{ "cells": [ { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 5, "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": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python version 3.10.6 (main, Nov 14 2022, 16:10:14) [GCC 11.3.0]\n" ] } ], "source": [ "import sys #only needed to determine Python version number\n", "print('Python version ' + sys.version)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# M62_CM5 : Convergence et A-stabilité des schémas multipas linéaires\n", "$\\renewcommand{\\R}{\\mathbb{R}}$ $\\renewcommand{\\N}{\\mathbb{N}}$ $\\renewcommand{\\dt}{\\mathrm{d}t}$ $\\renewcommand{\\dx}{\\mathrm{d}x}$ $\\renewcommand{\\dtau}{\\mathrm{d}\\tau}$ $\\renewcommand{\\CC}[1]{\\mathscr{C}}$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "Considérons le problème de Cauchy\n", "\n", ">trouver une fonction $y \\colon I\\subset \\mathbb{R} \\to \\mathbb{R}$ définie sur un intervalle $I=[t_0,T]$ telle que\n", ">$$\\begin{cases}\n", "y'(t) = \\varphi(t,y(t)), &\\forall t \\in I=[t_0,T],\\\\\n", "y(t_0) = y_0,\n", "\\end{cases}$$\n", ">avec $y_0$ une valeur donnée et supposons que l'on ait montré l'existence et l'unicité d'une solution $y$ pour $t\\in I$.\n", "\n", "\n", "
\n", "\n", "Considérons une méthode numérique à $q=p+1$ étapes (=pas) linéaire.\n", "Elle s'écrit sous la forme générale\n", "$$\n", "u_{n+1} \n", "= \n", "\\sum_{j=0}^p a_ju_{n-j}\n", "+\n", "h\\sum_{j=0}^p b_j\\varphi(t_{n-j},u_{n-j})\n", "+\n", "hb_{-1}\\varphi(t_{n+1},u_{n+1}),\n", "\\qquad\n", "n=p,p+1,\\dots,N-1\n", "$$\n", "où les $\\{a_k\\}$ et $\\{b_k\\}$ sont des coefficients donnés et $p\\ge0$ un entier.\n", "\n", "
\n", "\n", "\n", "\n", "**Remarques** :\n", "- Si $b_{-1}=0$ la méthode est explicite, sinon implicite.\n", "- Les données initiales $u_0, u_1, \\dots, u_p$ doivent être fournies. Mis à part $u_0$, qui est égale à $y_0$ donné, les autres valeurs, $u_1, \\dots, u_p$ peuvent être obtenues à l’aide de méthodes suffisament précises. \n", "\n", "\n", "**Rappeles** :\n", "- Méthodes classiques (à $q=1$ pas)\n", " - Euler explicite \n", " $$\n", " u_{n+1}=u_n+h\\varphi(t_n,u_n)\n", " \\quad\\implies\\quad\n", " p=0,\\ a_0=1,\\ b_{-1}=0,\\ b_0=1;\n", " $$\n", " - Euler implicite \n", " $$\n", " u_{n+1}=u_n+h\\varphi(t_{n+1},u_{n+1})\n", " \\quad\\implies\\quad\n", " p=0,\\ a_0=1,\\ b_{-1}=1,\\ b_0=0;\n", " $$\n", " - Crank-Nicolson \n", " $$ \n", " u_{n+1}=u_n+\\frac{h}{2}\\left(\\varphi(t_n,u_n)+\\varphi(t_{n+1},u_{n+1})\\right)\n", " \\quad\\implies\\quad\n", " p=0,\\ a_0=1,\\ b_{-1}=\\frac{1}{2},\\ b_0=\\frac{1}{2}.\n", " $$\n", "- Méthodes à $q\\ge1$ pas \n", " - Les méthodes AB$_q$, AM$_q$, N$_q$, MS$_q$ et BFD$_q$ sont toutes des méthodes numériques à $q=p+1$ étapes (=pas) linéaires. \n", "- NB Les méthodes EM et Heun ne rentrent pas dans ce cadre: elles sont des méthodes de la famille Runge-Kutta.\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Polynômes caractéristiques\n", "Dans cette partie nous allons étudier d'abord la convergence puis la A-stabilité d'une méthode multistep. \n", "\n", "Dans l'analyse de ces méthodes, trois polynômes jouent un rôle clé. Pour cela, commençons par réécrire le schéma multistep comme suit:\n", "$$\n", "u_{n+1} -\\sum_{j=0}^p a_ju_{n-j}= h\\left(\\sum_{j=0}^p b_j\\varphi(t_{n-j},u_{n-j})+b_{-1}\\varphi(t_{n+1},u_{n+1})\\right).\n", "$$\n", "\n", "
\n", "\n", "**Définition.** \n", " \n", "Pour $r\\in\\mathbb{C}$, on associe à une méthode numérique linéaire multipas les trois polynômes caractéristiques suivants:\n", " \n", "- premier polynôme caractéristique\n", "$$\n", "\\varrho(r)=r^{p+1}-\\sum_{j=0}^p a_jr^{p-j}\n", "$$\n", " \n", "- second polynôme caractéristique\n", "$$\n", "\\sigma(r)=b_{-1}r^{p+1}+\\sum_{j=0}^p b_jr^{p-j}\n", "$$\n", " \n", "- polynôme de A-stabilité\n", "$$\n", "p(r) = \\varrho(r) - z \\sigma(r)\n", "$$\n", "\n", "
\n", "\n", "\n", "Formellement, \n", "- pour construire le premier polynôme caractéristique on ne regarde que le LHS et les $u_{n-j}$ deviennent des $r^{p-j}$,\n", "- pour construire le second polynôme caractéristique on ne regarde que le RHS divisé par $h$ et les $\\varphi(t_{n-j},u_{n-j})$ deviennent des $r^{p-j}$.\n", "\n", "On verra que les racines du polynôme $\\varrho$ sont liées à la zéro-stabilité tandis que celles du polynôme $p$ sont liées à la stabilité absolue (en association avec un choix particulier de $z=h\\lambda$).\n", "\n", "\n", "**Exemples** :\n", "- Euler explicite: $\\varrho(r)=r-1$ et $\\sigma(r)=1$ \n", "- Euler implicite: $\\varrho(r)=r-1$ et $\\sigma(r)=r$ \n", "- Crank-Nicolson: $\\varrho(r)=r-1$ et $\\sigma(r)=\\frac{1}{2}r+\\frac{1}{2}$\n", "- AB$_q$ ou AM$_q$: $\\varrho(r)=r^{q+1}-r^{q}=r^{q}(r-1)$ \n", "- N$_q$ ou MS$_q$: $\\varrho(r)=r^{q+1}-r^{q-1}=r^{q-1}(r^2-1)$\n", "- BDF$_2$: $\\varrho(r)=r^2-\\frac{4}{3}r+\\frac{1}{3}=(r-1)\\left(r-\\frac{1}{3}\\right)$ et $\\sigma(r)=\\frac{2}{3}$ \n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convergence d'un schéma multipas linéaire\n", "\n", "\n", "
\n", "Théorème (Dahlquist 1956). \n", " \n", "Une méthode linéaire multipas est **convergente** si et seulement si elle est \n", "- 1️⃣ **consistante** et \n", "- 2️⃣ **(zero)-stable.**\n", "\n", "
