{ "cells": [ { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 41, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import display, Latex\n", "from IPython.core.display import HTML\n", "css_file = './custom.css'\n", "HTML(open(css_file, \"r\").read()) " ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python version 3.8.5 (default, Jul 28 2020, 12:59:40) \n", "[GCC 9.3.0]\n" ] } ], "source": [ "import sys #only needed to determine Python version number\n", "print('Python version ' + sys.version)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# M62 TP 2 - Implémentation des schémas \"classiques\" et étude de la convergence" ] }, { "cell_type": "markdown", "metadata": { "hide_input": false }, "source": [ "## Rappel de CM : implémentation des schémas d'Euler explicite et implicite\n", "\n", "Considérons le problème de Cauchy\n", "\n", ">trouver la fonction $y \\colon I\\subset \\mathbb{R} \\to \\mathbb{R}$ définie sur l'intervalle $I=[0,1]$ telle que\n", ">$$\n", "\\begin{cases}\n", "y'(t) = -4y(t)+t^2, &\\forall t \\in I=[0,1],\\\\\n", "y(0) = 1\n", "\\end{cases}\n", "$$\n", "\n", "1. Calculer la solution exacte en utilisant le module `sympy`.\n", "1. Calculer la solution approchée obtenue avec la méthode d'**Euler explicite** avec $h=1/N$ et $N=8$ (pour bien visualiser les erreurs);\n", "2. Même exercice pour la méthode d'**Euler implicite**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction 1** \n", "Calculons la solution exacte en utilisant le module `sympy`:" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d t} y{\\left(t \\right)} = t^{2} - 4 y{\\left(t \\right)}$" ], "text/plain": [ "d 2 \n", "──(y(t)) = t - 4⋅y(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle y{\\left(t \\right)} = \\left(C_{1} + \\frac{\\left(8 t^{2} - 4 t + 1\\right) e^{4 t}}{32}\\right) e^{- 4 t}$" ], "text/plain": [ " ⎛ ⎛ 2 ⎞ 4⋅t⎞ \n", " ⎜ ⎝8⋅t - 4⋅t + 1⎠⋅ℯ ⎟ -4⋅t\n", "y(t) = ⎜C₁ + ─────────────────────⎟⋅ℯ \n", " ⎝ 32 ⎠ " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left\\{ C_{1} : \\frac{31}{32}\\right\\}$" ], "text/plain": [ "⎧ 31⎫\n", "⎨C₁: ──⎬\n", "⎩ 32⎭" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle y{\\left(t \\right)} = \\frac{t^{2}}{4} - \\frac{t}{8} + \\frac{1}{32} + \\frac{31 e^{- 4 t}}{32}$" ], "text/plain": [ " 2 -4⋅t\n", " t t 1 31⋅ℯ \n", "y(t) = ── - ─ + ── + ────────\n", " 4 8 32 32 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "y = sym.Function('y')\n", "edo= sym.Eq( sym.diff(y(t),t) , -4*y(t)+t**2 )\n", "display(edo)\n", "solgen = sym.dsolve(edo)\n", "display(solgen)\n", "\n", "t0=0\n", "y0=1\n", "consts = sym.solve( sym.Eq( y0, solgen.rhs.subs(t,t0)) , dict=True)[0]\n", "display(consts)\n", "solpar=solgen.subs(consts).simplify()\n", "display(solpar)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On définit la solution exacte à utiliser pour estimer les erreurs:" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [], "source": [ "sol_exacte = sym.lambdify(t,solpar.rhs,'numpy')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction 2 et 3** \n", "On commence par importer le module `matplotlib`et la fonction `fsolve` du module `scipy.optimize` pour résoudre l'équation implicite présente dans le schéma implicite:" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [], "source": [ "from matplotlib.pylab import *\n", "from scipy.optimize import fsolve" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On initialise le problème de Cauchy" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [], "source": [ "# variables globales\n", "t0 = 0\n", "tfinal = 1\n", "y0 = 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On définit l'équation différentielle : `phi` est une lambda function qui contient la fonction mathématique $\\varphi(t, y)=-4y+t^2$ dépendant des variables $t$ et $y$." ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [], "source": [ "phi = lambda t,y : -4*y+t**2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On écrit les schémas numériques : les valeurs $[u_0,u_1,\\dots,u_{N}]$ pour chaque méthode sont contenues dans le vecteur `uu`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Schéma d'Euler progressif :**\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{n+1}=u_n+h\\varphi(t_n,u_n)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [], "source": [ "def EE(phi, tt, y0):\n", " h = tt[1] - tt[0]\n", " uu = [y0]\n", " for i in range(len(tt) - 1):\n", " uu.append(uu[i] + h * phi(tt[i], uu[i]))\n", " return uu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Schéma d'Euler régressif :**\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{n+1}=u_n+h\\varphi(t_{n+1},u_{n+1})& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$\n", "\n", "Attention : $u_{n+1}$ est solution de l'équation $x=u_n+h\\varphi(t_{n+1},x)$, c'est-à-dire un zéro de la fonction (en générale non linéaire) $$x\\mapsto -x+u_n+h\\varphi(t_{n+1},x)$$" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [], "source": [ "def EI(phi, tt, y0):\n", " h = tt[1] - tt[0]\n", " uu = [y0]\n", " for i in range(len(tt) - 1):\n", " temp = fsolve(lambda x: -x + uu[i] + h * phi(tt[i + 1], x), uu[i])\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On introduit la discrétisation: les nœuds d'intégration $[t_0,t_1,\\dots,t_{N}]$ sont contenus dans le vecteur `tt`. \n", "On a $N+1$ points espacés de $h=\\frac{t_N-t_0}{N}$.\n", "\n", "On calcule les solutions exacte et approchées en ces points:" ] }, { "cell_type": "code", "execution_count": 50, "metadata": {}, "outputs": [], "source": [ "N = 8 \n", "tt=linspace(t0,tfinal,N+1)\n", "# print(tt)\n", "\n", "yy = [sol_exacte(t) for t in tt]\n", "# yy = sol_exacte(tt) # si vectorisée\n", "uu_ep = EE(phi, tt, y0)\n", "uu_er = EI(phi, tt, y0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On compare les graphes des solutions exacte et approchées et on affiche le maximum de l'erreur:\n", "$$\n", "\\max_n \\left| y(t_n)-u_n \\right|\n", "$$" ] }, { "cell_type": "code", "execution_count": 51, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(18, 7))\n", "\n", "subplot(1, 2, 1)\n", "plot(tt, yy, 'b-', tt, uu_ep, 'r-D')\n", "err_ep = max( [abs(uu_ep[i] - yy[i]) for i in range(N)] )\n", "# title(f'Euler explicite - max(|erreur|)= {err_ep:1.10f}') #syntaxe si python >=3.6\n", "title('Euler explicite - max(|erreur|)=%1.10f' %(err_ep)) #\"OLD\" syntaxe\n", "grid()\n", "\n", "subplot(1, 2, 2)\n", "plot(tt, yy, 'b-', tt, uu_er, 'r-D')\n", "err_er = max( [abs(uu_er[i] - yy[i]) for i in range(N)] )\n", "title('Euler implicite - max(|erreur|)=%1.10f' %(err_er)) #\"OLD\" syntaxe\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Rappel de CM : étude empirique de la convergence des schémas d'Euler explicite et implicite\n", "Considérons le même problème de Cauchy.\n", "\n", "1. On se propose d'estimer empiriquement l'ordre de convergence de la méthode d'**Euler explicite**. \n", "\t- On calcule d'abord la solution approchée avec différentes valeurs de $h_k=1/N_k$ \n", "\t- Pour chaque valeur de $h_k$, on calcule le maximum de la valeur absolue de l'erreur et on la sauvegarde dans le vecteur `err_ep` de sort que `err_ep[k]` contient $e_k=\\max_{i=0,\\dots,N_k}|y(t_i)-u_{i}|$. \n", "\t- Pour estimer l'ordre de convergence on affiche les points (`h[k]`,`err_ep[k]`) en echèlle logarithmique. On trouve ainsi une droite qui relie l'erreur au pas $k$ à l'erreur au pas $k+1$. \n", " Pour estimer la pente globale de cette droite (par des moindres carrés) on utilisers la fonction `polyfit` avec une régression linéaire. \t\n", "\n", "2. Même exercice pour estimer l'ordre de convergence de la méthode d'**Euler implicite**.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour chaque schéma, on calcule la solution approchée avec différentes valeurs de $h_k=1/N_k$ et on sauvegarde les valeurs de $h_k$ dans le vecteur `H`. \n", "\n", "Pour chaque valeur de $h_k$, on calcule le maximum de la valeur absolue de l'erreur et on sauvegarde toutes ces erreurs dans le vecteur `err_schema` de sort que `err_schema[k]` contient $e_k=\\max_{i=0,\\dots,N_k}|y(t_i)-u_{i}|$." ] }, { "cell_type": "code", "execution_count": 52, "metadata": {}, "outputs": [], "source": [ "H = []\n", "err_ep = []\n", "err_er = []\n", "\n", "N = 10\n", "for k in range(7):\n", "# N = 2**(k + 3)\n", " N+=20\n", " tt = linspace(t0, tfinal, N + 1)\n", " h = tt[1] - tt[0]\n", " yy = [sol_exacte(t) for t in tt]\n", " uu_ep = EE(phi, tt, y0)\n", " uu_er = EI(phi, tt, y0)\n", " H.append(h)\n", " err_ep.append(max([abs(uu_ep[i] - yy[i]) for i in range(len(yy))]))\n", " err_er.append(max([abs(uu_er[i] - yy[i]) for i in range(len(yy))]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour afficher l'ordre de convergence on utilise une échelle logarithmique, i.e. on représente $\\ln(h)$ sur l'axe des abscisses et $\\ln(\\text{err})$ sur l'axe des ordonnées. \n", "En effet, si $\\text{err}=Ch^p$ alors $\\ln(\\text{err})=\\ln(C)+p\\ln(h)$. \n", "En échelle logarithmique, $p$ représente donc la pente de la ligne droite $\\ln(\\text{err})$." ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(log(H), log(err_ep), 'r-o', label='Euler Explicite')\n", "plot(log(H), log(err_er), 'g-+', label='Euler Implicite')\n", "# loglog(H, err_ep, 'r-o', label='Euler Explicite')\n", "# loglog(H, err_er, 'g-+', label='Euler Implicite')\n", "xlabel('$\\ln(h)$')\n", "ylabel('$\\ln(e)$')\n", "legend(bbox_to_anchor=(1.04, 1), loc='upper left')\n", "grid(True)\n", "show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pour estimer l'ordre de convergence on doit estimer la pente de la droite qui relie l'erreur au pas $k$ à l'erreur au pas $k+1$ en echelle logarithmique.\n", "Pour estimer la pente globale de cette droite (par des moindres carrés) on peut utiliser la fonction `polyfit` (du module `numpy` que nous avons déjà importé avec `matplotlib.pylab`). " ] }, { "cell_type": "code", "execution_count": 54, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Euler progressif 1.03\n", "Euler regressif 0.98\n" ] } ], "source": [ "print ('Euler progressif %1.2f' %(polyfit(log(H),log(err_ep), 1)[0]))\n", "print ('Euler regressif %1.2f' %(polyfit(log(H),log(err_er), 1)[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice : implémentation et étude empirique de la convergence des méthodes d'Euler modifié, de Crank-Nicolson et de Heun\n", "Ajouter l'implémentation et l'étude empirique de la convergence des méthodes d'**Euler modifié**, de **Crank-Nicolson** et de **Heun** aux exercices 1 et 2." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction**\n", "\n", "On écrit les trois schémas:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Schéma d'Euler modifié:**\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "\\tilde u = u_n+\\frac{h}{2}\\varphi(t_n,u_n),\\\\\n", "u_{n+1}=u_n+h\\varphi\\left(t_n+\\frac{h}{2},\\tilde u\\right)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$\n", "qu'on peut réécrire sous la forme\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "k_1 = h\\varphi(t_n,u_n),\\\\\n", "u_{n+1}=u_n+h\\varphi\\left(t_n+\\frac{h}{2}, u_n+\\frac{k_1}{2}\\right)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 55, "metadata": {}, "outputs": [], "source": [ "def EM(phi,tt, y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(len(tt)-1):\n", " k1 = h * phi( tt[i], uu[i] )\n", " uu.append( uu[i]+h*phi( tt[i]+h/2 , uu[i]+k1/2 ) )\n", " return uu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Schéma de Crank-Nicolson :**\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\Bigl(\\varphi(t_n,u_n)+\\varphi(t_{n+1},u_{n+1})\\Bigr)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$\n", "avec $u_{n+1}$ zéro de la fonction $x\\mapsto -x+u_n+\\frac{h}{2}(\\varphi(t_n,u_n)+\\varphi(t_{n+1},x))$." ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [], "source": [ "def CN(phi,tt, y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(len(tt)-1):\n", " temp = fsolve(lambda x: -x+uu[i]+0.5*h*( phi(tt[i+1],x)+phi(tt[i],uu[i]) ), uu[i])\n", " uu.append(temp)\n", " return uu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Schéma de Heun:**\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "\\tilde u = u_n+h\\varphi(t_n,u_n)\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\Bigl(\\varphi(t_n,u_n)+\\varphi(t_{n+1},\\tilde u)\\Bigr)& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$\n", "qu'on peut réécrire sous la forme\n", "$$\n", "\\begin{cases}\n", "u_0=y_0,\\\\\n", "k_1 = h\\varphi(t_n,u_n),\\\\\n", "k_2 = h\\varphi(t_{n+1},u_n+k_1),\\\\\n", "u_{n+1}=u_n+\\frac{k_1+k_2}{2}& n=0,1,2,\\dots N-1\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 57, "metadata": {}, "outputs": [], "source": [ "def heun(phi,tt, y0):\n", " h = tt[1]-tt[0]\n", " uu = [y0]\n", " for i in range(len(tt)-1):\n", " k1 = h * phi( tt[i], uu[i] )\n", " k2 = h * phi( tt[i+1], uu[i] + k1 )\n", " uu.append( uu[i] + (k1+k2) /2 )\n", " return uu" ] }, { "cell_type": "code", "execution_count": 58, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "N = 8 \n", "tt=linspace(t0,tfinal,N+1)\n", "\n", "yy = [sol_exacte(t) for t in tt]\n", "uu_ep = EE(phi, tt, y0)\n", "uu_er = EI(phi, tt, y0)\n", "uu_em = EM(phi, tt, y0)\n", "uu_cn = CN(phi, tt, y0)\n", "uu_heun = heun(phi, tt, y0)\n", "\n", "figure(1, figsize=(18, 10))\n", "\n", "subplot(2, 3, 1)\n", "plot(tt, yy, 'b-', tt, uu_ep, 'r-D')\n", "err_ep = max( [abs(uu_ep[i] - yy[i]) for i in range(N)] )\n", "# title(f'Euler explicite - max(|erreur|)= {err_ep:1.10f}')\n", "title('Euler explicite - max(|erreur|)= %1.5f'%(err_ep))\n", "grid()\n", "\n", "subplot(2, 3, 2)\n", "plot(tt, yy, 'b-', tt, uu_er, 'r-D')\n", "err_er = max( [abs(uu_er[i] - yy[i]) for i in range(N)] )\n", "title('Euler implicite - max(|erreur|)=%1.5f' %(err_er))\n", "grid();\n", "\n", "\n", "subplot(2, 3, 4)\n", "plot(tt, yy, 'b-', tt, uu_em, 'r-D')\n", "err_ep = max( [abs(uu_em[i] - yy[i]) for i in range(N)] )\n", "title('Euler modifié - max(|erreur|)= %1.5f'%(err_ep))\n", "grid()\n", "\n", "subplot(2, 3, 5)\n", "plot(tt, yy, 'b-', tt, uu_cn, 'r-D')\n", "err_cn = max( [abs(uu_cn[i] - yy[i]) for i in range(N)] )\n", "title('Crank Nicolson - max(|erreur|)=%1.5f' %(err_cn))\n", "grid()\n", "\n", "subplot(2, 3, 6)\n", "plot(tt, yy, 'b-', tt, uu_heun, 'r-D')\n", "err_heun = max( [abs(uu_heun[i] - yy[i]) for i in range(N)] )\n", "title('Heun - max(|erreur|)=%1.5f' %(err_heun))\n", "grid();" ] }, { "cell_type": "code", "execution_count": 59, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Euler progressif 1.05\n", "Euler regressif 0.96\n", "Euler Modifié 2.08\n", "Cranck Nicolson 2.01\n", "Heun 2.08\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "H = []\n", "err_ep = []\n", "err_er = []\n", "err_em = []\n", "err_cn = []\n", "err_heun = []\n", "\n", "for k in range(7):\n", " N = 2**(k + 3)\n", " tt = linspace(t0, tfinal, N + 1)\n", " h = tt[1] - tt[0]\n", " yy = [sol_exacte(t) for t in tt]\n", " uu_ep = EE(phi, tt, y0)\n", " uu_er = EI(phi, tt, y0)\n", " uu_em = EM(phi, tt, y0)\n", " uu_cn = CN(phi, tt, y0)\n", " uu_heun = heun(phi, tt, y0)\n", " H.append(h)\n", " err_ep.append(max([abs(uu_ep[i] - yy[i]) for i in range(len(yy))]))\n", " err_er.append(max([abs(uu_er[i] - yy[i]) for i in range(len(yy))]))\n", " err_em.append(max([abs(uu_em[i] - yy[i]) for i in range(len(yy))]))\n", " err_cn.append(max([abs(uu_cn[i] - yy[i]) for i in range(len(yy))]))\n", " err_heun.append(max([abs(uu_heun[i] - yy[i]) for i in range(len(yy))]))\n", "\n", "figure(figsize=(10,7))\n", "loglog(H, err_ep, 'r-o', label='Euler Explicite')\n", "loglog(H, err_er, 'g-+', label='Euler Implicite')\n", "loglog(H, err_em, 'm-x', label='Euler Modife')\n", "loglog(H, err_cn, 'y-d', label='Crank Nicolson')\n", "loglog(H, err_heun, 'c-v', label='Heun')\n", "xlabel('$\\ln(h)$')\n", "ylabel('$\\ln(e)$')\n", "legend(bbox_to_anchor=(1.04, 1), loc='upper left')\n", "grid(True);\n", "\n", "print ('Euler progressif %1.2f' %(polyfit(log(H),log(err_ep), 1)[0]))\n", "print ('Euler regressif %1.2f' %(polyfit(log(H),log(err_er), 1)[0]))\n", "print ('Euler Modifié %1.2f' %(polyfit(log(H),log(err_em), 1)[0]))\n", "print ('Cranck Nicolson %1.2f' %(polyfit(log(H),log(err_cn), 1)[0]))\n", "print ('Heun %1.2f' %(polyfit(log(H),log(err_heun), 1)[0]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice : Fonction intégrale\n", "\n", "Il existe des fonctions définies par des intégrales qu'on ne peut pas calculer explicitement.\n", "Il est pourtant possible de calculer des valeurs approchées de ces fonctions. \n", "\n", ">Pour $x\\in\\left[0;\\frac{\\pi}{2}\\right]$ calculer et afficher la table des valeurs et tracer le graphe de la fonction\n", "$$\n", "x \\mapsto f(x)=\\int_0^x \\sqrt{1-\\frac{1}{4}\\sin^2(t)}\\mathrm{d}t \n", "$$\n", "en approchant numériquement un problème de Cauchy (lequel?) avec la méthode d'**Euler explicite**. \n", ">\n", ">Vérifier que $f\\left(\\frac{\\pi}{6}\\right)\\simeq0.51788193$ et $f\\left(\\frac{\\pi}{2}\\right)\\simeq1.46746221$.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction**" ] }, { "cell_type": "code", "execution_count": 60, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "from matplotlib.pylab import *\n", "# from scipy.optimize import fsolve\n", "\n", "def EE(phi, tt, y0):\n", " h = tt[1] - tt[0]\n", " uu = [y0]\n", " for i in range(len(tt) - 1):\n", " uu.append(uu[i] + h * phi(tt[i], uu[i]))\n", " return uu" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La fonction $f$ est solution du problème de Cauchy\n", "$$\n", "\\begin{cases}\n", "y'(t)= \\sqrt{1-\\frac{1}{4}\\sin^2(t)},\\\\\n", "y(0)=0.