{"metadata": {"kernelspec": {"display_name": "Python 3", "language": "python", "name": "python3"}, "celltoolbar": "None", "language_info": {"pygments_lexer": "ipython3", "nbconvert_exporter": "python", "version": "3.5.5", "mimetype": "text/x-python", "codemirror_mode": {"version": 3, "name": "ipython"}, "file_extension": ".py", "name": "python"}}, "nbformat_minor": 2, "nbformat": 4, "cells": [{"metadata": {}, "cell_type": "code", "source": ["import numpy as np\n", "import scipy as sp\n", "\n", "import matplotlib.pyplot as plt\n", "from scipy.integrate import odeint\n", "from numpy.linalg import inv"], "outputs": [], "execution_count": 1}, {"metadata": {"deletable": false}, "cell_type": "markdown", "source": ["$\\newcommand{\\R}{\\mathbb{R}}$\n", "$\\newcommand{\\N}{\\mathbb{N}}$\n", "\n", "# TP 3 : Sch\u00e9mas explicites pour les EDO\n", "\n", "L'objectif de ce TP est de mettre en oeuvre diff\u00e9rents sch\u00e9mas num\u00e9riques pour approcher la solution d'une \u00e9quation diff\u00e9rentielle ordinaire. Nous allons consid\u00e9rer diff\u00e9rents sch\u00e9mas num\u00e9riques, dont certains nous n'avons pas encore vus en cours. L'objectif est de comprendre ce que c'est une solution approch\u00e9e donn\u00e9e par une m\u00e9thode num\u00e9rique, mais aussi de comprendre des notions comme l' erreur entre la solution exacte et la solution approch\u00e9e, la convergence d'une m\u00e9thode num\u00e9rique et l' ordre de pr\u00e9cision d'une m\u00e9thode num\u00e9rique\n", "\n", "\n", "\n", "Dans ce TP on consid\u00e8re des \u00e9quations diff\u00e9rentielles ordinaires, ou des syst\u00e8mes d'\u00e9quations diff\u00e9rentielles ordinaires, de la forme\n", "\\begin{equation}\n", "\\label{EDO}\n", "\\left\\{\\begin{aligned}\n", " y'(t) & = f(t,y(t)), \\\\\n", " y(t_0) & = y_0,\n", "\\end{aligned} \\right.\n", "\\tag{EDO}\n", "\\end{equation}\n", "\n", "o\u00f9 $f$ : $I \\times \\R^n \\longrightarrow \\R^n$ est une\n", "fonction dans les conditions du th\u00e9or\u00e8me de Cauchy-Lipschitz, avec $I\\subseteq\\R$ un intervalle ouvert de $\\R$ et o\u00f9 $(t_0,y_0)\\in I\\times\\R^n$ est donn\u00e9. Le probl\u00e8me de Cauchy (EDO) admet alors une unique solution maximale d\u00e9finie dans un intervalle ouvert $J\\subseteq I$.\n", "\n", "\n", "On souhaite calculer une solution approch\u00e9e de ce probl\u00e8me dans un intervalle de la forme $[t_0,t_f]=[t_0,t_0+T]\\subseteq J$, avec $T>0$. Pour ce faire, on se donne $N\\in\\N$ et on consid\u00e8re une discr\u00e9tisation de $[t_0,t_0+T]$ de pas $h=\\frac TN,$ donn\u00e9e par les points \n", "$$\n", "t_0< t_1< \\cdots "], "image/png": 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\n"}}], "execution_count": 3}, {"metadata": {"deletable": false}, "cell_type": "markdown", "source": ["**Q2.b)** Donner les valeurs approch\u00e9es de $y(1)=e$ obtenues avec $h=1/10,\\ 1/100,\\ 1/1000$, et donner les erreurs entre la valeur exacte de $e$ et les valeurs approch\u00e9es obtenues avec ces pas de temps. Observer la d\u00e9croissance de l'erreur lorsque le pas de temps diminue.