\n", "\n", "### 1️⃣ Consistance\n", "Une méthode est dite consistante si $\\tau(h)=\\max_n |\\tau_n(h)|$ tend vers zéro quand $h$ tend vers zéro, où $\\tau_n(h)$ est l’erreur de troncature locale de la méthode multi-pas définie par\n", "$$\n", "\\tau_n(h)=\\frac{1}{h}\\left(y_{n+1}-\\sum_{j=0}^p a_jy_{n-j}-h\\sum_{j=0}^p b_j\\varphi(t_{n-j},y_{n-j})-hb_{-1}\\varphi(t_{n+1},y_{n+1})\\right).\n", "$$\n", "\n", "\n", "
\n", "\n", "**Définition.**\n", " \n", "Pour $i=0,1,\\dots$ introduisons la quantité\n", "$$\n", "\\xi(i) = \\sum_{j=0}^p (-j)^{i}a_j+i\\sum_{j=-1}^p (-j)^{i-1}b_j,\n", "$$\n", "ayant posé $(-j)^0=1$ même pour $j=0$.\n", " \n", "
\n", "\n", "On a\n", "- $\\xi(0)=\\sum_{j=0}^p a_j$\n", "- $\\xi(1)=\\sum_{j=0}^p -j a_j+\\sum_{j=-1}^p b_j$\n", "- $\\xi(2)=\\sum_{j=0}^p j^{2}a_j+2\\sum_{j=-1}^p -j b_j$\n", "- $\\xi(3)=\\sum_{j=0}^p (-j)^{3}a_j+3\\sum_{j=-1}^p j^{2}b_j$\n", "- $\\dots$\n", "\n", "\n", "\n", "\n", "**Exemple avec un schéma à $q=4$ pas et donc $p=3$**:\n", "- $\\xi(0)=\\Big(a_0+a_1+a_2+a_3\\Big)$\n", "- $\\xi(1)=-\\Big(a_1+2a_2+3a_3\\Big)+b_{-1}+\\Big(b_1+b_2+b_3\\Big)$\n", "- $\\xi(2)=\\Big(a_1+4a_2+9a_3\\Big)+2b_{-1}-2\\Big(b_1+2b_2+3b_3\\Big)$\n", "- $\\xi(3)=-\\Big(a_1+8a_2+27a_3\\Big)+3b_{-1}+3\\Big(b_1+4b_2+9b_3\\Big)$" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Méthode à q=2 pas, on affiche ξ(i) pour i=0,...,5\n" ] }, { "data": { "text/latex": [ "$\\displaystyle ξ(0) = a_{0} + a_{1}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle ξ(1) = - a_{1} + b_{0} + b_{1} + b_{-1}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle ξ(2) = a_{1} - 2 \\left(b_{1} - b_{-1}\\right)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle ξ(3) = - a_{1} + 3 \\left(b_{1} + b_{-1}\\right)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle ξ(4) = a_{1} - 4 \\left(b_{1} - b_{-1}\\right)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle ξ(5) = - a_{1} + 5 \\left(b_{1} + b_{-1}\\right)$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import display, Math, Latex\n", "from sympy import *\n", "\n", "def xi(i):\n", " aa = symbols(f'a_0:{q}')\n", " bb = symbols(f'b_0:{q}')\n", " bm1 = Symbol('b_{-1}')\n", " p = len(aa)\n", " sa = sum( [ (-j)**i * aa[j] for j in range(p) ] )\n", " sb = bm1+sum( [(-j)**(i-1) * bb[j] for j in range(1,p)] )\n", " # ??? si j=0 et i=0, il calcule (-j)**i =1 et on a bien a_0 dans la somme\n", " # mais si j=0 et i=1 il ne calcule pas b_0 et il faut l'ajouter à la main\n", " if i==1:\n", " sb += bb[0]\n", " return (sa).factor()+(i*sb).factor()\n", "\n", "\n", "p = 1 # j = 0...p # coeffs du schema\n", "omega = 5 # i = 0, ..., omega\n", "q = p+1\n", "print(f\"Méthode à q={p+1} pas, on affiche ξ(i) pour i=0,...,{omega}\")\n", "for i in range(omega+1):\n", " display(Math(f\"ξ({i}) = {latex(xi(i))}\") )\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Par un développement de Taylor (assez fastidieux), on peut montrer que:\n", "\n", "
\n", "\n", "Proposition [consistance = ordre 1] \n", "\n", "La méthode est consistante ssi $\\xi(0)=\\xi(1)=1$, autrement dit ssi \n", "$$\n", "\\begin{cases}\n", "\\displaystyle\\sum_{j=0}^p a_j=1,\n", "\\\\\n", "\\displaystyle-\\sum_{j=0}^p ja_j+\\sum_{j=-1}^p b_j=1.\n", "\\end{cases}\n", "$$\n", " \n", "
\n", "\n", "Remarque: la première condition de consistance (i.e. $\\xi(0)=1$) équivaut à $\\varrho(1)=0$, la deuxième (i.e. $\\xi(1)=1$) à $\\varrho'(1)=\\sigma(1)$.\n", "\n", "\n", "Si, de plus, $\\tau(h)=\\mathscr{O}(Ch^\\omega)$, on dit que la méthode est d'ordre $\\omega$. Par des développements de Taylor, on peut montrer que la méthode est d'ordre $\\omega$ ssi $\\xi(0)=\\xi(1)=\\dots=\\xi(\\omega)=1$, autrement dit: \n", "\n", "
\n", "\n", "**Proposition [ordre $>1$]**\n", " \n", "La méthode est d'ordre $\\omega\\ge2$ ssi $\\xi(0)=\\xi(1)=\\dots=\\xi(\\omega)=1$, autrement dit ssi elle est consistante et, de plus,\n", "$$\n", "\\sum_{j=0}^p (-j)^{i}a_j+i\\sum_{j=-1}^p (-j)^{i-1}b_j=1 \\quad i=2,\\dots,\\omega.\n", "$$\n", "\n", "
\n", "\n", "\n", "\n", "\n", "**Exemple**: schéma AB$_2$\n", "- Schéma: $u_{n+1}=u_{n}+ \\frac{h}{2} \\big(3\\varphi_{n}-\\varphi_{n-1}\\big)$\n", "- Coefficients: $q=2$, $p=1$, $a_0=1$, $a_1=0$, $b_0=\\frac{3}{2}$, $b_1=-\\frac{1}{2}$, $b_{-1}=0$\n", "- Consistance: $\\begin{cases}\\xi(0)=1+0=1\\\\\\xi(1)=-(0a_0+1a_1)+(b_{-1}+b_0+b_1)=1\\end{cases}$\n", "- Ordre $\\omega$: \n", " - pour $i=2$ on a $\\xi(2)=a_1+2b_{-1}-2b_1=1$ donc $\\omega\\ge2$,\n", " - pour $i=3$ on a $\\xi(3)=-a_1+3b_{-1}+3b_1\\neq1$ donc $\\omega<3$\n", " - on conclut que l'ordre $\\omega$ est $2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2️⃣ Zéro-stabilité\n", "\n", " \n", "\n", "
\n", "Proposition [zéro-stabilité et condition des racines]\n", "\n", "Soient $r_0, r_1,\\dots, r_p$ les $p+1$ racines du polynôme $\\varrho$ (dans $\\mathbb{C}$). On peut montrer que la méthode est **zéro-stable** ssi \n", "$$\n", "\\begin{cases}\n", "|r_j|\\le1 \\quad\\text{pour tout }j=0,\\dots,p\n", "\\\\\n", "\\varrho'(r_j)\\neq0 \\text{ si } |r_j|=1.\n", "\\end{cases}\n", "$$\n", "
\n", "\n", "En particulier:\n", "- les méthodes à un pas (EE, EI, CN) vérifient $\\varrho(r)=r-1$: le polynôme $\\varrho$ n'a qu'une racine, c'est $r=1$. Toutes ces méthodes sont donc zéro-stables. On peut donc conclure que pour les méthodes à un pas, \"consistance $=$ convergence\";\n", "- plus généralement, les méthodes de Adam à $q$ pas vérifient $\\varrho(r)=r^{p+1}-r^p=r^p(r-1)$: il n'y a que deux racines, la racine $1$ de multiplicité $1$ et la racine $0$ de multiplicité $p$. Toutes ces méthodes sont donc zéro-stables, ici aussi on peut dire \"consistance $=$ convergence\";\n", "- les méthodes de Nystrom et Milne-Simpson à $q$ pas vérifient $\\varrho(r)=r^{p+1}-r^{p-1}=r^{p-1}(r-1)(r+1)$: il n'y a que trois racines, les racines $\\pm1$ de multiplicité $1$ et la racine $0$ de multiplicité $p-1$. Toutes ces méthodes sont donc zéro-stables, ici aussi on peut dire \"consistance $=$ convergence\";\n", "- enfin, on peut montrer que les méthodes BDF sont zéro-stables ssi $p\\le4$ (et donc $q\\le5$, voir les calculs `sympy` ci-dessous)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3️⃣ Ordre de convergence\n", "\n", "*Le 🎅 n'existe pas* : la zero stabilité implique une restriction sur l’ordre atteignable pour une méthode multipas. On appelle cette contrainte la première barrière de Dahlquist :\n", "\n", "
\n", "\n", "Première barrière de Dahlquist [limitation de l'ordre] \n", "\n", "L’ordre $\\omega$ d’une méthode multipas à $q)$ étapes convergente satisfait les inégalités suivantes:\n", "- si $b_{-1}=0$ (la méthode est explicite) alors $\\omega\\le q$\n", "- si $b_{-1}\\neq0$ (la méthode est implicite) on doit considérér deux cas \n", " - si $q$ est impair alors $\\omega\\le q+1$\n", " - si $q$ est pair alors $\\omega\\le q+2$\n", " \n", "
\n", "\n", "\n", "**Exemples** :\n", "- Soit une méthode explicite ($b_{-1}=0$):\n", " - si elle est à $q=1$ pas alors son ordre de consistance est au plus $\\omega=q=1$; (exemple: AB$_1$=EE qui a ordre 1)\n", " - si elle est à $q=2$ pas alors son ordre de consistance est au plus $\\omega=q=2$; (exemple: AB$_2$ qui a ordre 2)\n", " \n", "- Soit une méthode implicite ($b_{-1}\\neq0$):\n", " - si elle est à $q=1$ pas alors son ordre de consistance est au plus $\\omega=q+1=2$; (exemple: AM$_1$=CN qui a ordre 2) \n", " (Cas particulier: AM$_0$=EI est aussi à un pas mais avec notre notation on dirait à 0 pas et on trouve que l'ordre est $q+1=1$)\n", " - si elle est à $q=2$ pas, alors son ordre de consistance est au plus $\\omega=q+2=4$; (exemple: AM$_2$ qui a ordre 3 et MS$_2$ qui a ordre 4)." ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "C'est une méthode à 4 pas d'ordre au plus 6\n", "==========================\n", "La méthode est consistante d'ordre >=1 si \n" ] }, { "data": { "text/latex": [ "$\\displaystyle a_{0} + a_{1} + a_{2} + a_{3}\\mathtt{\\text{=1}}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle - a_{1} - 2 a_{2} - 3 a_{3} + b_{0} + b_{1} + b_{2} + b_{3} + b_{-1}\\mathtt{\\text{=1}}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "==========================\n", "La méthode est consistante d'ordre >=2 si \n" ] }, { "data": { "text/latex": [ "$\\displaystyle a_{1} + 4 a_{2} + 9 a_{3} - 2 \\left(b_{1} + 2 b_{2} + 3 b_{3} - b_{-1}\\right)\\mathtt{\\text{=1}}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "==========================\n", "La méthode est consistante d'ordre >=3 si \n" ] }, { "data": { "text/latex": [ "$\\displaystyle - a_{1} - 8 a_{2} - 27 a_{3} + 3 \\left(b_{1} + 4 b_{2} + 9 b_{3} + b_{-1}\\right)\\mathtt{\\text{=1}}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "==========================\n", "La méthode est consistante d'ordre >=4 si \n" ] }, { "data": { "text/latex": [ "$\\displaystyle a_{1} + 16 a_{2} + 81 a_{3} - 4 \\left(b_{1} + 8 b_{2} + 27 b_{3} - b_{-1}\\right)\\mathtt{\\text{=1}}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "==========================\n", "La méthode est consistante d'ordre >=5 si \n" ] }, { "data": { "text/latex": [ "$\\displaystyle - a_{1} - 32 a_{2} - 243 a_{3} + 5 \\left(b_{1} + 16 b_{2} + 81 b_{3} + b_{-1}\\right)\\mathtt{\\text{=1}}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "==========================\n", "La méthode est consistante d'ordre >=6 si \n" ] }, { "data": { "text/latex": [ "$\\displaystyle a_{1} + 64 a_{2} + 729 a_{3} - 6 \\left(b_{1} + 32 b_{2} + 243 b_{3} - b_{-1}\\right)\\mathtt{\\text{=1}}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from IPython.display import display, Math, Latex\n", "def prlat(*args):\n", " str = ''\n", " for arg in args:\n", " str += latex(arg)\n", " display(Math(str))\n", " \n", "# j = 0...p # coeffs du schema\n", "# q = p+1 # nb de pas\n", "# ω # ordre de la méthode\n", "\n", "p = 3\n", "q = p+1 \n", "if q%2==0:\n", " ordre_max = q+2\n", "else:\n", " ordre_max = q+1\n", "\n", "print(f\"C'est une méthode à {q} pas d'ordre au plus {ordre_max}\")\n", "\n", "from sympy import *\n", "\n", "aa = symbols(f'a_0:{q}')\n", "bb = symbols(f'b_0:{q}')\n", "bm1 = Symbol('b_{-1}')\n", "\n", "i=1\n", "sa=sum( [-j*aa[j] for j in range(len(aa))] )\n", "sb=bm1+sum( [bb[j] for j in