\n", "\\end{cases}\n", "$$\n", "En effet, $f(0)=0$ et si on intègre l'EDO entre $0$ et $x$ on a \n", "$$\n", "f(x)=\\int_0^x \\sqrt{1-\\frac{1}{4}\\sin^2(t)}\\mathrm{d}t=\\int_0^x y'(t)\\mathrm{d}t=y(x)-y(0)=y(x).\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On définit l'équation différentielle : `phi` est une *lambda function* qui contient la fonction mathématique $\\varphi(t, y)$ dépendant des variables $t$ et $y$ (même si $y$ n'apparaît pas explicitement)." ] }, { "cell_type": "code", "execution_count": 61, "metadata": {}, "outputs": [], "source": [ "phi = lambda t,y : sqrt(1-0.25*(sin(t))**2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "et la condition initiale" ] }, { "cell_type": "code", "execution_count": 62, "metadata": {}, "outputs": [], "source": [ "t0, y0 = 0, 0\n", "tfinal = pi/2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On introduit la discrétisation: les nœuds d'intégration $[t_0,t_1,\\dots,t_{N}]$ sont contenus dans le vecteur `tt`. \n", "Comme nous devons éstimer ensuite $f$ en $\\frac{\\pi}{6}$ et $\\frac{\\pi}{2}$, faisons en sort davoir ces deux valeurs dans nos noeuds de discrétisation. \n", "Étant donné que \n", "- $t_0=0$, \n", "- $t_N=\\frac{\\pi}{2}$ et \n", "- $t_i=t_0+ih$ avec $h=\\frac{t_N-t_0}{N}=\\frac{\\pi}{2N}$, \n", "\n", "on a $\\frac{\\pi}{6}=i\\frac{\\pi}{2N}$ ssi $i=\\frac{2N}{6}=\\frac{N}{3}$ et bien sûr $\\frac{\\pi}{2}=t_{N}$. Pour que $i\\in\\mathbb{N}$ on choisira $N$ multiple de $3$." ] }, { "cell_type": "code", "execution_count": 63, "metadata": {}, "outputs": [], "source": [ "N =12*1000\n", "tt=linspace(t0,tfinal,N+1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On calcule la solution approchée:" ] }, { "cell_type": "code", "execution_count": 64, "metadata": {}, "outputs": [], "source": [ "uu = EE(phi,tt, y0)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On vérifie que $f(\\pi/6)\\simeq0.51788193$ et $f(\\pi/2)\\simeq1.46746221$ et on affiche le graphe de la fonction approchée." ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "f(pi/6)=0.517884\n", "f(pi/2)=1.46747\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "indice=int(N/3)\n", "# print(f\"f(pi/{pi/tt[indice]})={uu[indice]}\") # NEW syntaxe\n", "# print(f\"f(pi/{pi/tt[-1]})={uu[-1]}\") # NEW syntaxe\n", "print(\"f(pi/%g)=%g\" %(pi/tt[indice],uu[indice])) # OLD syntaxe\n", "print(\"f(pi/%g)=%g\" %(pi/tt[-1],uu[-1])) # OLD syntaxe\n", "plot(tt,uu)\n", "plot([tt[0],tt[indice],tt[indice]],[uu[indice],uu[indice],0],'m--');\n", "plot([tt[0],tt[-1],tt[-1]],[uu[-1],uu[-1],0],'c--');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Et `sympy` ? " ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{d}{d t} y{\\left(t \\right)} = \\sqrt{1 - \\frac{\\sin^{2}{\\left(t \\right)}}{4}}$" ], "text/plain": [ " _____________\n", " ╱ 2 \n", "d ╱ sin (t) \n", "──(y(t)) = ╱ 1 - ─────── \n", "dt ╲╱ 4 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\int \\sqrt{1 - \\frac{\\sin^{2}{\\left(t \\right)}}{4}}\\, dt$" ], "text/plain": [ "⌠ \n", "⎮ _____________ \n", "⎮ ╱ 2 \n", "⎮ ╱ sin (t) \n", "⎮ ╱ 1 - ─────── dt\n", "⎮ ╲╱ 4 \n", "⌡ " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "y = sym.Function('y')\n", "edo= sym.Eq( sym.diff(y(t),t) , sym.sqrt(1-sym.Rational(1,4)*(sym.sin(t))**2) )\n", "display(edo)\n", "# solgen = sym.dsolve(edo)\n", "# display(solgen)\n", "\n", "t = sym.Symbol('t')\n", "f=sym.Integral(sym.sqrt(1-sym.Rational(1,4)*(sym.sin(t))**2))\n", "display(f)\n", "# f.doit()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice : Système de deux EDO avec invariant\n", "\n", ">Considérons le problème de Cauchy\n", "$$\n", "\\begin{cases}\n", "x'(t)= -y(t) ,\\\\\n", "y'(t)= x(t), & t\\in[0;4\\pi]\\\\\n", "x(0)=1,\\\\\n", "y(0)=0.\n", "\\end{cases}\n", "$$\n", ">1. **Invariant** \n", "Vérifier que $I(t)=x^2(t) + y^2(t)$ est un invariant pour le système. \n", ">1. **Approximations** \n", "Dans une simulation numérique on aimerait que l'invariant soit préservé aussi bien que possible. Nous allons regarder ce qui se passe avec certaines méthodes vues en cours. \n", "On notera $u_n\\approx x_n=x(t_n)$ et $w_n\\approx y_n=y(t_n)$. \n", "À chaque instant $t_n$, on calculera $J_n\\approx I_n=I(t_n)$. \n", "Choisissons $h=t_{n+1}-t_n=\\pi/48$.