\n", "\n", "**Q2.c)** Tracer, sur une autre figure, la diff\u00e9rence en valeur absolue entre la solution exacte et la solution approch\u00e9e, en fonction du temps **(i.e. $|y(t_n)-y^n|$ en fonction de $t_n$)**, en utilisant des discr\u00e9tisations de $[0,1]$ avec des pas de temps $h$ \u00e9gaux \u00e0 $1/10,\\ 1/100,\\ 1/1000.$ **Vous devez alors tracer trois courbes et observer que lorsque le pas diminue, cette diff\u00e9rence s'approche de plus en plus de 0.**"]}, {"metadata": {}, "cell_type": "code", "source": ["plt.figure(2)\n", "for h in H:\n", " T,y=euler_exp(f,t0,tf,y0,h)\n", " plt.plot(T,np.abs(u(T)-y[:,0]),label=('h=%s' %h))\n", " valfin=np.append(valfin,y[-1]) # la valeur approch\u00e9e de e=y(1) est la derni\u00e8re position du vecteur y\n", " errvalfin=np.append(errvalfin,np.exp(1)-y[-1])\n", "plt.legend()\n", "plt.title('|sol exacte - sol approch\u00e9e| pour diff\u00e9rentes valeurs du pas h')\n", "\n", "\n", "# Affichage des valeurs approch\u00e9es de exp(1) (solution exacte en t=1)\n", "print('\\n\\n')\n", "\n", "print('e^1 et valeurs approch\u00e9es avec h=1/10, 1/100 et 1/1000')\n", "print(valfin[0], valfin[1], valfin[2], valfin[3])\n", "print('\\n\\n')\n", "\n", "# Affichage de l'erreur entre val approch\u00e9 et valeur exacte en t=1\n", "print('erreur en t=1 : |y(tN) -y^N| avec h=1/10, 1/100 et 1/1000')\n", "print(abs(errvalfin[0]), abs(errvalfin[1]), abs(errvalfin[2]))\n", "print('\\n\\n')\n"], "outputs": [{"output_type": "stream", "text": ["\n", "\n", "\n", "e^1 et valeurs approch\u00e9es avec h=1/10, 1/100 et 1/1000\n", "2.718281828459045 2.44140625 2.5937424601 2.704813829421526\n", "\n", "\n", "\n", "erreur en t=1 : |y(tN) -y^N| avec h=1/10, 1/100 et 1/1000\n", "0.2768755784590451 0.124539368359045 0.013467999037519274\n", "\n", "\n", "\n"], "name": "stdout"}, {"metadata": {}, "output_type": "display_data", "data": {"text/plain": ["
"], "image/png": 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\n"}}], "execution_count": 47}, {"metadata": {"deletable": false}, "cell_type": "markdown", "source": ["**Q3)** Testez votre fonction `euler_exp` sur le mod\u00e8le logistique\n", "$$\n", "(P_1)\\ \\ \\ \\ \n", "\\begin{cases}\n", "y'(t)=c y (1 - \\frac{y}{b}),\\\\\n", "y(0)=a,\n", "\\end{cases}\n", "$$\n", "dont la solution exacte est\n", "$$\n", "y(t) = \\frac{b}{1 + \\frac{b-a}{a} e^{-ct}},\n", "$$\n", "avec les donn\u00e9es $c=1$, $b=2$, $a=0.1$, dans l'intervalle $[0,15]$, avec un pas $h=0.2$. Tracer sur la m\u00eame fen\u00eatre la solution exacte et la solution approch\u00e9e, obtenue avec le pas $h$ et avec un pas \u00e9gal \u00e0 $\\frac h2$."]}, {"metadata": {}, "cell_type": "code", "source": ["def f1(y,t,b=2.,c=1.):\n", " return c*y*(1.-y/b)\n", "\n", "# Solution exacte du mod\u00e8le logistique (P1) (exo 2, Q3)\n", "def u1(t,a=0.1,b=2.,c=1.):\n", " return b/(1+(np.exp(-c*t))*(b-a)/a)\n", "\n", "t0=0\n", "tf=15\n", "y0=np.array([0.1])\n", "h=0.2\n", "\n", "# solutions approch\u00e9es par E. exp, avec pas h et avec pas h/2\n", "T1,y1=euler_exp(f1,t0,tf,y0,h)\n", "T2,y2=euler_exp(f1,t0,tf,y0,h/2)\n", "\n", "# pour repr\u00e9senter la solution exacte\n", "pas=10**(-4)\n", "vect=np.arange(t0,tf+pas,pas)\n", "\n", "plt.figure(3)\n", "plt.plot(vect,u1(vect),label='sol exacte')\n", "plt.plot(T1, y1,label='sol app h=0.2')\n", "plt.plot(T2, y2,label='sol app h/2')\n", "plt.legend()\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n", "plt.title('Eq. logistique : solution exacte et solutions approch\u00e9es par E. explicite')\n", "\n", "\n"], "outputs": [{"metadata": {}, "output_type": "execute_result", "data": {"text/plain": ["Text(0.5,1,'Eq. logistique : solution exacte et solutions approch\u00e9es par E. explicite')"]}, "execution_count": 48}, {"metadata": {}, "output_type": "display_data", "data": {"text/plain": ["
"], "image/png": 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\n"}}], "execution_count": 48}, {"metadata": {"deletable": false}, "cell_type": "markdown", "source": ["**Q4)** Testez ensuite votre fonction dans le cas vectoriel $n>1$ ($n=2$) sur le probl\u00e8me\n", "$$\n", "(P_2)\\ \\ \\ \\\n", "\\begin{cases}\n", "y''(t) = -y(t) + \\cos(t) \\\\\n", "y(0) = 5,\\ \\ y'(0) = 1, \n", "\\end{cases}\n", "$$\n", "dont la solution exacte est \n", "\n", "$$\n", "y(t) = \\frac{1}{2} \\sin(t) t + 5 \\cos(t) + \\sin(t),\n", "$$\n", "\n", "dans l'intervalle $[0,15]$, avec un pas $h=0.2$.\\\\\n", "Pour ce faire, il faut \u00e9crire l'\u00e9quation d'ordre 2 de $(P_2)$ sous la forme d'un syst\u00e8me de deux \u00e9quations d'ordre 1 dans les nouvelles variables $u(t)=y(t)$ et $v(t)=y'(t)$. On se ram\u00e8nera alors \u00e0 la r\u00e9solution d'une \u00e9quation de la forme\n", "\n", "$$\n", "X'=F(t,X),\\ \\ \\ \\textrm{avec}\\ X=(u,v)=(y,y')^T.\n", "$$\n", "\n", "Repr\u00e9senter \u00e0 nouveau la solution exacte et la solution approch\u00e9e dans une m\u00eame fen\u00eatre graphique.\n", "\n", "**Remarque :** La solution $y$ de $(P_2)$ correspond \u00e0 la premi\u00e8re composante du vecteur $X$ ci-dessus. Votre fonction `euler_ex`! retournera dans ce cas, si vous avez respect\u00e9 la structure conseill\u00e9e, un tableau de taille $(N+1)\\times2$, $N$ \u00e9tant le nombre de points de la discr\u00e9tisation. Ce tableau donne les valeurs approch\u00e9es de $X$ au points de la discr\u00e9tisation consid\u00e9r\u00e9e, la premi\u00e8re colonne correspondant \u00e0 la premi\u00e8re composante de $X$, la seconde \u00e0 la seconde composante de $X$. La solution approch\u00e9e de $(P_2)$ que l'on cherche correspond alors \u00e0 la premi\u00e8re colonne de ce tableau."]}, {"metadata": {}, "cell_type": "code", "source": ["\n", "# EDO d'ordre 2 (P2) y''=-y+cos(t) sous forme d'un syst\u00e8me de 2 \u00e9q. d'ordre 1 (exo 2, Q4)\n", "def f2(y,t): # \u00c9criture vectorielle u=y, v=y'\n", " return np.array([y[1],-y[0]+np.cos(t)])\n", "\n", "def u2(t):\n", " return np.sin(t)*t/2+5*np.cos(t)+np.sin(t)\n", "\n", "# Le syst\u00e8me s'\u00e9crit U'=F(t,U), avec U=(y,y') et F(t,U)=(y',-y+cos(t)) : VOIR AU D\u00c9BUT COMMENT D\u00c9FINIR LA FONCTION F.