pas 9" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#trace la solutions exacte\n", "xexact=np.arange(t0,tfinal,1e-2)\n", "yexact=np.exp(-xexact);\n", "plt.plot(xexact,yexact,'r');\n", "plt.plot(t,yapp,'-k')#trace la solution approchee\n", "plt.legend(['solution exacte', 'solution approchee trapèzes implicites'])\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#trace l'erreur en fonction du pas en coordonnées log-log \n", "plt.loglog(pas, erreur,'-og')\n", "plt.loglog(pas,np.power(pas,2),'--og')\n", "plt.legend(['schéma trapèze implicite','pente 2'],loc='best')\n", "plt.xlabel('log pas')\n", "plt.ylabel('log erreur')\n", "plt.title('ordre de convergence du schéma des trapèzes implicites')\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "#solveur basé sur schéma RK45 de Scipy\n", "sol = solve_ivp(fun, [t0, tfinal], [1], 'RK45',dense_output=True)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0. , 0.10001999, 0.61293194, 1.20083981, 1.80458359,\n", " 2.41190597, 3.02019605, 3.62771743, 4.1587852 , 4.67089781,\n", " 5. ])" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "#les temps choisis automatiquement par le solveur\n", "sol.t" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(sol.t, sol.y.T, '-ob')\n", "# il faut transposer y pour qu'il ait le meme format que t \n", "plt.plot(t,yapp,'-k')\n", "t_eval=np.arange(t0,tfinal,1e-2)\n", "plt.plot(t_eval, np.exp(-t_eval),'-r')\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n", "plt.legend(['RK45','Trapèzes implicites', 'sol. exacte'], shadow=True)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " ***La solution générale de l'équation différentielle est $ y(t) = C \\, \\exp(3t) + \\exp(-t).$\n", " Pour la solution exacte vérifiant la condition initiale, $y(t) = \\exp(-t)$ i.e. $C=0.$\n", "Les schémas numériques en s'écartant un peu de la solution exacte calculent des approximations avec $C \\ll 1$ mais non rigoureusement nul. Au bout d'un certain temps le terme $C \\, \\exp(3t)$ devient dominant.***" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# tracé de solutions voisines de la solution qui s'en écartent progressivement.\n", "plt.plot(t_eval, np.exp(-t_eval),'r')\n", "for C in [-3e-7, -2e-7, -1e-7,-0.5e-7,0.5e-7,1e-7, 2e-7, 3e-7 ]:\n", " plt.plot(t_eval, C*np.exp(3*t_eval)+ np.exp(-t_eval))\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n", "plt.title('sol C exp(3t) + exp(-t) pour C entre -3e-7 et 3e-7')\n", "plt.show()" ] } ], "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": 2 }