\n", " 1. Dans un premier temps on se propose d'appliquer la méthode d'**Euler explicite** à la résolution du système. \n", " 1. Tracer $(t_n,u_n)$ et $(t_n,w_n)$ sur un même graphique; \n", " 2. sur un autre graphique tracer $(t_n,J_n)$; \n", " 3. tracer enfin $(u_n,w_n)$ sur un autre graphique et vérifier que la solution numérique tourne vers l’extérieur \n", " 4. Après avoir constaté que l'invariant $J_n$ n'est pas conservé mais augment au cours du temps, montrer analytiquement que $J_n=(1+h^2)^n$. \n", " 1. Même exercice pour le schéma d'**Euler implicite** (la linéarité du second membre permet de rendre ce schéma explicite). Que peut-on constater? Commenter les résultats et écrire l'expression analytique de $J_n$. \n", " 1. Même exercice pour le schéma de **Crank Nicolson** (la linéarité du second membre permet de rendre ce schéma explicite). Que peut-on constater? Commenter les résultats et écrire l'expression analytique de $J_n$. \n", ">1. **Solution exacte** \n", "Dans ce cas il est même possible de calculer analytiquement la solution exacte. Calculer donc la solution exacte avec le module `sympy`." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Correction**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Invariant**\n", "\n", "Pour tout $t$ on a\n", "$$\n", "I'(t)=\\left(x^2(t) + y^2(t)\\right)' = 2x'(t)x(t)+2y'(t)y(t)=-2x(t)y(t)+2x(t)y(t)=0\n", "$$\n", "donc $I(t)=I(0)=0^2+1^2=1$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Approximations**\n", "\n", "On notera $u_n\\approx x_n=x(t_n)$ et $w_n\\approx y_n=y(t_n)$.\n", "\n", "À chaque instant $t_n$, on calculera $J_n=u_n^2+w_n^2\\approx I_n=I(t_n)$.\n", "\n", "Choisissons $h=t_{n+1}-t_n=\\frac{\\pi}{48}$." ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "from matplotlib.pylab import *\n", "# from scipy.optimize import fsolve # non necessaire car on resout l'equation implicite a la main\n", "\n", "t0 = 0\n", "tfinal = 4*pi\n", "\n", "h = pi/48\n", "tt = arange(t0,tfinal+h/2,h)\n", "\n", "x0 = 1\n", "y0 = 0\n", "\n", "phi1 = lambda t,x,y : -y\n", "phi2 = lambda t,x,y : x" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Euler explicite**\n", "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=u_n+h\\varphi_1(t_n,u_n,w_n)=u_n-hw_n,\\\\\n", "w_{n+1}=w_n+h\\varphi_2(t_n,u_n,w_n)=w_n+hu_n\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [], "source": [ "def EE(phi1,phi2,tt,x0,y0):\n", "\tuu = [x0]\n", "\tww = [y0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tuu.append(uu[i]+h*phi1(tt[i],uu[i],ww[i]))\n", "\t\tww.append(ww[i]+h*phi2(tt[i],uu[i],ww[i]))\n", "\treturn [uu,ww]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On a\n", "$$\n", "J_{n+1}\n", "=u_{n+1}^2+w_{n+1}^2\n", "=(u_n-hw_n)^2+(w_n+hu_n)^2\n", "=(1+h^2)(u_n^2+w_n^2)\n", "=(1+h^2)J_n\n", "$$\n", "soit encore\n", "$$\n", "J_n=(1+h^2)^nJ_0=(1+h^2)^n.\n", "$$\n", "On voit que \n", "- l'invariant n'est conservé que si $h=0$, ce qui est impossible,\n", "- pour $h$ fixé, $\\lim\\limits_{n\\to+\\infty}J_n=+\\infty$,\n", "- pour $n$ fixé, l'erreur $|J_n-I_n|$ diminue comme $h^2$." ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "[uu_ep, ww_ep] = EE(phi1,phi2,tt,x0,y0)\n", "JJ_ep = [(uu_ep[i])**2+(ww_ep[i])**2 for i in range(len(tt))]\n", "\n", "\n", "figure(figsize=(18,5))\n", "\n", "subplot(1,3,1)\n", "plot(tt,uu_ep,tt,ww_ep)\n", "xlabel('t')\n", "legend(['x(t)','y(t)'])\n", "title('Euler progressif - x(t) et y(t)') \n", "\n", "subplot(1,3,2)\n", "plot(tt,JJ_ep)\n", "xlabel('t')\n", "title('Euler progressif - Invariant')\n", "\n", "subplot(1,3,3)\n", "plot(uu_ep,ww_ep)\n", "xlabel('x(t)')\n", "ylabel('y(t)')\n", "title('Euler progressif - y(x)'); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Euler implicite**\n", "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=u_n+h\\varphi_1(t_{n+1},u_{n+1},w_{n+1})=u_n-hw_{n+1},\\\\\n", "w_{n+1}=w_n+h\\varphi_2(t_{n+1},u_{n+1},w_{n+1})=w_n+hu_{n+1}\n", "\\end{cases}\n", "$$\n", "En resolvant le système linéaire on obtient une écriture explicite\n", "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=\\dfrac{u_n-hw_{n}}{1+h^2},\\\\\n", "w_{n+1}=\\dfrac{w_n+hu_{n}}{1+h^2}.