\n", "\n", "t0=0\n", "tf=15\n", "\n", "h=0.2\n", "y0=np.array([5.,1.])\n", "\n", "# pour repr\u00e9senter la solution exacte\n", "vect=np.linspace(t0,tf+pas,1000)\n", "\n", "T,y=euler_exp(f2,t0,tf,y0,h)\n", "\n", "plt.figure(4)\n", "plt.plot(vect,u2(vect),label='sol exacte')\n", "plt.plot(T,y[:,0],label='sol app h=0.2') # on repr\u00e9sente y, donc uniquement la premi\u00e8re colonne de la solution (y[:,0]=y,y[:,1]=y') \n", "plt.title('y\\'\\'=-y+cos(t) : solution exacte et solutions approch\u00e9es par E. explicite')\n", "plt.legend()\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n", "\n", "# COMMENTAIRE :\n", "# L'approximation n'est pas tr\u00e8s bonne (autrement dit l'erreur est grande), on voit dans la figure, cela veut dire qu'on n'a pas utilis\u00e9 un pas suffisamment petit. Pour voir si le sch\u00e9ma est bien convergent, on divise le pas par 10, puis par 100 \n", "\n", "h=0.02\n", "T,y=euler_exp(f2,t0,tf,y0,h)\n", "plt.figure(5)\n", "plt.plot(vect,u2(vect),label='sol exacte')\n", "plt.plot(T,y[:,0],label='sol app h=0.02')\n", "h=0.002\n", "T,y=euler_exp(f2,t0,tf,y0,h)\n", "plt.plot(T,y[:,0],label='sol app h=0.002')\n", "plt.legend()\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n", "plt.title('y\\'\\'=-y+cos(t) : solution exacte et solutions approch\u00e9es par E. explicite')\n", "\n", "# COMMENTAIRE :\n", "# Les r\u00e9sultats sont rassurants, le sch\u00e9ma semble bien converger.\n", "\n", "\n"], "outputs": [{"metadata": {}, "output_type": "execute_result", "data": {"text/plain": ["Text(0.5,1,\"y''=-y+cos(t) : solution exacte et solutions approch\u00e9es par E. explicite\")"]}, "execution_count": 49}, {"metadata": {}, "output_type": "display_data", "data": {"text/plain": ["
"], "image/png": 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\n"}}, 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\n"}}], "execution_count": 49}, {"metadata": {"deletable": false}, "cell_type": "markdown", "source": ["### Exercice 2 : \u00c9tude de l'erreur et convergence du sch\u00e9ma d'Euler explicite\n", "\n", " Dans cet exercice on essaie de comprendre ce que c'est l'erreur associ\u00e9 \u00e0 un sch\u00e9ma num\u00e9rique et ce que c'est un sch\u00e9ma num\u00e9rique convergent.\n", " \n", "On se donne un probl\u00e8me de Cauchy de la forme (EDO) et une m\u00e9thode num\u00e9rique pour approcher la solution de (EDO) dans un intervalle de la forme $[t_0,t_0+T]$. Pour un certain pas de temps $h$ fix\u00e9 (ou pour un certain nombre de points de la discr\u00e9tisation $N$ fix\u00e9), l'erreur globale entre la solution approch\u00e9e associ\u00e9e \u00e0 une discr\u00e9tisation de pas $h$ de l'intervalle $[t_0,t_0+T]$ et la solution exacte est donn\u00e9e par :\n", "\n", "\\begin{equation*}\n", "E_h = \\max_{k=0,\\cdots,N}( |y(t_k)-y^{k}|). \n", "\\end{equation*}\n", "\n", "Ci dessus, $y(t_k)$ est la solution exacte \u00e0 l'instant $t_k$ et $y^{k}$ la valeur approch\u00e9e de $y(t^k),$ donn\u00e9e par le sch\u00e9ma num\u00e9rique.\n", "\n", "**Remarque 1 :** l'erreur globale $E$ d\u00e9pend du pas $h$, ou, de mani\u00e8re \u00e9quivalente, du nombre de points $N$ de la discr\u00e9tisation. Pour des valeurs de $N$ diff\u00e9rentes, ou de mani\u00e8re \u00e9quivalente pour des valeurs de $h$ diff\u00e9rentes, les discr\u00e9tisations de l'intervalle $[t_0,t_0+T]$ sont diff\u00e9rentes (elles ont un nombre de points diff\u00e9rent), et les solutions approch\u00e9es sont diff\u00e9rentes. On s'attend \u00e0 que, lorsque $N$ augmente, ou de mani\u00e8re \u00e9quivalente lorsque $h$ diminue, l'erreur $E_h$ diminue, puisque l'on consid\u00e8re dans ce cas de plus en plus de points dans la discr\u00e9tisation de l'intervalle $[t_0,t_0+T]$ et les approximations que l'on a faites pour construire le sch\u00e9ma num\u00e9rique deviennent alors de plus en plus pr\u00e9cises.\n", "\n", "**Remarque 2 :** Parfois dans la litt\u00e9rature on ne sp\u00e9cifie pas la d\u00e9pendance de $E$ par rapport \u00e0 $h$, mais on doit toujours garder \u00e0 l'esprit cette d\u00e9pendance et que l'erreur est donc une fonction de $h$"]}, {"metadata": {"deletable": false}, "cell_type": "markdown", "source": ["Consid\u00e9rons le probl\u00e8me\n", "$$\n", "(P_3)\\ \\ \\ \\\n", "\\begin{cases}\n", "y'(t)=\\frac{\\cos(t)-y(t)}{1+t},\\\\\n", "y(0)=-\\frac14, \n", "\\end{cases}\n", "$$\n", "dont la solution exacte est \n", "$$\n", "y(t) = \\frac{\\sin(t)-1/4}{1 + t}.\n", "$$\n", "\n", "**Q1)** Calculez les solutions approch\u00e9es de $(P_3)$ obtenues avec le sch\u00e9ma d'Euler explicite, avec $h=1/2^s$ pour $s = 1,2,...,8$ ; repr\u00e9sentez dans la m\u00eame figure la diff\u00e9rence en valeur absolue entre la solution exacte et la solution approch\u00e9e, en fonction du temps, pour chaque valeur de $h$."]}, {"metadata": {}, "cell_type": "code", "source": ["\n", "# EDO (P3) y'=(cos(t)-y)/(1+t) (exo 3)\n", "def f3(y,t):\n", " return (np.cos(t)-y)/(1+t)\n", "\n", "# Solution exacte du probl\u00e8me (P3) y'=(cos(t)-y)/(1+t), y(0)=-1/4 (exo 3)\n", "def u3(t):\n", " return (np.sin(t)-1./4)/(1+t)\n", "\n", "\n", "t0=0\n", "tf=20\n", "y0=np.array([-1./4])\n", "h=0.5\n", "\n", "vect=np.linspace(t0,tf+pas,1000)\n", "\n", "# listes ou on va garder les pas de temps et les erreurs globales correspondantes a chaque pas de temps\n", " \n", "vec_h=[]\n", "vec_err=[]\n", "\n", "# figure o\u00f9 l'on va afficher la diff\u00e9rence en valeur absolue entre sol exacte et sol approch\u00e9e\n", "plt.figure(6)\n", "\n", "for k in range(8):\n", " T,y=euler_exp(f3,t0,tf,y0,h)\n", " plt.plot(T,np.abs(u3(T)-y[:,0]),label=h) # !!!! ATTENTION !!!! il faut faire np.abs(u3(T)-y) si on utilise la version scalaire d'Euler explicite\n", " E=max(abs(y[:,0]-u3(T))) # !!!! ATTENTION !!!! E=max(abs(y-u2(T))) si on utilise la version scalaire d'Euler explicite\n", " vec_h.append(h)\n", " vec_err.append(E)\n", " print('erreur global pour h=',h,' est \u00e9gale \u00e0 ',E)\n", " print('\\n')\n", " h=h/2\n", "plt.legend()\n", "plt.title('y\\'=(cos(t)-y)/(1+t) : |sol. exacte - sol. approch\u00e9e| pour diff\u00e9rentes valeurs du pas h')\n", " \n", "\n"], "outputs": [{"output_type": "stream", "text": ["erreur global pour h= 0.5 est \u00e9gale \u00e0 0.24679202822617596\n", "\n", "\n", "erreur global pour h= 0.25 est \u00e9gale \u00e0 0.11040093896816727\n", "\n", "\n", "erreur global pour h= 0.125 est \u00e9gale \u00e0 0.05280190074448804\n", "\n", "\n", "erreur global pour h= 0.0625 est \u00e9gale \u00e0 0.02585727613212707\n", "\n", "\n", "erreur global pour h= 0.03125 est \u00e9gale \u00e0 0.012797869725736155\n", "\n", "\n", "erreur global pour h= 0.015625 est \u00e9gale \u00e0 0.006366858911482087\n", "\n", "\n", "erreur global pour h= 0.0078125 est \u00e9gale \u00e0 0.003175485838083414\n", "\n", "\n", "erreur global pour h= 0.00390625 est \u00e9gale \u00e0 0.0015857718084631434\n", "\n", "\n"], "name": "stdout"}, {"metadata": {}, "output_type": "execute_result", "data": {"text/plain": ["Text(0.5,1,\"y'=(cos(t)-y)/(1+t) : |sol. exacte - sol. approch\u00e9e| pour diff\u00e9rentes valeurs du pas h\")"]}, "execution_count": 50}, {"metadata": {}, "output_type": "display_data", "data": {"text/plain": ["
"], "image/png": 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\n"}}], "execution_count": 50}, {"metadata": {"deletable": false}, "cell_type": "markdown", "source": ["**Q2)** Calculer, pour chaque valeur de $h=1/2^s,\\ s = 1,2,...,8,$ l'erreur globale $E_h$ correspondante. V\u00e9rifiez que $E_h$ diminue et s'approche de $0$ lorsque $h$ diminue.\n", "\n", "**On dira qu'une m\u00e9thode num\u00e9rique converge si $\\displaystyle{\\lim_{h\\to0}E_h}=0$.**\n", "\n", "Repr\u00e9sentez ensuite, en \u00e9chelle logarithmique, l'erreur en fonction du pas de temps $h$, autrement dit, repr\u00e9sentez $\\log(E_h)$ en fonction de $\\log(h)$. Vous devez obtenir des points qui sont \u00e0 peu pr\u00e8s align\u00e9s sur une droite de pente 1. V\u00e9rifiez graphiquement que c'est le cas, en estimant la pente de la droite passant au plus pr\u00eat des points (ou en repr\u00e9sentant une droite de pente $1$ qui passe par un des points et en v\u00e9rifiant que tous les points sont \u00e0 peu pr\u00e8s sur cette droite).\n", "\n", "*Ceci signifie que $\\log(E_h) \\sim C+\\log(h)$ et donc que $E_h\\sim \\widetilde{C}h$, pour certaines constantes $C$ et $\\widetilde{C}$. On dit que la m\u00e9thode d'Euler explicite est d' ordre 1 : c'est l'ordre de la puissance de $h$ dans cette relation. On a donc que l'erreur globale $E_h$ tend vers 0 comme $h$. L'ordre d'une m\u00e9thode donne une indication sur sa vitesse de convergence. Une m\u00e9thode d'ordre $p$ est une m\u00e9thode dont l'erreur globale tend vers $0$ comme $h^p$. Donc plus l'ordre est \u00e9lev\u00e9, plus la m\u00e9thode converge plus vite*\n", "\n", "**Remarque :** pour \u00e9tudier num\u00e9riquement l'ordre d'une m\u00e9thode, on utilise souvent l'\u00e9chelle logarithmique pour tracer l'erreur en fonction du pas de discr\u00e9tisation $h$. La pente de la droite obtenue donne l'ordre $p$ de la m\u00e9thode : si $E_h \\sim Ch^p$ alors $\\log(E_h)\\sim \\log(C) + p\\log(h)$."]}, {"metadata": {}, "cell_type": "code", "source": ["\n", "plt.figure(7)\n", "plt.plot(vec_h,vec_err,'x-',label='erreur')\n", "plt.plot(vec_err,vec_err,'x-',label='droite de pente 1') #Ceci affiche une droite de pente 1.\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.legend()\n", "plt.title('Erreur global en fonction de h, en \u00e9chelle logarithmique')\n", "plt.xlabel('log(h)')\n", "plt.ylabel('log($E_h$)')\n", "\n"], "outputs": [{"metadata": {}, "output_type": "execute_result", "data": {"text/plain": ["Text(0,0.5,'log($E_h$)')"]}, "execution_count": 51}, {"metadata": {}, "output_type": "display_data", "data": {"text/plain": ["
"], "image/png": 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\n"}}], "execution_count": 51}, {"metadata": {"deletable": false}, "cell_type": "markdown", "source": ["### Exercice 3 : Un sch\u00e9ma d'ordre 2\n", "\n", "**Q1)** \u00c0 l'image de ce que vous avez fait pour le sch\u00e9ma d'Euler explicite, \u00e9crire une fonction python de la forme `Heun(fct, t0, tf, y0, h)` prenant les m\u00eames arguments que la fonction `euler_exp` et retournant les m\u00eames tableaux. "]}, {"metadata": {}, "cell_type": "code", "source": ["def Heun(f,t0,tf,y0,h):\n", " T=np.arange(t0,tf+h,h)\n", " N=T.size\n", " y=np.zeros((N,y0.size))\n", " y[0,:]=y0\n", " for n in range(N-1):\n", " p1=f(y[n,:],T[n])\n", " p2=f(y[n,:]+h*p1,T[n+1])\n", " y[n+1,:]=y[n,:]+h*(p1+p2)/2\n", " return T,y\n"], "outputs": [], "execution_count": 52}, {"metadata": {"deletable": false}, "cell_type": "markdown", "source": ["**Q2)** Pour le probl\u00e8me $(P_1),$ comparez les solutions approch\u00e9es obtenues avec la m\u00e9thode d'Euler explicite et avec la m\u00e9thode de Heun avec le m\u00eame pas de temps. Pour ce faire, repr\u00e9senter dans la m\u00eame fen\u00eatre graphique la solution exacte et les solutions approch\u00e9es obtenues avec chacune des m\u00e9thodes. Quelle m\u00e9thode semble \u00eatre plus pr\u00e9cise ? Pour le confirmer, repr\u00e9senter dans une autre figure la diff\u00e9rence, en valeur absolue, entre la solution exacte et la solution approch\u00e9e, pour les deux m\u00e9thodes."]}, {"metadata": {}, "cell_type": "code", "source": ["t0=0\n", "tf=15\n", "y0=np.array([0.1])\n", "h=0.5\n", "\n", "Teul,yeul=euler_exp(f1,t0,tf,y0,h)\n", "Theun,yheun=Heun(f1,t0,tf,y0,h)\n", "\n", "vect=np.linspace(t0,tf,1000)\n", "\n", "plt.figure(8)\n", "plt.plot(vect,u1(vect),label='sol. exacte')\n", "plt.plot(Teul, yeul,label='sol. Euler exp.')\n", "plt.plot(Theun, yheun,label='sol. Heun')\n", "plt.legend()\n", "plt.xlabel('t')\n", "plt.ylabel('y')\n", "plt.title('(P1) : sol. exacte et sol. approch\u00e9es par E. exp et Heun')\n", "\n", "plt.figure(9)\n", "plt.plot(Teul, abs(yeul[:,0]-u1(Teul)),label='erreur Eul. exp.')\n", "plt.plot(Theun, abs(yheun[:,0]-u1(Theun)),label='erreur Heun')\n", "plt.legend()\n", "plt.title('|sol. exacte - sol. approchee| pour Eul. exp et Heun')\n", "\n", "# COMMENTAIRE :\n", "# Pour la m\u00eame valeur du pas, la solution approch\u00e9e obtenue avec le sch\u00e9ma d'Heun est plus pr\u00e9cise (plus proche de la solution exacte) que celle obtenue par le sch\u00e9ma d'Euler explicite. \n"], "outputs": [{"metadata": {}, "output_type": "execute_result", "data": {"text/plain": ["Text(0.5,1,'|sol. exacte - sol. approchee| pour Eul. exp et Heun')"]}, "execution_count": 53}, {"metadata": {}, "output_type": "display_data", "data": {"text/plain": ["
"], "image/png": 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\n"}}, 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\n"}}], "execution_count": 53}, {"metadata": {"deletable": false}, "cell_type": "markdown", "source": ["**Q3)** Reprenez l'exercice **2** pour la m\u00e9thode de Heun. V\u00e9rifiez graphiquement que cette m\u00e9thode est d'ordre $2,$ en repr\u00e9sentant l'erreur globale en fonction du pas de discr\u00e9tisation en \u00e9chelle logarithmique et en estimant la pente de la droite passant au plus pr\u00eat des points correspondant \u00e0 cette repr\u00e9sentation ou en repr\u00e9sentant une droite de pente $2$ qui passe par un des points."]}, {"metadata": {}, "cell_type": "code", "source": ["t0=0\n", "tf=20\n", "y0=np.array([-1./4])\n", "h=0.5\n", "\n", "# listes ou on va garder les pas de temps et les erreurs globales correspondantes a chaque pas de temps\n", " \n", "vec_h=[]\n", "vec_err=[]\n", "\n", "for k in range(8):\n", " T,y=Heun(f3,t0,tf,y0,h)\n", " E=max(abs(y[:,0]-u3(T))) \n", " vec_h.append(h)\n", " vec_err.append(E)\n", " h=h/2\n", "\n", "plt.figure(10)\n", "plt.plot(vec_h,vec_err,'x-',label='erreur')\n", "plt.plot(vec_h,vec_h,'x-',label='droite de pente 1') #Ceci affiche une droite de pente 1.\n", "plt.plot(vec_h,np.array(vec_h)**2,'x-',label='droite de pente 2') #Ceci affiche une droite de pente 2.\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.legend()\n", "plt.title('sch. Heun : erreur global en fonction de h, en \u00e9chelle logarithmique')\n", "plt.xlabel('log(h)')\n", "plt.ylabel('log($E_h$)')\n", "\n", "# COMMENTAIRE :\n", "#En \u00e9chelle logarithmique, les points correspondant \u00e0 l'erreur globale du sch\u00e9ma d'Heun en fonction de h semblent bien \u00e0 \n", "#peu pr\u00e9s align\u00e9s sur une droite de pente 2 puisque l'on a repr\u00e9sent\u00e9 une droite de pente 2 \u00e0 cot\u00e9 qui semble parall\u00e8le \u00e0 \n", "#la ligne qui contient les points. Cela montre que le sch\u00e9ma d'Heun est d'ordre 2. Il est donc plus pr\u00e9cis que le sch\u00e9ma d'Euler \n", "#(car l'erreur tend vers 0 comme h^2, alors que pour Euler l'erreur tend vers 0 comme h).\n", "\n"], "outputs": [{"metadata": {}, "output_type": "execute_result", "data": {"text/plain": ["Text(0,0.5,'log($E_h$)')"]}, "execution_count": 54}, {"metadata": {}, "output_type": "display_data", "data": {"text/plain": ["
"], "image/png": 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\n"}}], "execution_count": 54}, {"metadata": {}, "cell_type": "code", "source": [], "outputs": [], "execution_count": null}, {"metadata": {}, "cell_type": "code", "source": [], "outputs": [], "execution_count": null}, {"metadata": {}, "cell_type": "code", "source": [], "outputs": [], "execution_count": null}]}