range(len(bb))] )\n", "print(f\"==========================\\nLa méthode est consistante d'ordre >={i} si \")\n", "prlat(sum(aa).factor(),\"=1\" )\n", "prlat((sa).factor()+(i*sb).factor(),\"=1\")\n", "\n", "for i in range(2,ordre_max+1):\n", " sa=sum( [(-j)**i*aa[j] for j in range(len(aa))] )\n", " sb=bm1+sum( [(-j)**(i-1)*bb[j] for j in range(1,len(bb))] )\n", " print(f\"==========================\\nLa méthode est consistante d'ordre >={i} si \")\n", " prlat((sa).factor()+(i*sb).factor(),\"=1\" )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Récapitulatif des méthodes multipas vues jusqu'ici:" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " EE_AB1\n", "\tq = 1\n", "\tExplicite\n", "\tConsistance: True\n", "\tOrdre 1\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r - 1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " EI_AM0_BDF1\n", "\tq = 1\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 1\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r - 1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " CN_AM1\n", "\tq = 1\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 2\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r - 1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AB2\n", "\tq = 2\n", "\tExplicite\n", "\tConsistance: True\n", "\tOrdre 2\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - r$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AB3\n", "\tq = 3\n", "\tExplicite\n", "\tConsistance: True\n", "\tOrdre 3\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{3} - r^{2}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AB4\n", "\tq = 4\n", "\tExplicite\n", "\tConsistance: True\n", "\tOrdre 4\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{4} - r^{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AB5\n", "\tq = 5\n", "\tExplicite\n", "\tConsistance: True\n", "\tOrdre 5\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{5} - r^{4}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AM2\n", "\tq = 2\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 3\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - r$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AM3\n", "\tq = 3\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 4\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{3} - r^{2}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AM4\n", "\tq = 4\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 5\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{4} - r^{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " BDF2\n", "\tq = 2\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 2\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - \\frac{4 r}{3} + \\frac{1}{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0.333333333333333, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " BDF3\n", "\tq = 3\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 3\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{3} - \\frac{18 r^{2}}{11} + \\frac{9 r}{11} - \\frac{2}{11}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0, \\ 0.426401432711221, \\ 0.426401432711221\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " BDF4\n", "\tq = 4\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 4\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{4} - \\frac{48 r^{3}}{25} + \\frac{36 r^{2}}{25} - \\frac{16 r}{25} + \\frac{3}{25}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0, \\ 0.56086151609339, \\ 0.56086151609339, \\ 0.38147840911841\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " BDF5\n", "\tq = 5\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 5\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{5} - \\frac{300 r^{4}}{137} + \\frac{300 r^{3}}{137} - \\frac{200 r^{2}}{137} + \\frac{75 r}{137} - \\frac{12}{137}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0, \\ 0.708710816266406, \\ 0.417600758175733, \\ 0.708710816266406, \\ 0.417600758175733\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " BDF6\n", "\tq = 6\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 6\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{6} - \\frac{120 r^{5}}{49} + \\frac{150 r^{4}}{49} - \\frac{400 r^{3}}{147} + \\frac{75 r^{2}}{49} - \\frac{24 r}{49} + \\frac{10}{147}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0, \\ 0.40612326685391, \\ 0.474034857706592, \\ 0.474034857706592, \\ 0.863380267869827, \\ 0.863380267869827\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " MS2\n", "\tq = 2\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 4\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - 1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%reset -f\n", "from matplotlib.pylab import *\n", "# rcdefaults()\n", "rcParams.update({'font.size': 16})\n", "\n", "from fractions import Fraction\n", "\n", "from IPython.display import display, Math\n", "import sympy as sym\n", "sym.init_printing()\n", "r=sym.Symbol('r')\n", "\n", "\n", "sc = { \"EE_AB1\" : { \"aa\":[1], \"bb\":[ 1], \"bm1\":0 },\n", " \"EI_AM0_BDF1\" : { \"aa\":[1], \"bb\":[ 0], \"bm1\":1 },\n", " \"CN_AM1\" : { \"aa\":[1], \"bb\":[Fraction(1,2)], \"bm1\":1/2 }, \n", " \"AB2\": { \"aa\":[1,0], \"bb\":[Fraction(3,2),Fraction(-1,2)], \"bm1\":0 }, \n", " \"AB3\": { \"aa\":[1,0,0], \"bb\":[Fraction(23,12),Fraction(-16,12), Fraction(5,12)], \"bm1\":0 }, \n", " \"AB4\": { \"aa\":[1,0,0,0], \"bb\":[Fraction(55,24),Fraction(-59,24), Fraction(37,24), Fraction(-9,24)], \"bm1\":0 }, \n", " \"AB5\": { \"aa\":[1,0,0,0,0], \"bb\":[Fraction(1901,720), Fraction(-2774,720), Fraction(2616,720), Fraction(-1274,720), Fraction(251,720)], \"bm1\":0 }, \n", " \"AM2\": { \"aa\":[1,0], \"bb\":[Fraction(8,12),Fraction(-1,12)], \"bm1\":Fraction(5,12) }, \n", " \"AM3\": { \"aa\":[1,0,0], \"bb\":[Fraction(19,24),Fraction(-5,24),Fraction(1,24)], \"bm1\":Fraction(9,24) }, \n", " \"AM4\": { \"aa\":[1,0,0,0], \"bb\":[Fraction(646,720),Fraction(-264,720),Fraction(106,720),Fraction(-19,720)], \"bm1\":Fraction(251,720) }, \n", " \"BDF2\": { \"aa\":[Fraction(4,3),Fraction(-1,3)], \"bb\":[0,0], \"bm1\":Fraction(2,3) }, \n", " \"BDF3\": { \"aa\":[Fraction(18,11),Fraction(-9,11),Fraction(2,11)], \"bb\":[0,0,0], \"bm1\":Fraction(6,11) }, \n", " \"BDF4\": { \"aa\":[Fraction(48,25),Fraction(-36,25),Fraction(16,25),Fraction(-3,25)], \"bb\":[0,0,0,0], \"bm1\":Fraction(12,25) }, \n", " \"BDF5\": { \"aa\":[Fraction(300,137),Fraction(-300,137),Fraction(200,137),Fraction(-75,137),Fraction(12,137)], \"bb\":[0,0,0,0,0], \"bm1\":Fraction(60,137) }, \n", " \"BDF6\": { \"aa\":[Fraction(120,49),Fraction(-150,49),Fraction(400,147),Fraction(-75,49),Fraction(24,49),Fraction(-10,147)], \"bb\":[0,0,0,0,0,0], \"bm1\":Fraction(20,49) }, \n", " \"MS2\": { \"aa\":[0,1], \"bb\":[Fraction(4,3),Fraction(1,3)], \"bm1\":Fraction(1,3) }\n", " } \n", "\n", "\n", "for schema in sc.keys():\n", " print(\"\\n\",schema)\n", " q=len(sc[schema][\"aa\"])\n", " p=q-1\n", " print(f\"\\tq = {q}\")\n", " aa=sc[schema][\"aa\"]\n", " bb=sc[schema][\"bb\"]\n", " bm1=sc[schema][\"bm1\"]\n", " \n", " if bm1==0:\n", " print(\"\\tExplicite\")\n", " else:\n", " print(\"\\tImplicite\")\n", " print(\"\\tConsistance: \",end=\"\")\n", " \n", " ordre=[]\n", " ordre.append( sum(aa)==1 and sum([-j*aa[j] for j in range(len(aa))])+bm1+sum(bb)==1 )\n", " print(ordre[-1])\n", " i=1\n", " while ordre[-1]:\n", " i+=1\n", " ordre.append( sum([(-j)**i*aa[j]+i*(-j)**(i-1)*bb[j] for j in range(len(aa))])+i*bm1==1)\n", " print(f\"\\tOrdre {len(ordre)-1}\")\n", " \n", " rho=array([1])\n", " rho=append(rho,-array(aa))\n", " display(Math(r'\\varrho(r)='+sym.latex(sym.expand(poly1d(rho)(r)))))\n", "# print(f\"\\tZéro-stabilité: |r_j|= {abs(roots(rho))}\")\n", "# print(\"\\tRacines: \",end=\"\")\n", "# display(sym.solve(sym.expand(poly1d(rho)(r))))\n", " display( Math(r' \\{|r_j|\\} = '+sym.latex( [abs(rac).simplify().evalf() for rac in sym.solve(sym.expand(poly1d(rho)(r)))] )))\n", " \n", " \n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A-stabilité\n", "\n", "La première barrière de Dalquist affirme qu'on peut augmenter arbitrairement l'ordre d'un schéma multipas en augmentant le nombre de pas. La convergence dépend ensuite juste du premier polynôme caractéristique. Cependant, dans la section précédente, on a considéré la résolution du problème de Cauchy sur des intervalles bornés et la convergence suppose $h\\to0$. \n", "\n", "Il existe tutefois de nombreuses situations dans lesquelles le problème de Cauchy doit être intégré sur des intervalles en temps très grands ou même infini. Dans ce cas, même pour $h$ fixé, $N$ tend vers l’infini, et\n", "un résultat comme la zéro-stabilité n’a plus de sens puisque le membre de droite contient lq quantité non bornée ($T-t_0$). \n", "On s’intéresse donc à des méthodes capables d’approcher la solution pour des intervalles en temps arbitrairement grands, même pour des pas de temps $h$ \"assez grands\".\n", "\n", ">Soit $\\lambda\\in\\mathbb{C}$ un nombre complexe tel que $\\Re(\\lambda)=-\\beta<0$ et considérons le problème de Cauchy\n", "$$\\begin{cases}\n", "y'(t)=\\lambda y(t), &\\text{pour }t>0,\\\\\n", "y(0)=1\n", "\\end{cases}$$\n", "Sa solution est $y(t)=e^{\\lambda t}$ et comme $\\Re(\\lambda)<0$ alors $$\\lim_{t\\to+\\infty}|y(t)|=0.$$\n", ">\n", ">Soit $h>0$ un pas de temps donné, $t_n=nh$ pour $n\\in\\mathbb{N}$ et notons $u_n\\approx y(t_n)$ une approximation de la solution $y$ au temps $t_n$.\n", ">\n", ">Si, sous d'éventuelles conditions sur $h$, on a\n", "$$\n", "\\lim_{n\\to+\\infty} |u_n| =0,\n", "$$\n", "alors on dit que le schéma est A-stable (absolument stable)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Région de A-stabilité\n", "On appelle **région de stabilité absolue $A$** d’une méthode numérique l’ensemble des nombres complexes $z = h\\lambda$ pour lesquels la méthode est absolument stable:\n", "$$\n", "A=\\Big\\{z = h\\lambda \\in \\mathbb{C} \\ \\Big| \\ |u_n|\\xrightarrow[n\\to+\\infty]{}0 \\Big\\}\n", "$$\n", "Une méthode numérique est inconditionellement A-stable si $\\mathbb{C}^-\\subset A$ où $\\mathbb{C}^-=\\{z\\in\\mathbb{C}|\\Re(z)<0\\}$.\n", "\n", "Une méthode à $q=p+1$ pas appliquée à ce problème modèle conduit à l'équation récurrente à\n", "$$\n", "u_{n+1}=\\sum_{j=0}^p a_j u_{n-j} + z \\sum_{j=0}^p b_ju_{n-j} + z b_{-1}u_{n+1}\n", "$$\n", "\n", "\n", "
\n", "\n", "Condition des racines stricte: \n", "une méthode multipas linéaire vérifie la condition des racines stricte (éventuellement sous conditions sur $h$) si les racines du polynôme $p$ sont dans le disque unité ouvert de $\\mathbb{C}$:\n", " \n", "$$\n", "\\text{il existe $h_0>0$ tel que }\\quad |r_j(z)|<1 \\quad\\text{pour tout }j=0,\\dots,p;\\ \\forall h\\le h_0\n", "$$\n", "
\n", "\n", "
\n", "\n", "Proposition. \n", "Une méthode multipas linéaire est absolument stable si et seulement si son polynôme de stabilité vérifie la condition des racines stricte.\n", "\n", "
\n", "\n", "\n", "
\n", "\n", "Deuxième barrière de Dahlquist [Conditions sur $h$] \n", "\n", "- Il n'existe pas de méthode multipas explicite inconditionellement A-stable.\n", "- Il n'existe pas de méthode multipas implicite d'ordre $>2$ inconditionellement A-stable.\n", "\n", "
\n", "\n", "**Conséquences:**\n", "- tous les schémas AB_q ont une condition de A-stabilité. \n", " Exemple: le schéma AB_1 (Euler explicite): $p(r)=(r-1)-z$. Il a une seule racine: $r=1+z$. On demande à ce que $|1+z|<1$. On obtient dans $\\mathbb{C}$ le cercle (ouvert) de centre $(-1,0)$ et rayon $1$. Si on considère le cas réel, i.e. $\\varphi(t,y)=\\beta y$ avec $\\beta=-\\Re(\\lambda)$, la condition devient $0<\\beta h<1$ comme nous avons déjà trouvé lors du cours CM-3.\n", " \n", "- les schémas AM_q avec $q>1$ ont une condition de A-stabilité. \n", " Exemple: le schéma AM_0 (Euler implicite): $p(r)=(r-1)-zr$. Il a une seule racine: $r=\\frac{1}{1+z}$. On demande à ce que $\\left|\\frac{1}{1+z}\\right|<1$. On obtient dans $\\mathbb{C}$ la partie exterieure du cercle (fermé) de centre $(1,0)$ et rayon $1$. Comme $\\mathbb{C}^-$ est contenu dans cette region, la méthode est inconditionellement A-stable. \n", " Exemple: le schéma AM_1 (Crank-Nicolson): $p(r)=(r-1)-z\\frac{1}{2}(r+1)$. Il a une seule racine: $r=\\frac{2+z}{2-z}$. On demande à ce que $\\left|\\frac{2+z}{2-z}\\right|<1$. On obtient dans $\\Re(z)<1$. Comme $\\mathbb{C}^-$ est contenu de cette region, la méthode est inconditionellement A-stable.\n" ] }, { "attachments": { "A_stab_Adams.png": { "image/png": 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} }, "cell_type": "markdown", "metadata": {}, "source": [ "**Régions de A-stabilité de diverses méthodes d'Adams-Bashforth (à gauche) et d'Adams-Moulton (à droite).** \n", "Source: A. Quarteroni, F. Saleri, P. Gervasio *Calcul Scientifique: Cours, exercices corrigés et illustrations en Matlab et Octave.*\n", "\n", "On remarque que les régions de stabilité absolue des méthodes d'Adams-Bashforth et d'Adams-Moulton sont bornées et diminuent quand l'ordre\n", "augmente.\n", "\n", "![A_stab_Adams.png](attachment:A_stab_Adams.png)" ] }, { "attachments": { "A_stab_BDF.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "**Régions de A-stabilité de diverses méthodes BDF.** \n", "Source: A. Quarteroni, F. Saleri, P. Gervasio *Calcul Scientifique: Cours, exercices corrigés et illustrations en Matlab et Octave.*\n", "\n", "On remarque que les régions de stabilité absolue des méthodes BDF, pour $q\\le6$, sont non bornées. En particulier, elles contiennent toujours les réels négatifs.\n", "\n", "![A_stab_BDF.png](attachment:A_stab_BDF.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Tracer les régions de A-stabilité.** \n", "Posons $z=h\\lambda$.\n", "Il est en général difficile de déterminer la région de stabilité absolue car on doit décider pour quels $z\\in\\mathbb{C}$ les racines du polynôme de stabilité vérifient la condition de racines stricte (i.e. $|r| < 1$). \n", "Il est plus aisé de déterminer la frontière de cette région car au moins une des racines de $p$ à la frontière est de module $1$. \n", "On a donc $|r| = 1$ sur $\\partial A$. \n", "La frontière de $A$ est alors un sous ensemble des points $z\\in\\mathbb{C}$ pour lesquels $r=e^{i\\vartheta}$, $\\vartheta\\in\\mathbb{R}$. \n", "On remplace alors $r =e^{i\\vartheta}$ dans $p$ et comme $e^{i\\vartheta}$ est racine, $p(e^{i\\vartheta}) = 0$ et on résoud l’équation. On obtient $z = z(\\vartheta)$ ce qui donne une courbe dans $\\mathbb{C}$ en fonction de l’angle $\\vartheta$, ce qui décrit donc une courbe polaire.\n", "Par conséquent, pour obtenir une représentation approchée de $\\partial A$, il suffit d’évaluer le second membre pour diverses valeurs de $r$ sur le cercle unité, diverses valeurs de $\\vartheta\\in\\mathbb{R}$ et $r=e^{i\\vartheta}$. " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "# plt.rcdefaults()\n", "plt.rcParams.update({'font.size': 16})\n", "import numpy as np\n", "\n", "\n", "from IPython.display import display, Math\n", "\n", "import sympy as sp\n", "sp.init_printing()\n", "def polyCar(schema):\n", " sp.var('r z')\n", " p,aa,bb,bm1=schema[\"p\"],schema[\"aa\"],schema[\"bb\"],schema[\"bm1\"] \n", " rho = r**(p+1)-sum(aa[j]*r**(p-j)for j in range(p+1)) \n", " sigma = bm1*r**(p+1)+sum(bb[j]*r**(p-j)for j in range(p+1))\n", " display(Math(r'\\varrho(r)='+sp.latex(rho)))\n", " display(Math(r'\\sigma(r)='+sp.latex(sigma)))\n", " \n", "\n", "def polyCarIMPL(schema):\n", " sp.var('r z')\n", " p,aa,bb,bm1=schema[\"p\"],schema[\"aa\"],schema[\"bb\"],schema[\"bm1\"] \n", " rho=r**(p+1)-sum(aa[j]*r**(p-j)for j in range(p)) \n", " sigma=bm1*r**(p+1)+sum(bb[j]*r**(p-j)for j in range(p))\n", " display(Math(r'\\varrho(r)='+sp.latex(rho)))\n", " display(Math(r'\\sigma(r)='+sp.latex(sigma)))\n", " \n", " \n", "\n", "# Returns > 1 if argument is not in region of absolute stability\n", "def stabilityFunction(z,schema):\n", " schema[\"aa\"] = [float(a) for a in schema[\"aa\"]]\n", " schema[\"bb\"] = [float(b) for b in schema[\"bb\"]]\n", " schema[\"bm1\"] = float(schema[\"bm1\"])\n", " pol = np.array(schema[\"aa\"])+z*np.array(schema[\"bb\"])\n", " pol = np.append([1-z*schema[\"bm1\"]],-pol)\n", " return max(abs(np.roots(pol)))\n", "\n", "\n", "def Astabilite(schema):\n", " schema[\"aa\"] = [float(a) for a in schema[\"aa\"]]\n", " schema[\"bb\"] = [float(b) for b in schema[\"bb\"]]\n", " schema[\"bm1\"] = float(schema[\"bm1\"])\n", " p,aa,bb,bm1=schema[\"p\"],schema[\"aa\"],schema[\"bb\"],schema[\"bm1\"]\n", " \n", " # cc liste de points sur le circle unitaire\n", " rr = np.linspace(0,2*np.pi,201)\n", " cc = np.cos(rr)+1j*np.sin(rr) \n", " ## ff fonction vectorisée qui donne zz\n", " ff = lambda cc,p,aa,bb,bm1 : (cc**(p+1)-np.polyval(aa,cc))/(bm1*cc**(p+1)+np.polyval(bb,cc)) \n", " zz = ff(cc,p,aa,bb,bm1)\n", " \n", " plt.figure(figsize=(18,7))\n", " plt.subplot(1,2,1)\n", " plt.plot(zz.real,zz.imag,'r')\n", " plt.grid(True)\n", "# plt.axis('equal')\n", " plt.xlabel(r'$\\Re(h\\lambda)$')\n", " plt.ylabel(r'$\\Im(h\\lambda)$');\n", " plt.title(schema[\"Nom\"])\n", " Lx,Ly = plt.xlim(),plt.ylim()\n", " \n", " plt.subplot(1,2,2)\n", " x = np.linspace(Lx[0],Lx[1], 300)\n", " y = np.linspace(Ly[0],Ly[1], 300)\n", " [X,Y] = np.meshgrid(x,y)\n", " Z = np.zeros(X.shape)\n", " for m in range(X.shape[0]):\n", " for n in range(X.shape[1]):\n", " Z[m,n] = stabilityFunction(X[m,n] + 1j * Y[m,n], schema)\n", " plt.contour(X, Y, Z, [1], colors='k')\n", " plt.contourf(X, Y, Z, [0,1], colors=[[1, 0.5, 0.8]])\n", " return None" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r - 1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "EE = { \"Nom\":\"EE=AB1\", \"p\":0, \"aa\":[1], \"bb\":[1], \"bm1\":0 }\n", "polyCar(EE)\n", "Astabilite(EE) " ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - r$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=\\frac{3 r}{2} - \\frac{1}{2}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AB2 = { \"Nom\":\"AB2\", \"p\":1, \"aa\":[1,0], \"bb\":[sp.Rational(3,2),-sp.Rational(1,2)], \"bm1\":0 }\n", "polyCar(AB2)\n", "Astabilite(AB2)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{3} - r^{2}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=\\frac{23 r^{2}}{12} - \\frac{4 r}{3} + \\frac{5}{12}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AB3 = { \"Nom\":\"AB3\", \"p\":2, \"aa\":[1,0,0], \"bb\":[sp.Rational(23,12),-sp.Rational(16,12), sp.Rational(5,12)], \"bm1\":0 }\n", "polyCar(AB3)\n", "Astabilite(AB3)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{4} - r^{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=\\frac{55 r^{3}}{24} - \\frac{59 r^{2}}{24} + \\frac{37 r}{24} - \\frac{3}{8}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AB4 = { \"Nom\":\"AB4\", \"p\":3, \"aa\":[1,0,0,0], \"bb\":[sp.Rational(55,24),-sp.Rational(59,24), sp.Rational(37,24), -sp.Rational(9,24)], \"bm1\":0 }\n", "polyCar(AB4)\n", "Astabilite(AB4)" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{5} - r^{4}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=\\frac{1901 r^{4}}{720} - \\frac{1387 r^{3}}{360} + \\frac{109 r^{2}}{30} - \\frac{637 r}{360} + \\frac{251}{720}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AB5 = { \"Nom\":\"AB5\", \"p\":4, \"aa\":[1,0,0,0,0], \"bb\":[sp.Rational(1901,720), -sp.Rational(1387,360), sp.Rational(109,30), -sp.Rational(637,360), sp.Rational(251,720)], \"bm1\":0 }\n", "polyCar(AB5)\n", "Astabilite(AB5)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=r$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "AM0 = { \"Nom\":\"AM0=EI\", \"p\":0, \"aa\":[1], \"bb\":[0], \"bm1\": 1 }\n", "polyCarIMPL(AM0)\n", "#Astabilite(AM0)" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - r$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=\\frac{r^{2}}{2} + \\frac{r}{2}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "AM1 = { \"Nom\":\"AM1=CN\", \"p\":1, \"aa\":[1], \"bb\":[sp.Rational(1,2)], \"bm1\": sp.Rational(1,2) }\n", "polyCarIMPL(AM1)\n", "#Astabilite(AM1)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - r$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=\\frac{5 r^{2}}{12} + \\frac{2 r}{3} - \\frac{1}{12}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AM2 = { \"Nom\":\"AM2\", \"p\":1, \"aa\":[1,0], \"bb\":[sp.Rational(8,12),-sp.Rational(1,12)], \"bm1\":sp.Rational(5,12) }\n", "polyCar(AM2)\n", "Astabilite(AM2)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{3} - r^{2}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=\\frac{3 r^{3}}{8} + \\frac{19 r^{2}}{24} - \\frac{5 r}{24} + \\frac{1}{24}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AM3 = { \"Nom\":\"AM3\", \"p\":2, \"aa\":[1,0,0], \"bb\":[sp.Rational(19,24),-sp.Rational(5,24),sp.Rational(1,24)], \"bm1\":sp.Rational(9,24) }\n", "polyCar(AM3)\n", "Astabilite(AM3)" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{4} - r^{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=\\frac{251 r^{4}}{720} + \\frac{323 r^{3}}{360} - \\frac{11 r^{2}}{30} + \\frac{53 r}{360} - \\frac{19}{720}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AM4 = { \"Nom\":\"AM4\", \"p\":3, \"aa\":[1,0,0,0], \"bb\":[sp.Rational(646,720), sp.Rational(-264,720), sp.Rational(106,720), sp.Rational(-19,720)], \"bm1\":sp.Rational(251,720) }\n", "polyCar(AM4)\n", "Astabilite(AM4)" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - 1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=\\frac{r^{2}}{3} + \\frac{4 r}{3} + \\frac{1}{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "MS2 = { \"Nom\":\"MS2\", \"p\":1, \"aa\":[0,1], \"bb\":[sp.Rational(4,3),sp.Rational(1,3)], \"bm1\":sp.Rational(1,3) }\n", "polyCar(MS2)\n", "#Astabilite(MS2)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - r$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=r^{2}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BDF1 = { \"Nom\":\"BDF1=EI\", \"p\":1, \"aa\":[1], \"bb\":[0], \"bm1\":1 }\n", "polyCarIMPL(BDF1)\n", "Astabilite(BDF1)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - \\frac{4 r}{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\sigma(r)=\\frac{2 r^{2}}{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BDF2 = { \"Nom\":\"BDF2\", \"p\":1, \"aa\":[sp.Rational(4,3),-sp.Rational(1,3)], \"bb\":[0], \"bm1\":sp.Rational(2,3) }\n", "polyCarIMPL(BDF2)\n", "Astabilite(BDF2)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BDF3 = { \"Nom\":\"BDF3\", \"p\":2, \"aa\":[sp.Rational(18,11),-sp.Rational(9,11),sp.Rational(2,11)], \"bb\":[0], \"bm1\":sp.Rational(6,11) }\n", "#polyCarIMPL(BDF3)\n", "Astabilite(BDF3)" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BDF4 = { \"Nom\":\"BDF4\", \"p\":3, \"aa\":[sp.Rational(48,25),-sp.Rational(36,25),sp.Rational(16,25),-sp.Rational(3,25)], \"bb\":[0], \"bm1\":sp.Rational(12,25) }\n", "# polyCarIMPL(BDF4)\n", "Astabilite(BDF4)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BDF5 = { \"Nom\":\"BDF5\", \"p\":4, \"aa\":[sp.Rational(300,137),-sp.Rational(300,137),sp.Rational(200,137),-sp.Rational(75,137),sp.Rational(12,137)], \"bb\":[0], \"bm1\":sp.Rational(60,137) }\n", "# polyCar(BDF5)\n", "Astabilite(BDF5)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BDF6 = { \"Nom\":\"BDF6\", \"p\":5, \"aa\":[sp.Rational(120,49),-sp.Rational(150,49),sp.Rational(400,147),-sp.Rational(75,49),sp.Rational(24,49),-sp.Rational(10,147)], \"bb\":[0], \"bm1\":sp.Rational(20,49) }\n", "# polyCar(BDF6)\n", "Astabilite(BDF6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice\n", ">Pour les méthodes d'Euler explicite et implicite:\n", "> 1. Trouver les coefficients $p\\ge0$, $\\{a_k\\}$ et $\\{b_k\\}$ tels que $$\n", "u_{n+1} = \\sum_{j=0}^p a_ju_{n-j}+h\\sum_{j=0}^p b_j\\varphi(t_{n-j},u_{n-j})+hb_{-1}\\varphi(t_{n+1},u_{n+1}),\n", "\\qquad\n", "n=p,p+1,\\dots,N-1\n", "$$\n", "> 1. Écrire le premier polynôme caractéristique $$\n", "\\varrho(r)=r^{p+1}-\\sum_{j=0}^p a_jr^{p-j}\n", "$$\n", "et en calculer les racines.\n", "> 1. Montrer que la méthode est zéro-stable, i.e. que $$\n", "\\begin{cases}\n", "|r_j|\\le1 \\quad\\text{pour tout }j=0,\\dots,p\n", "\\\\\n", "\\varrho'(r_j)\\neq0 \\text{ si } |r_j|=1.\n", "\\end{cases}\n", "$$\n", "> 1. Montrer que la méthode est consistante, i.e. $$\n", "\\begin{cases}\n", "\\displaystyle\\sum_{j=0}^p a_j=1,\n", "\\\\\n", "\\displaystyle-\\sum_{j=0}^p ja_j+\\sum_{j=-1}^p b_j=1\n", "\\end{cases}\n", "$$\n", "> 1. Étudier l'ordre de consistance $\\omega\\ge2$ $$\n", "\\sum_{j=0}^p (-j)^{i}a_j+i\\sum_{j=-1}^p (-j)^{i-1}b_j=1 \\quad i=2,\\dots,\\omega.\n", "$$\n", ">5. Étudier la A-stabilité" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Euler explicite\n", "\n", "1. $u_{n+1}=u_n+h\\varphi(t_n,u_n)$ donc $p=0$, $a_0=1$, $b_{-1}=0$, $b_0=1$\n", "2. $\\varrho(r)=r-1$ donc il n'y a qu'une racine: $r_0=1$\n", "3. $|r_0|=1$ et $\\varrho'(1)=1$\n", "4. $a_0=1$ et $-0a_0+b_{-1}+b_0=1$\n", "4. Pour $i=2$ on a $(-0^2a_0)+2((+1)^{1}b_{-1}+0^{1}b_0)=0\\neq1$ donc $\\omega0$ et $\\Re(\\lambda)<0$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "colab": { "collapsed_sections": [], "default_view": {}, "name": "EdoExplicites.ipynb", "provenance": [], "version": "0.3.2", "views": {} }, "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": "3.10.6" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": true, "latex_user_defs": false, "report_style_numbering": true, "user_envs_cfg": true }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "", "title_sidebar": "Contents", "toc_cell": true, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "307px" }, "toc_section_display": true, "toc_window_display": false }, "vscode": { "interpreter": { "hash": "916dbcbb3f70747c44a77c7bcd40155683ae19c65e1c03b4aa3499c5328201f1" } } }, "nbformat": 4, "nbformat_minor": 4 }