\n", "\\end{cases}\n", "$$" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [], "source": [ "# Notons que ici il est inutile de passer phi1,phi2 car non utilisées explicitement dans le code\n", "def EI(phi1,phi2,tt,x0,y0):\n", "\tuu = [x0]\n", "\tww = [y0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tuu.append((uu[i]-h*ww[i])/(1+h**2))\n", "\t\tww.append((ww[i]+h*uu[i])/(1+h**2))\n", "\treturn [uu,ww]\n" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [], "source": [ "# VERSION AVEC fsolve (non demandé)\n", "from scipy.optimize import fsolve\n", "\n", "def EI(phi1,phi2,tt,x0,y0):\n", "\tuu = [x0]\n", "\tww = [y0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tsys = lambda z : [ -z[0]+uu[i]+h*phi1(tt[i+1],z[0],z[1]) , -z[1]+ww[i]+h*phi2(tt[i+1],z[0],z[1]) ]\n", "\t\tutemp,wtemp = fsolve( sys , (uu[i],ww[i]) ) \n", "\t\tuu.append(utemp)\n", "\t\tww.append(wtemp)\n", "\treturn [uu,ww]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On a\n", "$$\n", "J_{n+1}\n", "=u_{n+1}^2+w_{n+1}^2\n", "=\\frac{(u_n-hw_n)^2+(w_n+hu_n)^2}{(1+h^2)^2}\n", "=(u_n^2+w_n^2)\\frac{1+h^2}{(1+h^2)^2}\n", "=\\frac{1+h^2}{(1+h^2)^2}J_n\n", "=\\frac{1}{1+h^2}J_n\n", "$$\n", "soit encore\n", "$$\n", "J_n=\\left(\\frac{1}{1+h^2}\\right)^nJ_0=\\left(\\frac{1}{1+h^2}\\right)^n.\n", "$$\n", "On voit que \n", "- l'invariant n'est conservé que si $h=0$, ce qui est impossible,\n", "- pour $h$ fixé, $\\lim\\limits_{n\\to+\\infty}J_n=0^+$,\n", "- pour $n$ fixé, l'erreur $|J_n-I_n|$ diminue comme $h^2$." ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "[uu_er, ww_er] = EI(phi1,phi2,tt,x0,y0)\n", "JJ_er = [(uu_er[i])**2+(ww_er[i])**2 for i in range(len(tt))]\n", "\n", "figure(figsize=(18,5))\n", "\n", "subplot(1,3,1)\n", "plot(tt,uu_er,tt,ww_er)\n", "xlabel('t')\n", "legend(['x(t)','y(t)'])\n", "title('Euler regressif - x(t) et y(t)') \n", "\n", "subplot(1,3,2)\n", "plot(tt,JJ_er)\n", "xlabel('t')\n", "title('Euler regressif - Invariant')\n", "\n", "subplot(1,3,3)\n", "plot(uu_er,ww_er)\n", "xlabel('x(t)')\n", "ylabel('y(t)')\n", "title('Euler regressif - y(x)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Crank Nicolson**\n", "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=u_n+\\frac{h}{2}\\Big(\\varphi_1(t_{n},u_{n},w_{n})+\\varphi_1(t_{n+1},u_{n+1},w_{n+1})\\big)=u_n-\\frac{h}{2}w_{n}-\\frac{h}{2}w_{n+1},\\\\\n", "w_{n+1}=w_n+\\frac{h}{2}\\Big(\\varphi_2(t_{n},u_{n},w_{n})+\\varphi_2(t_{n+1},u_{n+1},w_{n+1})\\big)=w_n+\\frac{h}{2}u_{n}+\\frac{h}{2}u_{n+1}.\n", "\\end{cases}\n", "$$\n", "En resolvant le système linéaire on obtient une écriture explicite:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\begin{cases}\n", "u_0=1,\\\\\n", "w_0=0,\\\\\n", "u_{n+1}=\\dfrac{(4-h^2)u_n-4hw_{n}}{4+h^2},\\\\\n", "w_{n+1}=\\dfrac{(4-h^2)w_n+4hu_{n}}{4+h^2}.\n", "\\end{cases}\n", "$$\n", "De plus, on a\n", "\\begin{align*}\n", "J_{n+1}\n", "&=u_{n+1}^2+w_{n+1}^2\n", "\\\\\n", "&=\\frac{((4-h^2)u_n-4hw_n)^2+((4-h^2)w_n+4hu_n)^2}{(4+h^2)^2}\n", "\\\\\n", "&=\\frac{(4-h^2)^2u_n^2+16h^2w_n^2-8(4-h^2)hu_nw_n+(4-h^2)^2w_n^2+16h^2u_n^2+8(4-h^2)hu_nw_n}{(4+h^2)^2}\n", "\\\\\n", "&=\\frac{\\big((4-h^2)^2+16h^2\\big)(u_n^2+w_n^2)}{(4+h^2)^2}\n", "\\\\\n", "&=\\frac{(4+h^2)^2(u_n^2+w_n^2)}{(4+h^2)^2}\n", "\\\\\n", "&=(u_n^2+w_n^2)=J_n\n", "\\end{align*}\n", "\n", "\n", "On voit que l'invariant est conservé pour tout $h$\n", "\n", "Vérifions ces calculs avec `sympy`:" ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle \\left\\{ u_{np1} : \\frac{- dt^{2} u_{n} - 4 dt w_{n} + 4 u_{n}}{dt^{2} + 4}, \\ w_{np1} : \\frac{- dt^{2} w_{n} + 4 dt u_{n} + 4 w_{n}}{dt^{2} + 4}\\right\\}$" ], "text/plain": [ "⎧ 2 2 ⎫\n", "⎪ - dt ⋅uₙ - 4⋅dt⋅wₙ + 4⋅uₙ - dt ⋅wₙ + 4⋅dt⋅uₙ + 4⋅wₙ⎪\n", "⎨uₙₚ₁: ─────────────────────────, wₙₚ₁: ─────────────────────────⎬\n", "⎪ 2 2 ⎪\n", "⎩ dt + 4 dt + 4 ⎭" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle u_{n}^{2} + w_{n}^{2}$" ], "text/plain": [ " 2 2\n", "uₙ + wₙ " ] }, "execution_count": 73, "metadata": {}, "output_type": "execute_result" } ], "source": [ "import sympy as sym\n", "sym.init_printing()\n", "\n", "sym.var('u_n, u_np1, w_n, w_np1, dt')\n", "eq1 = sym.Eq( u_np1 , u_n-dt/2*w_n-dt/2*w_np1 )\n", "eq2 = sym.Eq( w_np1 , w_n+dt/2*u_n+dt/2*u_np1 )\n", "sol=sym.solve([eq1,eq2],[u_np1,w_np1],dict=True)[0]\n", "display(sol)\n", "\n", "J_np1=u_np1**2+w_np1**2\n", "J_np1.subs(sol).simplify()" ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [], "source": [ "# Notons que ici il est inutile de passer phi1,phi2 car non utilisées explicitement dans le code\n", "def cn(phi1,phi2,tt,x0,y0):\n", "\tuu = [x0]\n", "\tww = [y0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tuu.append(((4-h**2)*uu[i]-4*h*ww[i])/(4+h**2))\n", "\t\tww.append(((4-h**2)*ww[i]+4*h*uu[i])/(4+h**2))\n", "\treturn [uu,ww]" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [], "source": [ "# VERSION AVEC fsolve (non demandé)\n", "from scipy.optimize import fsolve\n", "\n", "def cn(phi1,phi2,tt,x0,y0):\n", "\tuu = [x0]\n", "\tww = [y0]\n", "\th = tt[1]-tt[0]\n", "\tfor i in range(len(tt)-1):\n", "\t\tsys = lambda z : [ -z[0]+uu[i]+h/2*(phi1(tt[i],uu[i],ww[i])+phi1(tt[i+1],z[0],z[1])) , \n", " -z[1]+ww[i]+h/2*(phi2(tt[i],uu[i],ww[i])+phi2(tt[i+1],z[0],z[1])) ]\n", "\t\tutemp,wtemp = fsolve( sys , (uu[i],ww[i]) ) \n", "\t\tuu.append(utemp)\n", "\t\tww.append(wtemp)\n", "\treturn [uu,ww]" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "[uu_cn, ww_cn] = cn(phi1,phi2,tt,x0,y0)\n", "JJ_cn = [(uu_cn[i])**2+(ww_cn[i])**2 for i in range(len(tt))]\n", "\n", "figure(figsize=(18,5))\n", "\n", "subplot(1,3,1)\n", "plot(tt,uu_cn,tt,ww_cn)\n", "xlabel('t')\n", "legend(['x(t)','y(t)'])\n", "title('Crank Nicolson - x(t) et y(t)') \n", "\n", "subplot(1,3,2)\n", "plot(tt,JJ_cn)\n", "xlabel('t')\n", "title('Crank Nicolson - Invariant')\n", "\n", "subplot(1,3,3)\n", "plot(uu_cn,ww_cn)\n", "xlabel('x(t)')\n", "ylabel('y(t)')\n", "title('Crank Nicolson - y(x)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution exacte**\n", "\n", "La solution exacte est\n", "\\begin{align*}\n", "x(t)&=\\cos(t),\\\\\n", "y(t)&=\\sin(t).\n", "\\end{align*}\n", "Cette solution est périodique de période $2\\pi$ et on a bien\n", "$$\n", "I(t)=x^2(t) + y^2(t) = 1 \\quad \\forall t.\n", "$$\n", "Vérifions-le avec le module `sympy`:" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d t} x{\\left(t \\right)} = - y{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(x(t)) = -y(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{d}{d t} y{\\left(t \\right)} = x{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(y(t)) = x(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left[ x{\\left(t \\right)} = - C_{1} \\cos{\\left(t \\right)} - C_{2} \\sin{\\left(t \\right)}, \\ y{\\left(t \\right)} = - C_{1} \\sin{\\left(t \\right)} + C_{2} \\cos{\\left(t \\right)}\\right]$" ], "text/plain": [ "[x(t) = -C₁⋅cos(t) - C₂⋅sin(t), y(t) = -C₁⋅sin(t) + C₂⋅cos(t)]" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left\\{ C_{1} : -1, \\ C_{2} : 0\\right\\}$" ], "text/plain": [ "{C₁: -1, C₂: 0}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle x{\\left(t \\right)} = \\cos{\\left(t \\right)}$" ], "text/plain": [ "x(t) = cos(t)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle y{\\left(t \\right)} = \\sin{\\left(t \\right)}$" ], "text/plain": [ "y(t) = sin(t)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()\n", "\n", "t = sym.Symbol('t')\n", "x = sym.Function('x')\n", "y = sym.Function('y')\n", "edo1 = sym.Eq( sym.diff(x(t),t) , -y(t) )\n", "edo2 = sym.Eq( sym.diff(y(t),t) , x(t) )\n", "display(edo1)\n", "display(edo2)\n", "solgen = sym.dsolve([edo1,edo2],[x(t),y(t)])\n", "display(solgen)\n", "\n", "t_0=0\n", "x_0=1\n", "y_0=0\n", "consts = sym.solve( [ sym.Eq( x_0, solgen[0].rhs.subs(t,t_0)) , sym.Eq( y_0, solgen[1].rhs.subs(t,t_0)) ] , dict=True)[0]\n", "display(consts)\n", "solpar_1=solgen[0].subs(consts)\n", "solpar_2=solgen[1].subs(consts)\n", "display(solpar_1)\n", "display(solpar_2)\n", "\n", "func_1 = sym.lambdify(t,solpar_1.rhs,'numpy')\n", "func_2 = sym.lambdify(t,solpar_2.rhs,'numpy')\n", "\n", "from matplotlib.pylab import *\n", "figure(figsize=(17,7))\n", "tt=linspace(0,30,501)\n", "xx=func_1(tt)\n", "yy=func_2(tt)\n", "subplot(1,2,1)\n", "plot(tt,xx,tt,yy)\n", "legend([r'$x(t)$',r'$y(t)$'])\n", "subplot(1,2,2)\n", "plot(xx,yy)\n", "xlabel(r'$x$')\n", "ylabel(r'$y$')\n", "axis('equal');" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "hide_input": false, "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": "3.8.5" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "308px" }, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }