{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n", "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.core.display import HTML\n", "css_file = './custom.css'\n", "HTML(open(css_file, \"r\").read())" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Last Updated On: 2021-01-28 10:33:09.538752\n" ] } ], "source": [ "from datetime import datetime\n", "print('Last Updated On: ', datetime.now())" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# M62_TP1 EDO : calcul approché VS formel." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calcul approché avec la fonction `odeint` du module `SciPy`\n", "--- " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "L'ECUE M62 n'est qu'une introduction aux méthodes numériques d'approximation d'EDO en utilisant Python comme langage commun de programmation. \n", "Nous allons étudier, programmer et tester plusieurs méthodes numériques.\n", "\n", "Cependant toutes ces méthodes (et bien plus) se trouvent déjà dans le module `SciPy`. \n", "Bien sûr vous devez toujours faire un peu de programmation avec Python pour les utiliser et une compréhension des fondements de la méthode numérique que vous utilisez est toujours indispensables. \n", "\n", "Voyons sur trois exemples comment utiliser la fonction `odeint` du module `SciPy` pour approcher la solution d'abord d'une EDO ensuite d'un système d'EDO (ce qui inclut les équations différentielles d'ordre 2 ou plus)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Principe d'utilisation de `odeint`\n", "\n", "Le principe d’utilisation de `odeint` (pour intégrer numériquement des équations différentielles) est le suivant: pour avoir une estimation numérique de la solution du problème de \n", " $$\\begin{cases}\n", " \\mathbf{y}'(t)=\\boldsymbol{\\varphi}(t,\\mathbf{y}(t)),\\\\\n", " \\mathbf{y}(t_0)=\\mathbf{y}_0\n", " \\end{cases}$$\n", "avec $\\mathbf{y}(t)=(y_1(t),y_2(t),\\dots,y_n(t))$ le vecteur des fonctions recherchées, dépendant de la variable $t$ et $\\boldsymbol{\\varphi}=(\\varphi_1,\\varphi_2,\\dots,\\varphi_n)$ une fonction de forme quelconque, on donne comme argument la fonction $\\boldsymbol{\\varphi}$ (qui doit avoir deux paramètres, même dans le cas autonome, avec $t$ comme deuxième paramètre), la condition initiale $\\mathbf{y}_0$ et le domaine de temps qui nous intéresse (qui commence à $t_0$). Elle retourne un tableau `Numpy` (même si $t$ était une liste). \n", "\n", "Notons que la résolution de $y''(t)=F(t,y(t),y'(t))$ passera par celle du système différentiel\n", "$$\\begin{cases}\n", "y_1'(t)=y_2(t),\\\\\n", "y_2'(t)=F(t,y_1(t),y_2(t))\n", "\\end{cases}$$\n", "avec \n", "$y(t)=y_1(t)$, \n", "$y'(t)=y_1'(t)=y_2(t)$ \n", "et \n", "$\\varphi_1(t,y_1(t),y_2(t))=y_2(t)$, \n", "$\\varphi_2(t,y_1(t),y_2(t))=F(t,y_1(t),y_2(t))$. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’une équation différentielle d'ordre 1\n", "\n", "En guise d’exemple, considérons le problème de Cauchy $y(0)=1$ et une équation logistique simple de la forme\n", "$$\n", "y'(t)=\\frac{3}{2} y(t) \\left( 1-\\frac{y(t)}{6} \\right). \n", "$$\n", "On crée alors la fonction $\\varphi$" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "# def phi(y,t):\n", "# return 1.5*y*(1-y/6)\n", "# ou \n", "phi = lambda y,t : 1.5*y*(1-y/6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La fonction `odeint` peut être appelée avec au minimum trois arguments: \n", "- la fonction $\\varphi$, \n", "- la valeur $y(t_0)$, \n", "- le vecteur $t$ (qui commence à $t_0$) où la fonction $y$ sera évaluée.\n", "\n", "Elle renvoi un vecteur `sol` contenant l'évaluation de la solution en les points du vecteur $t$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "t0 = 0\n", "y0 = 1\n", "tt = linspace(t0,5,201)\n", "sol = odeint(phi,y0,tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La solution peut alors être tracée simplement " ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(tt,sol)\n", "xlabel('t')\n", "ylabel('y')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "NB: le nombre de points en lesquels les résultats sont évalués n’est pas (du moins directement) relié à la précision des calculs internes (ne pas imaginer que cela fixe le pas de la méthode, en particulier)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Champ de vecteurs\n", "\n", "Bien qu'il soit trés rare que l'on puisse résoudre explicitement une équation différentielle donnée, on peut souvent avoir une idée de l’allure des graphes des solutions en observant le champs de vecteurs associé. \n", "En effet le graphe d'une solution de l'équation $y'(t)=\\varphi(t,y(t))$ est par définition tangent à son vecteur vitesse $(1,y'(t))$ et donc au vecteur $(1, \\varphi(t,y(t))$. \n", "La connaissance de la fonction $\\varphi$ en chaque point $(t,y)$ permet donc de représenter facilement ces vecteurs tangents même si l'on ne connait pas les solutions. \n", "Et si l'on en trace un grand nombre, uniformément répartis dans le plan $(t, y)$, on obtient une représentation\n", "du champ de vecteurs associé à l'équation différentielle qui permet souvent de deviner les graphes des solutions puisqu'il s'agit des courbes qui sont tangentes en tous leurs points aux vecteurs de ce champs de vecteurs. \n", "Il est alors intéressant d'y superposer la solution numérique obtenue avec `odeint`.\n", "\n", "La fonction `quiver` du module `matplotlib` permet de tracer un champ de vecteurs.\n", "Utilisons-la pour obtenir celui associé à notre équation différentielle.\n", "La courbe rouge est la solution déterminée par `odeint`." ] }, { "cell_type": "code", "execution_count": 7, "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", "\n", "# quiverplot\n", "# define a grid and compute direction at each point\n", "g1 = linspace(0,5,21)\n", "g2 = linspace(0,8,21)\n", "T,Y = meshgrid(g1,g2) # create a grid\n", "DT, DY = 1, phi(Y,T) # compute growth rate on the grid\n", "M = sqrt(DT**2+DY**2) # norm growth rate \n", "M[ M==0 ] = 1 # avoid zero division errors \n", "quiver(T,Y, DT/M, DY/M, M, pivot='mid')\n", "\n", "plot(tt,sol,'r')\n", "grid()\n", "xlabel('t')\n", "ylabel('y')\n", "title('Champ des pentes');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’un système d'équations différentielles d'ordre 1\n", "\n", "Considérons deux espèces: une proie (des lièvres par exemple) et un prédateur (des lynx par exemple). \n", "Ces deux populations sont représentées par $y_1(t)$ et $y_2(t)$ des fonctions continues du temps $t$. \n", "Si on suppose qu’il n’y a aucune autre intervention extérieur, une modélisation possible pour ce genre de système a été proposée indépendamment par Alfred James Lotka en 1925 et Vito Volterra en 1926:\n", "$$\n", "\\begin{cases}\n", "y_1'(t) = y_1(t)(a-by_2(t)) &[\\stackrel{\\text{déf}}{=}\\varphi_1(y_1(t),y_2(t),t)] \\quad\\text{équation équation des proies}\\\\\n", "y_2'(t) =-y_2(t)(c-dy_1(t)) &[\\stackrel{\\text{déf}}{=}\\varphi_2(y_1(t),y_2(t),t)] \\quad\\text{équation équation des prédateurs}\n", "\\end{cases}\n", "$$\n", "soit encore en notation matricielle\n", "$$\n", " \\begin{pmatrix}\n", " y_1\\\\\n", " y_2\n", " \\end{pmatrix}'(t)\n", " =\n", " \\begin{pmatrix}\n", " \\varphi_1(y_1(t),y_2(t),t)\\\\\n", " \\varphi_2(y_1(t),y_2(t),t)\n", " \\end{pmatrix}.\n", "$$\n", "\n", "On suppose qu’à ce jour il y a $y_1(0)=2$ unités de proies (une unités = $1000$ animaux) et $y_2(0)=1$ unités de prédateurs et on se demande comment vont évoluer les populations de ces deux espèces. \n", "Pour les simulations on prendra $a=2$, $b=1$, $c=1$ et $d=0.3$. \n", "\n", "Soit $\\mathbf{y}(t)\\stackrel{\\text{déf}}{=}(y_1(t),y_2(t))$ le vecteur des deux fonctions inconnues. \n", "On commence par créer la fonction vectorielle \n", "$$\n", "\\boldsymbol{\\varphi}(\\mathbf{y},t)=(\\varphi_1(\\mathbf{y},t),\\varphi_2(\\mathbf{y},t))\n", "$$" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [], "source": [ "# yy est une liste a deux composantes\n", "pphi = lambda yy,t : [ yy[0]*(2-yy[1]) , -yy[1]*(1-0.3*yy[0]) ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "En faisant varier le temps sur l'intervalle $[0;20]$ et en prenant comme condition initiale le vecteur $\\mathbf{y}_0=(2,1)$ on écrit" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [], "source": [ "t0 = 0\n", "yy0 = [2,1]\n", "tt = linspace(t0,20,201)\n", "sol = odeint(pphi,yy0,tt)\n", "sol_1 = sol[:,0] # [y_1(t) for t in tt]\n", "sol_2 = sol[:,1] # [y_2(t) for t in tt]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le tracé des évolutions de $y_1$ et $y_2$ en fonction du temps $t$ peut être obtenu par " ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "plot(tt,sol_1,tt,sol_2)\n", "grid()\n", "xlabel('t')\n", "ylabel('y')\n", "legend([r\"$y_1(t)$ proies\",\"$y_2(t)$ prédateurs\"]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Le tracé des évolutions de $y_2$ en fonction de $y_1$ peut être obtenu par" ] }, { "cell_type": "code", "execution_count": 12, "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(sol_1,sol_2)\n", "grid()\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(10,7))\n", "Y1,Y2 = meshgrid(linspace(min(sol_1),max(sol_1),21),linspace(min(sol_2),max(sol_2),21))\n", "V1,V2 = pphi([Y1,Y2],tt) \n", "r1=sqrt(1+V1**2)\n", "r2=sqrt(1+V2**2)\n", "quiver(Y1, Y2, V1/r1, V2/r2) \n", "plot(sol_1,sol_2)\n", "grid()\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considérons la fonction\n", "$$\n", "E(t)=dy_1(t)+by_2(t)-c\\ln(y_1(t))-a\\ln(y_2(t))\n", "$$\n", "Vérifions analytiquement que la fonction $E$ est une intégrale première du système, c’est-à-dire que si $(y_1, y_2)$ est une solution alors l’application $E$ est constante:\n", "\\begin{align}\n", "E'(t)\n", "&=dy_1'(t)+by_2'(t)-\\frac{c}{y_1(t)}y_1'(t)-\\frac{a}{y_2(t)}y_2'(t)\n", "\\\\\n", "&=\\left(d-\\frac{c}{y_1(t)}\\right)y_1'(t)+\\left(b-\\frac{a}{y_2(t)}\\right)y_2'(t)\n", "\\\\\n", "&=\\left(d-\\frac{c}{y_1(t)}\\right)y_1(t)(a-by_2(t))-\\left(b-\\frac{a}{y_2(t)}\\right)y_2(t)(c-dy_1(t))\n", "\\\\\n", "&=(dy_1(t)- c)(a-by_2(t))-(by_2(t)-a)(c-dy_1(t))\n", "\\\\\n", "&=(dy_1(t)- c)(a-by_2(t))-(a-by_2(t))(dy_1(t)- c)\n", "=0.\n", "\\end{align}\n", "Vérifions cette propriété numériquement:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "7.942278004158254e-07\n" ] }, { "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", "# valeur pour t=0\n", "E0 = 0.3*yy0[0]+yy0[1]-log(yy0[0])-2*log(yy0[1])\n", "plot([tt[0],tt[-1]],[E0,E0])\n", "\n", "EE = 0.3*sol_1+sol_2-log(sol_1)-2*log(sol_2)\n", "print(max(abs(EE-E0)))\n", "plot(tt,EE)\n", "xlabel('t')\n", "ylabel('E')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution approchée d’une équation différentielle d'ordre 2\n", "\n", "Considérons l'EDO $y''(t)=-\\sin(y(t))$ qui décrit le mouvement d'un pendule non amorti, équivalente au système différentiel\n", "$$\n", "\\begin{cases}\n", "y_1'(t)=y_2(t),\\\\\n", "y_2'(t)=-\\sin(y_1(t))\n", "\\end{cases}\n", "$$\n", "avec $y(0)=0$ et $y'(0)=1$. " ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pphi = lambda yy,t : [ yy[1], -sin(yy[0]) ]\n", "\n", "t0 = 0\n", "yy0 = [0,1]\n", "tt = linspace(t0,10,1001)\n", "sol = odeint(pphi,yy0,tt)\n", "\n", "figure(figsize=(18,7))\n", "\n", "subplot(1,2,1)\n", "plot(tt,sol[:,0],tt,sol[:,1])\n", "xlabel('t')\n", "ylabel('y')\n", "grid()\n", "\n", "subplot(1,2,2)\n", "plot(sol[:,0],sol[:,1])\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$')\n", "grid()\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considérons l'énergie suivante (somme de l'énergie potentielle et de l'énergie cinétique):\n", "$$\n", "E(t)=-\\cos(y_1(t))+\\frac{1}{2}(y_2(t))^2\n", "$$\n", "Vérifions analytiquement que la fonction $E$ est conservée au cours du temps:\n", "\\begin{align}\n", "E'(t)\n", "&=\\sin(y_1(t))y_1'(t)+y_2(t)y_2'(t)\n", "\\\\\n", "&=-y_2'(t)y_1'(t)+y_1'(t)y_2'(t)\n", "=0.\n", "\\end{align}\n", "Vérifions cette propriété numériquement:" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9.448590565508397e-08\n" ] }, { "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", "# valeur pour t=0\n", "E0 = -cos(yy0[0])+yy0[1]**2/2\n", "plot([tt[0],tt[-1]],[E0,E0])\n", "\n", "EE = -cos(sol[:,0])+sol[:,1]**2/2\n", "print(max(abs(EE-E0)))\n", "plot(tt,EE)\n", "xlabel('t')\n", "ylabel('E')\n", "grid(); " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Calcul analytique avec le module `sympy`\n", "--- \n", "https://docs.sympy.org/latest/modules/solvers/ode.html" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import sympy as sym\n", "sym.init_printing()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution analytique d’une équation différentielle d'ordre 1\n", "\n", "Considérons le problème de Cauchy\n", "$$\\begin{cases}\n", "u'(x)=-3x^2u(x)+6x^2,\\\\\n", "u(0)=4.\n", "\\end{cases}$$" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d x} u{\\left(x \\right)} = - 3 x^{2} u{\\left(x \\right)} + 6 x^{2}$" ], "text/plain": [ "d 2 2\n", "──(u(x)) = - 3⋅x ⋅u(x) + 6⋅x \n", "dx " ] }, "execution_count": 19, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x = sym.Symbol('x')\n", "u = sym.Function('u')\n", "phi = 6*x**2-3*x**2*u(x)\n", "edo = sym.Eq( sym.diff(u(x),x) , phi )\n", "edo" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle u{\\left(x \\right)} = C_{1} e^{- x^{3}} + 2$" ], "text/plain": [ " 3 \n", " -x \n", "u(x) = C₁⋅ℯ + 2" ] }, "execution_count": 20, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solgen = sym.dsolve(edo,u(x))\n", "solgen" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Prise en compte des conditions initiales:" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left\\{ C_{1} : 2\\right\\}$" ], "text/plain": [ "{C₁: 2}" ] }, "execution_count": 21, "metadata": {}, "output_type": "execute_result" } ], "source": [ "x0=0\n", "u0=4\n", "consts = sym.solve( sym.Eq( u0, solgen.rhs.subs(x,x0)) , dict=True)[0]\n", "consts" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle u{\\left(x \\right)} = 2 + 2 e^{- x^{3}}$" ], "text/plain": [ " 3\n", " -x \n", "u(x) = 2 + 2⋅ℯ " ] }, "execution_count": 22, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solpar=solgen.subs(consts)\n", "solpar" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On transforme le résultat en une fonction:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "func = sym.lambdify(x,solpar.rhs,'numpy')" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from matplotlib.pylab import *\n", "figure(figsize=(10,7))\n", "xx=linspace(0,3,101)\n", "yy=func(xx)\n", "plot(xx,yy)\n", "xlabel('x')\n", "ylabel('u')\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exemple de résolution analytique d’un système d'équations différentielles d'ordre 1\n", "\n", "$$\n", " \\begin{pmatrix}\n", " y_1\\\\\n", " y_2\n", " \\end{pmatrix}'(t)\n", " =\n", " \\begin{pmatrix}\n", " \\varphi_1(t, y_1(t),y_2(t))\\\\\n", " \\varphi_2(t, y_1(t),y_2(t))\n", " \\end{pmatrix}\n", " =\n", " \\begin{pmatrix}\n", " y_1(t)-y_2(t)\\\\\n", " y_2(t)-y_1(t)\n", " \\end{pmatrix}.\n", "$$\n", "avec $t\\in[0;10]$ et en prenant comme condition initiale le vecteur $\\mathbf{y}_0=(2,1)$." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{y_{1}}{\\left(t \\right)} = \\operatorname{y_{1}}{\\left(t \\right)} - \\operatorname{y_{2}}{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(y₁(t)) = y₁(t) - y₂(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{d}{d t} \\operatorname{y_{2}}{\\left(t \\right)} = - \\operatorname{y_{1}}{\\left(t \\right)} + \\operatorname{y_{2}}{\\left(t \\right)}$" ], "text/plain": [ "d \n", "──(y₂(t)) = -y₁(t) + y₂(t)\n", "dt " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left[ \\operatorname{y_{1}}{\\left(t \\right)} = - C_{1} e^{2 t} - C_{2}, \\ \\operatorname{y_{2}}{\\left(t \\right)} = C_{1} e^{2 t} - C_{2}\\right]$" ], "text/plain": [ "⎡ 2⋅t 2⋅t ⎤\n", "⎣y₁(t) = - C₁⋅ℯ - C₂, y₂(t) = C₁⋅ℯ - C₂⎦" ] }, "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", "\n", "y1 = sym.Function('y1')\n", "y2 = sym.Function('y2')\n", "\n", "phi1 = y1(t)-y2(t)\n", "phi2 = y2(t)-y1(t)\n", "\n", "edo1 = sym.Eq( sym.diff(y1(t),t) , phi1 )\n", "edo2 = sym.Eq( sym.diff(y2(t),t) , phi2 )\n", "display(edo1)\n", "display(edo2)\n", "\n", "solgen = sym.dsolve([edo1,edo2],[y1(t),y2(t)])\n", "display(solgen)" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left\\{ C_{1} : - \\frac{1}{2}, \\ C_{2} : - \\frac{3}{2}\\right\\}$" ], "text/plain": [ "{C₁: -1/2, C₂: -3/2}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\operatorname{y_{1}}{\\left(t \\right)} = \\frac{e^{2 t}}{2} + \\frac{3}{2}$" ], "text/plain": [ " 2⋅t \n", " ℯ 3\n", "y₁(t) = ──── + ─\n", " 2 2" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\operatorname{y_{2}}{\\left(t \\right)} = \\frac{3}{2} - \\frac{e^{2 t}}{2}$" ], "text/plain": [ " 2⋅t\n", " 3 ℯ \n", "y₂(t) = ─ - ────\n", " 2 2 " ] }, "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": [ "t0 =0\n", "y1_0=2\n", "y2_0=1\n", "consts = sym.solve( [sym.Eq( y1_0, solgen[0].rhs.subs(t,t0)) , \n", " sym.Eq( y2_0, solgen[1].rhs.subs(t,t0)) ] , dict=True)[0]\n", "display(consts)\n", "\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=(18,7))\n", "\n", "tt=linspace(0,3,101)\n", "yy_1=func_1(tt)\n", "yy_2=func_2(tt)\n", "\n", "subplot(1,2,1)\n", "plot(tt,yy_1,tt,yy_2)\n", "legend([r'$y_1$',r'$y_2$'])\n", "xlabel(r'$t$')\n", "ylabel(r'$y$')\n", "\n", "subplot(1,2,2)\n", "plot(yy_1,yy_2)\n", "xlabel(r'$y_1$')\n", "ylabel(r'$y_2$');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercices" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (sympy)\n", ">Calculer la solution **exacte** du problème de Cauchy \n", "$$\\begin{cases}\n", "y'(t)=\\dfrac{3}{2} y(t) \\left( 1-\\dfrac{y(t)}{6} \\right),& t>0\\\\\n", "y(0)=1.\n", "\\end{cases}$$" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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R4qoI6xmVWxoUDxgcqHJA8uIeqfDM24DKCBJhEAYEHHAWlKLw7Mm9/8QLhgbM8+UgUadkMBZmDKhyQPJCUCj3nwOQo9JLL1W654qwFcN42wcr6ZXMKh2MdNaTf5bknnleqtwos8qMGxzUnSufxrxm4IDkBBkjKMSTgPRtsWcqG4GihM/uMQuuxlsxiLdyHui60oWldP/MJmQm4fCWT7+ENmBwIOIAxyiU1Hw2GNXsfnyfVN/N2/8BsZY9ZW1BfzAAAAAASUVORK5CYII=\n", "text/latex": [ "$\\displaystyle \\frac{d}{d t} y{\\left(t \\right)} = \\frac{3 \\left(1 - \\frac{y{\\left(t \\right)}}{6}\\right) y{\\left(t \\right)}}{2}$" ], "text/plain": [ " ⎛ y(t)⎞ \n", " 3⋅⎜1 - ────⎟⋅y(t)\n", "d ⎝ 6 ⎠ \n", "──(y(t)) = ─────────────────\n", "dt 2 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/latex": [ "$\\displaystyle \\left[ y{\\left(t \\right)} = \\frac{6 \\left(- e^{3 t} + \\sqrt{e^{C_{1} + 3 t}}\\right)}{e^{C_{1}} - e^{3 t}}, \\ y{\\left(t \\right)} = - \\frac{6 \\left(e^{3 t} + \\sqrt{e^{C_{1} + 3 t}}\\right)}{e^{C_{1}} - e^{3 t}}\\right]$" ], "text/plain": [ "⎡ ⎛ ___________⎞ ⎛ ___________⎞ ⎤\n", "⎢ ⎜ 3⋅t ╱ C₁ + 3⋅t ⎟ ⎜ 3⋅t ╱ C₁ + 3⋅t ⎟ ⎥\n", "⎢ 6⋅⎝- ℯ + ╲╱ ℯ ⎠ -6⋅⎝ℯ + ╲╱ ℯ ⎠ ⎥\n", "⎢y(t) = ───────────────────────────, y(t) = ───────────────────────────⎥\n", "⎢ C₁ 3⋅t C₁ 3⋅t ⎥\n", "⎣ ℯ - ℯ ℯ - ℯ ⎦" ] }, "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", "phi= sym.Rational(3,2)*y(t)*(1-y(t)/6)\n", "edo= sym.Eq( sym.diff(y(t),t) , phi )\n", "display(edo)\n", "solgen = sym.dsolve(edo,y(t))\n", "display(solgen)" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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4/bbmGg7UzbNtCQKbQLjeLZBy+uOr1sv1ZGy9f5ONRLXYk7FyERVxHNW41SeFZn1L/iKOqkZyaev9G8mez8XrGvszLzaRkiJzXIXVdhdQ+HrNElzoSfi79f5NwiRV8j9bX3OkHHMAsQAAAABJRU5ErkJggg==\n", "text/latex": [ "$\\displaystyle y{\\left(t \\right)} = \\frac{6 \\left(- e^{3 t} + \\sqrt{e^{C_{1} + 3 t}}\\right)}{e^{C_{1}} - e^{3 t}}$" ], "text/plain": [ " ⎛ ___________⎞\n", " ⎜ 3⋅t ╱ C₁ + 3⋅t ⎟\n", " 6⋅⎝- ℯ + ╲╱ ℯ ⎠\n", "y(t) = ───────────────────────────\n", " C₁ 3⋅t \n", " ℯ - ℯ " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solgen=solgen[0]\n", "display(solgen)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left\\{ C_{1} : \\log{\\left(25 \\right)}\\right\\}$" ], "text/plain": [ "{C₁: log(25)}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle y{\\left(t \\right)} = \\frac{6 \\left(- e^{3 t} + 5 \\sqrt{e^{3 t}}\\right)}{25 - e^{3 t}}$" ], "text/plain": [ " ⎛ ______⎞\n", " ⎜ 3⋅t ╱ 3⋅t ⎟\n", " 6⋅⎝- ℯ + 5⋅╲╱ ℯ ⎠\n", "y(t) = ────────────────────────\n", " 3⋅t \n", " 25 - ℯ " ] }, "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": [ "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)\n", "display(solpar)\n", "\n", "func = sym.lambdify(t,solpar.rhs,'numpy')\n", "\n", "from matplotlib.pylab import *\n", "figure(figsize=(10,7))\n", "tt=linspace(0,3,101)\n", "yy=func(tt)\n", "plot(tt,yy)\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (scipy)\n", ">Calculer la solution **approchée** du problème de Cauchy\n", "$$\\begin{cases}\n", "y'(t)=\\sin\\left(t y(t)\\right), & t>0\\\\\n", "y(0)=a\n", "\\end{cases}$$\n", "pour $a=-2,-1,-\\frac{1}{2},-\\frac{1}{10},0,\\frac{1}{10},\\frac{1}{2},1,2$ et afficher le champ de vecteurs." ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint\n", "\n", "phi = lambda y,t : sin(t*y)\n", "tt = linspace(0,10,201)\n", "\n", "figure(figsize=(10,7))\n", "\n", "T,Y = meshgrid(linspace(0,10,31),linspace(-3,3,31))\n", "DT, DY = 1, phi(Y,T) \n", "M = sqrt(DT**2+DY**2) # norm growth rate \n", "M[ M == 0] = 1 # avoid zero division errors \n", "quiver(T,Y, DT/M, DY/M, M, pivot='mid')\n", "grid()\n", "\n", "for y0 in [-2, -1, -0.5, -0.1, 0, 0.1, 0.5, 1, 2]:\n", " sol=odeint(phi,y0,tt)\n", " plot(tt,sol,lw=2);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (sympy - système)\n", "> 1. Calculer la solution générale **exacte** du système \n", "$$\n", "\\begin{pmatrix}\n", "x(t)\\\\\n", "y(t)\n", "\\end{pmatrix}'\n", "=\n", "\\begin{pmatrix}\n", "0&1\\\\\n", "-1&0\n", "\\end{pmatrix}\n", "\\begin{pmatrix}\n", "x(t)\\\\\n", "y(t)\n", "\\end{pmatrix}\n", "$$\n", ">1. Pour $x(0)=-1$ et $y(0)=1$, afficher $t\\mapsto x$ et $t\\mapsto y$ dans un même graphe.\n", ">2. Afficher ensuite $x\\mapsto y$.\n", ">1. Calculer analytiquement $E'(t)$ avec\n", "$$\n", "E(t)=\\frac{x^2(t)}{2}+\\frac{y^2(t)}{2}.\n", "$$\n", "\n" ] }, { "cell_type": "code", "execution_count": 31, "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" } ], "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)" ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left\\{ C_{1} : -1, \\ C_{2} : 1\\right\\}$" ], "text/plain": [ "{C₁: -1, C₂: 1}" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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"text/latex": [ "$\\displaystyle x{\\left(t \\right)} = \\sin{\\left(t \\right)} - \\cos{\\left(t \\right)}$" ], "text/plain": [ "x(t) = sin(t) - cos(t)" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle y{\\left(t \\right)} = \\sin{\\left(t \\right)} + \\cos{\\left(t \\right)}$" ], "text/plain": [ "y(t) = sin(t) + cos(t)" ] }, "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": [ "t_0=0\n", "x_0=-1\n", "y_0=1\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(0,30,101)\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": 33, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\frac{\\left(\\sin{\\left(t \\right)} - \\cos{\\left(t \\right)}\\right)^{2}}{2} + \\frac{\\left(\\sin{\\left(t \\right)} + \\cos{\\left(t \\right)}\\right)^{2}}{2}$" ], "text/plain": [ " 2 2\n", "(sin(t) - cos(t)) (sin(t) + cos(t)) \n", "────────────────── + ──────────────────\n", " 2 2 " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAAoAAAAOCAYAAAAWo42rAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAz0lEQVQoFXWS4Q2CMBCFhQkIbqAjqBvgBsoGOkf/GUbQFXQENjAyAhtA2AC/V3tGG2hyeXdfH71LSzKO48KWc64KeYeuiQrWiiVmBLyoL+hDG2iGiO3J2zTAM5qZKbAB1UdX1d6IHolGIFpP6kKnm7EA9JFJpZ8PLdIwy4TnD+U6MQ9IM82tb+s5g/GlTpyazQzWrdOM1lL3Fi9jn3tktyZWsYvaTqzteu7A7YRxA2vU1RtJboAePZiZXG1L4iT2+9ba0E8xEPopdoTe3r/YGx/SQ0OZAIYmAAAAAElFTkSuQmCC\n", "text/latex": [ "$\\displaystyle 0$" ], "text/plain": [ "0" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "E=(solpar_1.rhs)**2/2+(solpar_2.rhs)**2/2\n", "display(E)\n", "Ep=sym.diff(E,t).simplify()\n", "display(Ep)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (scipy - système)\n", "> 1. Calculer la solution particulière **approchée** du système \n", "$$\n", "\\begin{cases}\n", "x'(t)= -y(t)+y^2(t)x(t)\\\\\n", "y'(t)= x(t)-x^2(t)y(t)\n", "\\end{cases}\n", "$$\n", "avec $x(0)=0$ et $y(0)=1$.\n", ">1. Afficher $t\\mapsto x$ et $t\\mapsto y$ dans un même graphe pour $t\\in[0,14]$. \n", "Afficher ensuite $x\\mapsto y$.\n", ">1. Afficher\n", "$$\n", "E(t)=\\frac{x^2(t)}{2}+\\frac{y^2(t)}{2}.\n", "$$\n", "Calculer analytiquement $E'(t)$." ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "from scipy.integrate import odeint\n", "\n", "pphi = lambda yy,t : [ -yy[1]+(yy[1])**2*yy[0] , yy[0]-(yy[0])**2*yy[1] ]\n", "\n", "yy0 = [0,1]\n", "tt = linspace(0,14,201)\n", "sol = odeint(pphi,yy0,tt)\n", "solx,soly=sol[:,0],sol[:,1]\n", "\n", "figure(figsize=(17,7))\n", "\n", "subplot(1,2,1)\n", "plot(tt,solx,tt,soly)\n", "grid()\n", "legend([\"x\",\"y\"]);\n", "\n", "subplot(1,2,2) \n", "plot(solx,soly)\n", "grid()\n", "xlabel(r'$x$')\n", "ylabel(r'$y$')\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "E'(t)=x'(t)x(t)+y'(t)y(t)=0.\n", "$$" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "5.164118894729341e-07\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "figure(figsize=(17,7))\n", "\n", "E0 = yy0[0]**2+yy0[1]**2\n", "EE = solx**2+soly**2\n", "print(max(abs(E0-EE)))\n", "plot([tt[0],tt[-1]],[E0,E0])\n", "plot(tt,EE)\n", "grid();" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice (scipy - système - stabilité)\n", "> Considérons le système \n", "$$\n", "\\begin{cases}\n", "x'(t)= x^2(t)+y^2(t)-25\\\\\n", "y'(t)= x(t)y(t)-12\n", "\\end{cases}\n", "$$\n", ">1. Afficher le champ des vecteurs et les solutions stationnaires.\n", ">1. Calculer les solutions particulières **approchées** pour des données initiales proches des points stationnaires." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Les solutions stationnaires vérifient\n", "$$\n", "\\begin{cases}\n", "x^2+y^2=25\\\\\n", "xy=12\n", "\\end{cases}\n", "$$\n", "On résout $x^4-25x^2+12^2=0$:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-4. -3. 4. 3.] [-3. -4. 3. 4.]\n" ] } ], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "from matplotlib.pylab import * # importe aussi numpy sans alias\n", "\n", "# numpy calcule les racines d'un polynome\n", "x_sol=roots([1, 0, -25, 0, 12**2])\n", "y_sol=12/x_sol\n", "print(x_sol,y_sol)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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