{ "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: 2022-03-08 10:51:41.128079\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": { "toc": true }, "source": [ "

\n", "
" ] }, { "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_odeint(y,t):\n", "# return 1.5*y*(1-y/6)\n", "# ou \n", "\n", "# Attention à l'ordre des variables dans phi\n", "phi_odeint = 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_odeint,y0,tt)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "La solution peut alors être tracée simplement " ] }, { "cell_type": "code", "execution_count": 6, "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(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_odeint(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", "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_odeint = 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", "\n", "# V1\n", "# odeint revoie une matrice, la colonne j contient l'approximation de la j-ème composante de la fonction inconnue\n", "sol = odeint(pphi_odeint,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]\n", "\n", "# V2\n", "# Pour que odeint renvoit séparément les valeurs de la solution, il faut rajouter .T à la fin\n", "sol_1,sol_2 = odeint(pphi_odeint,yy0,tt).T" ] }, { "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_odeint([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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O/Y/wQ5e0KfV4iYiItGe1NfDPL8L+zXDjC1RsqfG7okBTj5eIiEhLrPW7guiteha2vOe25xl8pt/VBJ6Cl4iISFMqy2Ded+EXA6Bok9/VRK6uFt79NeSMg4nX+12NoOAlIiLSuO2L4P/OhPxHoKoU1r7od0WRW/U87NsE59wOSfpXfjzQX0FEROR4xdvh8SvA1sKXX4E+E2DDG35XFZm6Wnj3V26piNGf9bsaCVHwEhERaaiuDl76Btg6+NLLMHgajLgQdiyEiv1+Vxe+NS9A0QY4+/vq7Yoj+kuIiIg0lP+w22vwwp+5hUEBRl7ogtimf/tZWWQWPQI9h8PYy/2uRBpQ8BIREal3YCu8+WMYNhMm33T0/b6nQKcs2PC6f7VFoqwQtn0I465Sb1ec0V9DRESk3obXobrCrezecGPnpCQYcYHr8apNgHWw1r/ieujGaG5XvFHwEhERqXdwOySnQY8hJ3428gI4XOzmesW7tS+7NuSM87sSOY5nwcsY09EYs9AYs9wYs9oYc/dxn3/PGGONMVle1SAiIhKRgzugW7/Gh+eGzYSklPgfbjxUDJ++43q7GvbaSVzwcsugSmCmtbbMGJMKvG+MedVa+5ExZgBwPrDNw/uLiIhE5uAO6Na/8c86doP+U2DbgtjWFKmNb0BdNYy51O9KpBGe9XhZpyz0a2roVb/nwu+A2xv8LiIi4r+D26HbwKY/zxrpFiSNZ2tfgi59oN9kvyuRRhjr4f5TxphkYDEwHLjfWnuHMeZS4Fxr7beNMVuAXGttUSPfnQ3MBsjJyZk8Z84cz+oEKCsrIyMjw9N7xLMgtz/IbYdgt19tD2bbofH2m7pqzn73GrYO+jxbhlzX6PcGbHueYZ8+xvvTnqQmNf7++SXVVjLtgxvY1ed8No2Y3eg5+tt73/4ZM2YsttbmNvqhtdbzF9AdmA+cDHwMdAu9vwXIaun7kydPtl6bP3++5/eIZ0Fuf5Dbbm2w26+2B1ej7d+/2dq7ulq7+O9Nf3HtPHfOjnyvSmudT+a7+ja+2eQp+tvP9/weQL5tItPE5KlGa20xkAdcBgwBlod6u/oDS4wxvWNRh4iISJMO7nDHpuZ4AWQOc8d9n3hfTzQKlrqjhhnjlpdPNWYbY7qHfk4HzgOWWmt7WWsHW2sHAzuAU6y1u72qQ0REJCxHgteAps/pMRgw8R28egyB9B5+VyJN8PKpxj7AY6F5XknA09baeR7eT0REJHoHt7tjt35Nn5PaEboPiN8J9gVLoV/jU4skPngWvKy1K4BJLZwz2Kv7i4iIRKR4O3TOhtT05s/LHAb747DHq3wfFG+DKf/hdyXSDK1cLyIiAs2v4dVQz+Gw71PwcFWAqOwKze/q22yfh/hMwUtERAQiCF7DoPIglJ+wEpK/6ifW95ngbx3SLAUvERERa0PBq5mJ9fXqn2yMt+HGnUuh5wjo2NXvSqQZCl4iIiKHDkB1efg9XhB/E+wLlmqYMQEoeImIiISzlES97oPcZtnxtKRE6W4oLVDwSgAKXiIiIkeWkgijxys5xa3nFU9DjQXL3FHBK+4peImIiETS4wVunldb9HhZC5Vlrb9OwVIwSdB7fOuvJZ7ycgFVERGRxHBwOySnQees8M7vOQy2vAd1dZAURR9GXS2sfQne+y3sXgGderqJ8dPvgGEzI79ewVLIGgVpwd38OlGox0tERKR+KQljwju/5zCoroDSXZHf65O34YHT4Zkvu2uccyeM/owbusy7L/LrWauJ9QlEPV4iIiIHd7itgMLVc7g7Fq5rfouhhkoK4LU7Yc2LkDkUrv4bjL0MkpLd5+8OhLfvgQNboceg8GspKYDyvQpeCUI9XiIiIsXbwptYX69frhua3PhmeOevnQd/PgM2vAEzfwS3LoBxVx4NXQDjr3bHVc+FXwccXThVwSshKHiJiEiwHSqGsj1ujlW40jJg2AxY90rzWwfV1cEr34N/Xu+Wobj1Azj7+26z7eP1GAz9p0QXvEwy9B4X2ffEFwpeIiISbIXr3LHXmMi+N/ozcHAb7F7Z9DlLH4dFD8LU/4Svvnl08dWmjL8G9qyCvWvDr6NgKfQa2/Lm3hIXFLxERCTY9q5xx0iD16iL3BIO615p/PPyInjzxzDoTLjwXkjp0PI1T7rCXXPls+HVcGRi/cTw6xZfKXiJiEiw7V0HHTLCX8OrXucsGDC16eD1xo+gqhw+89vwn5bM6AVDzoFVzzY/hFmveBsc2q/5XQlEwUtERIKtcC1kjwo/HDU0+hLYsxIObDn2/c3vwfKnYNq33LUjMf4ad71tH7V8ribWJxwFLxERCba9ayMfZqw3+mJ3bNjrVVcHr/8Qug90E+kjNfYySO0My55o+dyCpZCUCjknRX4f8YWCl4iIBFf5PigvhOwog1fmUOh1EiyfA7U17r11L7vV6Gf8v+gmvKdlwLgrYNXclrcTKljqQldKWuT3EV8oeImISHAVhp4e7DU6+muc9V0XtN65z20FNP8XkDXSDRlGa9KNUF0Oa15o+hxr3ebYGmZMKFq5XkREgqt+2YZeY6O/xvir4ZP58O5voGKfC3PXPHrs4qiRGnCqW1ds6RMw6YbGz9m3CSoPKnglGPV4iYhIcO1dC2ndoEuf1l3n4l9B1gjIfwRyxsOYy1p3PWNc4Nq2AIo2nfh5bQ288l23ev6Qs1t3L4kpBS8REQmuwnVumDGaJxob6tDZ7b2YOQwu/BkktcG/Xidc61akn/cd16NWV3f0s3/fBZvfhc/8DjKHtP5eEjMaahQRkWCy1i2eOraVvVP1eo+Dby1pm2sBdOkN598N7/4aHr8cuvZzw4qdesKSx2DKf8Ck69vufhITCl4iIhJMZXvh0IHon2iMhTO+6QLWunmw9iU3NLpvEwyd4VbDl4Sj4CUiIsHUFk80xkJqRzeBf/zV7veaKkhObf3wqPhCwUtERIJpb2hz7Hju8WpMOHs+StzS5HoREQmmog3QsbvbH1EkRhS8REQkmIo2uIVONWQnMaTgJSIiwVS00a29JRJDCl4iIhI4yTXlULZbwUtiTsFLREQCp1PFTvdD1kh/C5HAUfASEZHA6VSxw/2g4CUxpuAlIiKB06liJySlQI/BfpciAaPgJSIigdOpYif0GOIWIhWJIc+ClzGmozFmoTFmuTFmtTHm7tD79xhjVhhjlhlj3jDG9PWqBhERkcZ0qtihYUbxhZc9XpXATGvtBGAiMMsYMxX4tbX2ZGvtRGAe8GMPaxARiY3KMti9yu8qJBy1NaQf2qUnGsUXngUv65SFfk0Nvay1tqTBaZ0B61UNIiIxYS08+xV4cKYLYBLfireSZGvU4yW+MNZ6l3uMMcnAYmA4cL+19o7Q+z8HbgQOAjOstYWNfHc2MBsgJydn8pw5czyrE6CsrIyMjAxP7xHPgtz+ILcdgt3+tmp7rz15jF37OwCWn3w3BzIntvqaXgvy371n0ULGr/o5Syb9ipJuo/wuJ+aC/LeH2LR/xowZi621uY195mnwOnITY7oDc4FvWmtXNXj/B0BHa+1dzX0/NzfX5ufne1pjXl4e06dP9/Qe8SzI7Q9y2yHY7W+TtpcVwv2nQvcBsHslnH07zPhBm9TnpSD/3fngD/Dmf8MdWyC9h9/VxFyg//bEpv3GmCaDV0yearTWFgN5wKzjPvoHcFUsahAR8cSr34eqMrjyQcgZB9s+9LsiaUnRBqpSuwUydIn/vHyqMTvU04UxJh04D1hnjGk4m/FSYJ1XNYiIeKp0N6yeC2d8C7JHwcDTYUc+1Fb7XZk0p2gjFZ36+12FBJSXPV59gPnGmBXAIuBNa+084D5jzKrQ+xcA3/awBhER7xQsdccR57vjoNOhugJ2rfCvJmmetVC0QcFLfJPi1YWttSuASY28r6FFEWkfCpaCSYLe493vA093x20LoP9k/+qSppXshEP7Ke83yO9KJKC0cr2ISLQKlkL2aOjQ2f3epbdbDX3bAn/rkqbtXAJASdfhPhciQaXgJSISDWuhYBn0OW7piIGnu+AVgyfGJQoFSyAphfLOQ/yuRAJKwUtEJBolBVC+F/oeN6Ni0OlQsQ+KNvpTlzRv5xLIOYm65A5+VyIBpeAlIhKN+on1fRvp8QItKxGP6upcL2U/zb8T/yh4iYhEY9cyMMlu7a6Geg6HtG5uMVWJL/s/gcqD0PcUvyuRAFPwEhGJRsFS6DUGOnQ69n1jIHMI7N/sT13StNDEevopeIl/FLxERCLV1MT6eplD4ICCV9wpWAKpnSArePszSvxQ8BIRidTBHVBRdOL8rno9hkDxNqitiW1d0rydS6DPBEj2bAlLkRYpeImIROrIxPoT1oh2ModCXQ0c3B67mqR5tdWwe4Xmd4nvFLxERCJVsBSSUiDnpMY/zwytEaXhxvixdy3UHNb8LvGdgpeISKQ2v+N6u1LTG/+8Ryh4aYJ9/CjQxHqJDwpeIiKRKN/n5goNP6/pc7r0gZSOsP/TtrlnTRVUH2qbawXV6rnQpe/RUCziEwUvEZFIfDofsM0Hr6Qk6DEYDmxp/f0OHYCHz4PfjIT598Kh4tZfM2h2r4JP8+C02W65DxEfKXiJiERi01uQ3qPpifX1erTBWl6HiuHxK9z8pAGnwju/hP89WYuzRuqjB9wyEpO/7HclIgpeIiJhq6uDTf+GYTMhKbn5czOHusn10W6WXVUBT1zlems+9zjc8Bzc8h7UVsLSJ6O7ZhCV7oYVT8OkG1xgFvGZgpeISLj2rHIbYw87t+VzM4dAdQWU7YnuXu/9Bnbmw9WPwKhZ7r0+J8OQs2HDa9EHuqBZ9JBb2uO0r/ldiQig4CUiEr5N/3bH4WEEr9Y82Vi0CT74A0y4DsZeeuxnIy90PWn7NkV+3aDZvhAWPgijL4Gew/yuRgQALd8rIhKuT96GnPHQpXfL5zZcy2vQ6eHfw1p49ftuqYrzf3ri5yMuBG5zvV5ZI8K/bqKrqYI1L8Dmd13oPLjDbUjef4oLVUkp7tWxG3TqCaufhw9+D137w8z/9rt6kSMUvEREwlFWCNsWwOnfCO/87gPBJEe+pMTal1zAm/VLyOjVyHUHQK+TYMPrcMY3I7t2Iqo+DIsehAUPQGmBC1XZo2HgVChc54ZkbV3j3530RbjwXujYNbY1izRDwUtEpCXWwrzvgElyw3/hSE6Fbv0jG2os3wf/uh1yxsGUm5s+b+SF8OEf3FOP6d3Dv36i2bUC5t4Ce9fA4LPg0j+4ZTwaLglRWebm0dXVQm0VHD4IFfsgIwcGnuZf7SJNUPASEWnJ0idg3Ty44GfQa3T438scEv62QdbCvG+70HD9M81v5DzyQnj/t65nbNyV4deTKOpqXbB8++fQKRO+8AyMvKDxc9My3EskQWhyvYhIc/ZvhtfudD0uU78e2Xczh4Y/1LjsSVj7Mpz73+7pxeb0n+KWRtj4RmT1JIL9m+HRS+DfP4FRF8GtC5oOXSIJSD1eIiLNeffX7nj5n92K9JHIHOZWni/dA11ymj6veDu8egcMOjO8OWRJyW7IbdNbrqfMq9XYa2tgx0LY9wkUb4PDxa43CusWJE3rAtmjYPRnm++hC9eq5+Clb7kh3Sv+Aid/XivNS7uj4CUi0pz9n7pV6rsPiPy7Q852x01vugU8m/LRn6HmMFz+QMsLs9YbOBVWPuMCUY9BkdfWnLK9sPhR9yrZ6d4zSZDWNVSfcWuUVVe4z7oPgmnfgkk3QkqHyO9XV+t6uD78AwyYClc9FN0/b5EEoOAlItKckp0wMILlIBrqPd5tzLzhtaaDV2UZLH0cxl4eWYDql+uOO/PbNnht+jc8d7PrqRs6w81r6zvRLctwfKiqrYGNr8N7v4VXboOFD8Glf4QBU8K/39YP4a17YNuHkPtVmHVfdOFNJEEoeImINKWuDkp2Qde+0X3fGDcRfuUzUFMJKWknnrP8KagsiXxl9ZyTIKUj7FgM466Krr6G6urcsGreL9y1b3qt5QcJklPc4qSjLnbLW7xyGzx8PuTe5IZMm1q0tPoQrH/VrSq/9QPonA2XPQCTrm99O0TinIKXiEhTKoqgrhq69ov+GqMugsV/cwFj2MxjP6urg4V/hb6nQP/cyK6bnAp9Jroer9Yq3j3VNzAAACAASURBVAZzb4Wt77vlMi75LXToFP73jXHbGg2eBm/9FPIfca/h58GgM1xvWWo67NvoNvze8LoLm137ufXKTrkxsvuJJDAFLxGRptTPb4q2xwvcPK+UdBc2jg9en86Hog1wxV+jm0TeP9f1GtVWuyAWjdVz3YR2a12v08QvRD+hPa0LXPxrOOs2Nz9syd+PbrNUr0tfGP0ZmPB596RouHPaRNoJBS8RkaaUFLhja4JXajoMPccNrc2679hQs+B+6NwLTro8umv3mwwL/uQ27+47KfLvfzIfnv2qu85VD0KPwdHVcbwuvWH6ne5VVe7+OVaVu6HHtC5tcw+RBKV1vEREmnIkeLViqBHcPK/irVC4/uh7a+fBJ2+5bX8am/sVjvrhyR2RDzemV+yCZ77sloP44ty2C13H69DZ7SnZd6JClwgKXiIiTSspgKRU6JTVuuuMnOWOy//hjpWl8Ortbs/FqbdGf91uA1yP2c7FkX3vcAnjVv3M9b5d+w+t/C4SQxpqFBFpSkkBdOkT+cKpx+vaF8ZcCh/83m0JlJzmrn3No9HPzQIXnPrnRt7jNf9eOlUUwI0vuG2NRCRm1OMlItKUkp2tm9/V0DWPwtnfd/s+5j/sllwYcGrrr9tvsnta8NCB8M7f/ykseohdfc51c89EJKY8C17GmI7GmIXGmOXGmNXGmLtD7//aGLPOGLPCGDPXGNPdqxpERFqlpKDtgldSMsz8EVz/LIz/HJx7V9tct36e184l4Z3/1k8hOZUtg7/QNvcXkYg0G7yMMbc3+Pma4z67t4VrVwIzrbUTgInALGPMVOBNYJy19mRgA/CDaAoXEfGUtW0bvOqNON89QZjeRv+fs+8pbh7aprdaPndHvls+4oxvUpWW2Tb3F5GItNTjdW2Dn48PSLOa+6J1ykK/poZe1lr7hrW2JvT+R0D/cIsVEYmZQweg5lDrn2j0WseuR1fHr61u+jxr4Y0fucn4Z3wrdvWJyDGMtbbpD41Zaq2ddPzPjf3exPeTgcXAcOB+a+0dx33+MvBPa+0TjXx3NjAbICcnZ/KcOXPCb1UUysrKyMgI7pM9QW5/kNsOwW5/c23vXLaFKfnfZvXY2ynsNS3GlUWmZ9HHjF91LyvH/Yh9WY3vk5hV+BHjVv+C9SNvZVffWYH+u4P+cx/UtkNs2j9jxozF1trGt6Ow1jb5ApY09nNjv7dwne7AfNwQY/17/w+YSyj8NfeaPHmy9dr8+fM9v0c8C3L7g9x2a4Pd/mbbvv51a+/qau22hTGrJ2rVldb+coi1//xi45/XVFn7h1Os/WOutTXV1tpg/92tDXb7g9x2a2PTfiDfNpFpWlpOYoIxpgQwQHroZ0K/dww3+Vlri40xebjhyVXGmC8BnwHODRUoIhJf2mK7oFhJ6QDjr3H7I1bsh07Hzd9a/Cjs2wTXPuU2thYR3zQ7x8tam2yt7Wqt7WKtTQn9XP97s4vPGGOy659YNMakA+cB64wxs4A7gEuttRVt1RARkTZVUgAmCTJy/K4kPBOug9oqWP38se9XlkLefTBomtuwW0R85eX/9ekDPBaa55UEPG2tnWeM2QSkAW8at2fZR9bar3lYh4hI5EoKIKN34vQQ9ZkAvcbCoodh8NmQPRJ2r4SXvwMVRXD+09Fvfi0ibcaz/0Wx1q4ATph8b60d7tU9RUTaTKkHS0l4yRg46zaY+zW4f4pbZmLXcjfsePUj0H+y3xWKCNoySESkcSUFkDXS7yoiM/5qGHI2LPk7rHoeTrkRzrsL0nv4XZmIhCh4iYg0pqQAhs7wu4rIZfSCs7/nXiISd7RXo4jI8Q6XQGVJYg01ikhCUPASETleSYE7KniJSBtT8BIROd6+Te6YOcTfOkSk3VHwEhE5XuE6d0y0yfUiEvcUvEREjle0AboNgLQuflciIu2MgpeIyPEK16m3S0Q8oeAlItJQXR0UboDs0X5XIiLtkIKXiEhDB7dBzSHIHuV3JSLSDil4iYg0VLjBHdXjJSIeUPASEWmo/onGbM3xEpG2p+AlItJQ4XrIyNH+hiLiCQUvEZGGCtdpfpeIeEbBS0SknrVuDS/N7xIRjyh4iYjUK93lNsfWGl4i4hEFLxGRekcm1qvHS0S8oeAlIlKvcL07KniJiEcUvES8Vl4Er94J+z/1uxJpSeF6SM+Ezll+VyIi7ZSCl4jX3robPv4zPHQebPvY72qkOYXr3RONxvhdiYi0UwpeIl7avRKWPA7jroaO3eCxz8LaeX5XJY2xFgrXaikJEfGUgpeIV6yF13/oFuK85Ddw81vQczi8fY/flUljyovg0AHN7xIRTyl4iXhlw2uw+V2Y/gMXvjplwsgLYN8mqK32uzo5XlH9xHr1eImIdxS8RLzyzi+h5wjIvenoe9mjoa5GE+3jUf1SElkKXiLiHQUvES+UFEDBUph0AySnHn2/vjelftkCiR+F66FDF+ja1+9KRKQdU/AS8cKG191x5Kxj369fEV3BK/7U79GoJxpFxEMKXiJe2PAadB904nyhDp2h28Cjw1oSPwq1R6OIeE/BS6StVVXAp3kw6qLGe0+yRx2dyC3x4dABKNsN2dqjUUS8peAl0ta2vAc1h2HkhY1/nj0KijZCXW1s65KmFW5wR/V4iYjHFLxE2tr6V6FDBgya1vjn2aNdMCveGtu6pGlHNsfWE40i4i0FL5G2ZK2bWD9sJqSkNX6OnmyMP4XrISXdzb8TEfGQgpdIW9q9EkoLTnyasSE92Rh/itZD1ghI0v8kioi39L8yIm1p87vuOPzcps9J7w5d+ih4xZPC9ZrfJSIx4VnwMsZ0NMYsNMYsN8asNsbcHXr/mtDvdcaYXK/uL+KLbQugxxDo0rv587JHaUmJeFFZCge3a36XiMSElz1elcBMa+0EYCIwyxgzFVgFXAm86+G9RWLPWtj2EQw8veVzs0ZB0Qb3HfHX7pXuqB4vEYkBz4KXdcpCv6aGXtZau9ZaqzEWaX/2fwoVRTDwtJbPzR4FVWVQstP7uqRJpq4WXv8hpGfCoDP8LkdEAiDFy4sbY5KBxcBw4H5r7cde3k/EV9sWuGM4PV71vSt710G3/t7VFCTWwq5lsHYe7NsEZXugugKyx0Cfk2HYudDr2F6tAdvnuj01r/4bdMr0qXARCRJjYzDUYYzpDswFvmmtXRV6Lw/4nrU2v4nvzAZmA+Tk5EyeM2eOpzWWlZWRkZHh6T3iWZDb31ZtH7Xuj2QVfcwH0x5vcb+/5JoKznz/C2wZfC1bB1/b6nu3RqL/7ZNrDtG34FX6FrxO+uHd1JlkDnfsTWVaD6xJpXP5FtKqDgBwsOsodveeSXnnQRhby4TlP6YoayprTrrd51bEXqL/3VsryO0PctshNu2fMWPGYmtto/PYYxK8AIwxdwHl1trfhH7Po5ng1VBubq7Nz2/xtFbJy8tj+vTpnt4jngW5/W3W9j/mQs/h8IUw/0/CA6dD175ww3Otv3crJOzfvvoQfPQAfPgnOLQfBp8FJ38eRl9yYu9VyS5Y9RwseczNrQupSu1Gh+8sgc5ZMS7efwn7d28jQW5/kNsOsWm/MabJ4OXZUKMxJhuottYWG2PSgfOAX3p1PxFflRfBvo0w6Ybwv9N/Cqx5AerqtH5UJKx1uwO8dqdb/X/EBXDOHdC/mYeku/aBM74Bp3/dDUMe2AoHt7FiF+QGMHSJiH+8nOPVB3gsNM8rCXjaWjvPGHMF8EcgG3jFGLPMWtvEpnYiCWLbR+44cGr43xlwquuB2bdRSxmEa98nLnBtfMPNk7vxJRh6TvjfN8YtlJo1AoCyvDxv6hQRaYJnwctauwKY1Mj7c3HzvUTaj+0fQXIa9D3hP/JN639q6LsfRx+8Dh+ENS+6hVu3LnCTx8//KeScFN314lVlKbz/O/jwj+6f8wU/h9NugeRUvysTEYmIp081igTG1gXQ75Sm92dsTM/h0LE7bF8Ip9wY2f2qD8Oih+C9/3HzmzJyYMBpLoD935mQ+xW46NeJP4RZW+N6BfN+AeWFbg7X+T9teYFaEZE4peAl0lple2HnYjfPKBJJSW64ccei8L9TVwvL58D8e6Fkh9uMe8aPXOgzBir2w5s/dqFs3NUwKIylLdqatVC8zb3Se0DnbPeKJARWH4ZlT8KHf4ADW2DgGXDdP6H/ZM/KFhGJBQUvkdZa9wpgYcxnI/9u/1PdfKVDxW4Px6bUTyh/66dQuBb6ngKXP3Di/KZOmXDeT2Dp427408vgVVfn1so6sMVNWN+zyq0Cv3sVVB489tyUdMge6eZlde3r9qpMz4S0LpCaDrXVUHMI9m92QXTrB1CxD/pNhln3uU3HW1iiQ0QkESh4ibTW2pchc2h086oGTHHHnfkw/LzGz9m+EN74kZsL1nM4XPMYjL2s6SDSOQt6jjg64b8t1dbAJ2+7pzHXvQKHi49+ltrZ/TMYfzX0Huf2rKwscT2C+ze7wLj1QyjdDXXVTd+jx2DXkzfpizDkbAUuEWlXFLxEWuNQMWx+xy1TEE1A6DcZTBJsX9R48CrbC49e4nqHPvO/Lowkh/Ff24FTXSBsy6Uq9qyBubfA7hWQ1g1GX+yWcOgx2IWsHkPCu1ddnZuXVrEfqkqhqsLNjUtNh4zekJHdNvWKiMQhBS+R1tjwGtTVwJhLo/t+WhfoNdb1ZjVm7UtQWwVffD6yHrWBp7vhxqINJ2yTEzFr3dOEb98DaV3hqofdsGokDxI0lJTkeuW0fpaIBFCCP/Ik4rO1L0PXfm7OVbSGnANb3ne9W8db/QJkjXLhLBL164nV7x8ZLWvh1Tvgzf92C5V+/WM3lBht6BIRCTgFL5FoVZXDpn/D6M+0bjgv9yY352nxY8e+X7rHTTI/6fLIhzEzh7onCVszz6uuDl75Liz8C0z9Onz+CfVSiYi0koKXSLQ+eRtqDkf3NGNDWSPcZPL8R9zTffXWvgS2Dk66IvJrGuN6vbZHGbwqy+D5m11N074DF/5ck9xFRNqAgpdItArXu2NzewSG69TZUFoQWpoiZPULbvmFXmOiu+aAqW6ph9LdkX1vzxp4cAasngvn3uWWp1DoEhFpEwpeItEq3eUWCE1Nb/21RlwA3QfCwgdD1w4NM469PPprDgyt4RXJcOPWBfDQue5pzRtfhLO+q9AlItKGFLxEolVS4CbWt4WkZJhyM2x9H56/BZ79CmDd/K5o9TnZLVy66c3wzt+zGp76vFvg9GvvuTW0RESkTSl4iUSrpMCtwN5WJn0Rsse4/RYPbodxV0U/zAhuA+nxV8HSJ+Bft7vFT5tyYCs8fiWkdoIbntdeiCIiHtE6XiLRKimAPhPa7nqdMuHrbbza/Gf/4DbiXvAnt63PVQ+5+zS8bfkOePQbbsuem16DHoPatgYRETlCPV4i0aipgvK9blguniUluycSL/2j60n78xnuacx62xcyaemdUFMJN74EORGuFyYiIhFRj5dINMpCTwrGe/Cqd8qN0GciPHczPH6F66k7VAwlO6lOyyb1q69C5hC/qxQRafcUvESiUVLgjokSvMBNtp+dB3m/gN0r3VIVXfuytG4i0xS6RERiQsFLJBr1watLAgUvgA6d4IJ7jnmrOi/Pn1pERAJIc7xEopGIPV4iIuI7BS+RaJQUuKUXOnbzuxIREUkgCl4i0SgtcL1dWtVdREQioOAlEo22XjxVREQCQcFLJBolu9puuyAREQkMBS+RSNXVhYYa1eMlIiKRUfCKR7XVYK3fVUhTKoqgrkY9XiIiEjEFr3hjLdx/Grx6h9+VSFNKdrqjlpIQEZEIKXjFm+KtsP8TWPhXKFjmdzXSmCOLp2qoUUREIqPgFW925LtjShq8eruGHOPRkcVTNdQoIiKRUfCKNzsXQ0pHmHUfbP8YVjztd0VyvJICSEqBztl+VyIiIglGwSve7FgEfSbCKV+CvpPgzR9D9WG/q5KGSne5YcYk/ddHREQio39zxJOaKti1Avrnun+pT/s2lO2Gvav9rkwaKtmp+V0iIhIVBa94smcl1Fa64AWQM94d967zryY5UUmBnmgUEZGoKHjFkx2L3bFfKHhlDoHkNChc619NcqyqCijeDt0H+l2JiIgkIAWveLIzHzJyoFt/93tSMmSNhL0KXnFj8zuuV3LYDL8rERGRBORZ8DLGdDTGLDTGLDfGrDbG3B16P9MY86YxZmPo2MOrGhLOjnzX22XM0fd6jdFQYzxZ/y/o0AUGnel3JSIikoC87PGqBGZaaycAE4FZxpipwJ3AW9baEcBbod+lYr9bOLX/5GPf7zUaSnbA4RJ/6pKj6upgw+sw/FxI6eB3NSIikoA8C17WKQv9mhp6WeAy4LHQ+48Bl3tVQ0LZGZrf1X/Kse9nj3HHwvWxrUdOtGsplO2BURf5XYmIiCQoYz1cGd0YkwwsBoYD91tr7zDGFFtruzc454C19oThRmPMbGA2QE5OzuQ5c+Z4VidAWVkZGRkZnt6jOYO2PM2QLU/y3plPUZvS6cj7HQ/tYurHX2P9yK+zq+8Fnt3f7/b7Kdy2D978JIO2PssH0x6jJrVrDCqLDf3t1fYgCnL7g9x2iE37Z8yYsdham9voh9Zaz19Ad2A+MA4oPu6zAy19f/LkydZr8+fP9/wezXr2Zmt/e9KJ79fWWntPjrWv3unp7X1vv4/CbvsD06x9eJantfhBf/tgCnLbrQ12+4Pcdmtj034g3zaRaWLyVKO1thjIA2YBe4wxfQBCx72xqCHuFW2ArBEnvp+UBNmj9GSj34q3uXXWNMwoIiKt4OVTjdnGmO6hn9OB84B1wEvAl0KnfQl40asaEoa1ULTRLR3RmF5jFLz8tuwf7qjgJSIireBlj1cfYL4xZgWwCHjTWjsPuA843xizETg/9HuwlRRAdXnjPV7gglfZbjh0ILZ1ibPpLXjnlzD2sqb/RiIiImFI8erC1toVwKRG3t8HnOvVfRNS0QZ3bKrHq/7Jxr3rYNDpsalJnH2fwLM3ub/BZQ/4XY2IiCQ4z4KXRKBoozs2OdQ42h33rlHwaq3qQ7DqeVj1rOtBrKlkcsVhKBjpNr5O7w4dMqCuFvZthC3vg0mC6/4BacF9CkhERNqGglc8KNoAaV3ddkGN6TbAhYFCrWAftdoa+PD38OEfXeDKHAaZQyEljaqaXXBwp9s54PBBqKsGDHQfADknwdm3Q4/BfrdARETaAQWveFD/RGPDrYIaMgayR2uCfbQObIHnb4HtH8HIWXD612HwWUf+ea/My2P69OlHz6+pdA88pHb0pVwREWm/FLziwb5NMOTs5s/pNdptVyORWfsyzL3VhawrH4STP9fyd1LSvK9LREQCKSbreEkzKkuhZGfLT8tlj4HyQigvik1dia6uDt7+GfzzBsgeCV97P7zQJSIi4iEFL7/t2+SOTU2sr9er/slGDTe2qPoQPP1FePfXMOkG+PK/oMcgv6sSERFR8PJdS0801qsPXppg37zDB+GJq2DdKzDrPrj0T5qrJSIicUNzvPxWtAFMMvQY0vx5XfpAWje3pERbqqqAF77G0NIkmDA4sZ/eO7gDnrrWrXd21UMw/mq/KxIRETmGerz8VrQBModASofmzzMmtHVQG/d4vX0PrHmRAdtfhN9PhOf+w82P8pq1LvTVVLXN9da8CH+eBvs3wxfmKHSJiEhcUo+X35rbo/F4vUa7gGFt00tPRGLLB/DRn2HKzXyUfDqn1y6ARQ+5Segjzm/99Ut2wcqnXVjctxFK90B1xdEXQFIK5IyDfpNh1MUwdDokR/Afy6pyeO0HsOQx6DsJrnoYeg5rfe0iIiIeUPDyU22125Jm+HnhnZ89Bg49CmV7oUsTi62Gq7IMXvxPN+n8vLupXJAPZ/7CzY366IHWBa+iTfDe/8DKZ9xipF36QM/hMOgM6NAZUtNDx05wuBh2LoEVT0P+w24R2XFXw+iLYcDU5kNYwTJ47mb3gMKZ/wXTf9hyz6GIiIiPFLz8VLAUaiuhf2545x95snFN64PXB/8LB7bCTf86uhVOSgeYcrMbfty79uj9IrF9ITxxtQtcuTfB1FvdCvEtqamEjW/Asqdg0YPw0f2Q3gN6n+zmnXXp7YJqzWEo3eUWRd29Cjpnw5deankdNBERkTig4OWnLe+746Bp4Z3f8MnGYTOiv6+1sOKfMPxc1wvV0OSb3DIMH/8ffPb3kV1387vwj2tdKLzxJbflTrhS0mDMZ92rshQ+eRs2vOHaum4eVOxzw5Ip6ZDRy4Wx026Bs26DTpmR1SkiIuITBS8/bf3ADR92zgrv/M7ZkJ7Z+rW8CpZC8TY4545G7tHTzfFaPgfOvSu8UFO0yQ0T5j/iAtGNL7oeqmildYGxl7lXvbpaSEqO/poiIiJxQE81+qW2BrZ9BIPD7O2CBk82tjJ4rZ4LSakw+pLGPz/tVjekt/jR5q9TuhvmXA9/mgwLH3S9VV/+V+tCV1MUukREpB1Qj5dfdi2HqrLwhxnr9RrjJqJH+2SjtbDmBff0YHqPxs/JGQsDz4DlT7lJ643dZ9Xz8Mp33Srx038AuV9xQ4AiIiLSJPV4+WVrhPO76mWPhsoSt79jNAqWuGHGk65o/rwJ17o1xgqWnPjZ+tfg2Zvcoq+3vAfT71ToEhERCYOCl1+2fAA9R0T+dGKfCe5YsDS6+65+ITTMeHHz5510OSSnubleJ1zjeTfX7KtvuA2oRUREJCwKXn6oq4VtCyKb31Wv98kuOG1fGPl3rXXBa9iMpocZ63Xs5uaArXz22NXla2vcsg8jL4Tk1MhrEBERCTAFLz/sXumGCwedGfl3UztC34mwY1Hk393+MRwMY5ix3oTr4NB+2PTvo+/tWAiHDrjgJSIiIhFR8PLD1g/dMZoeL4D+p7qhxkj3OVz6BKR2hjGXhnf+sJluCYvlTx19b/2rrsdt2LmR3VtEREQUvHxRtAE69YSufaP7/oApbrmHPSvD/05VuVtG4qQrjq5U35LkFBj/OdjwmtvaCGDD6y4wduwaed0iIiIBp+Dlh7I9bv/CaPU/1R23RzDcuOYlt3zFpOsju9fpX3f7Kj7zJbd+WNF6GHlRZNcQERERQMHLH6W73WbQ0erWD7r2c/OtwrXsSbdn4sDTI7/XFX9189KeuNq9p/ldIiIiUVHw8kPZntav7t5/Svg9Xvs3w5b3YOIXolt0deQFMO07ULLDrSOWOSTya4iIiIhWro+5ujoXvFrT4wUw4FS3An3p7uZDnLWw4H7AuKcUozXzv+HgDhhydvTXEBERCTgFr1ir2Ad1Na2b4wUN5nkthLFNPKVYVwuv3gGLHoTJN0G3/tHfLzkFrn44+u+LiIiIhhpjrmy3O0a6Yv3x+pwMyR2anud16ICbEL/oQTjjm3DJb1t3PxEREWk1Ba9YK93jjhmtnOOVkuYmyi/5u3vasF5dLSx6CP5wCqx7BS68Fy74GSTpTy0iIuI3/ds41tqqxwvgsj9BSjo8cRUc3Amb34O/nA2v3Aa9xsLsd9xyECIiIhIXNMcr1kpDwau1PV4A3QfCDc/CIxfB/01zw4vdBsI1j8HYy6J7glFEREQ8ox6vWCvb4zagTu3YNtfrPR6ufdJdc8b/g28shJMuV+gSERGJQ+rxirXSXW3T29XQ0HPg28vb9poiIiLS5jzr8TLGDDDGzDfGrDXGrDbGfDv0/gRjzAJjzEpjzMvGmGBt+lfaBounioiISELycqixBrjNWjsGmAp83RgzFngIuNNaOx6YC3zfwxriT1kLC56KiIhIu+VZ8LLW7rLWLgn9XAqsBfoBo4B3Q6e9CVzlVQ1xx1rX49XaVetFREQkIRlrrfc3MWYwLmyNA14DfmmtfdEY813gbmttl0a+MxuYDZCTkzN5zpw5ntZYVlZGRkaGp/dIqS7jzA+uZ9Owr7BjwGWe3itSsWh/vApy2yHY7Vfbg9l2CHb7g9x2iE37Z8yYsdham9voh9ZaT19ABrAYuDL0+2jgjdB7dwH7WrrG5MmTrdfmz5/v+T3snjXW3tXV2hXPeH+vCMWk/XEqyG23NtjtV9uDK8jtD3LbrY1N+4F820Sm8fSpRmNMKvAc8KS19vlQ0FsHXBD6fCRwiZc1xJX6Nbw0x0tERCSQvHyq0QAPA2uttb9t8H6v0DEJ+BHwf17VEHfKQtsFtXaDbBEREUlIXj7VOA34IjDTGLMs9LoYuM4YswFYBxQAf/OwhvhyZNV6Ta4XEREJIs+GGq217wNNLZ/+e6/uG9fK9kCHDEgL7qRGERGRINOWQbFUuku9XSIiIgGm4BVLWrVeREQk0BS8Yqlst3q8REREAkzBK5ZK9+iJRhERkQBT8IqVwyVQXQ5d1OMlIiISVApesbJvkztmDvW3DhEREfGNglesFK53x+zR/tYhIiIivlHwipXCdZCUCj2G+F2JiIiI+ETBK1YK10PWCEj2dHtMERERiWMKXrFSuA6yR/ldhYiIiPhIwSsWqg/BgS2a3yUiIhJwCl6xULQRsOrxEhERCTgFr1jQE40iIiKCgldsFK4DkwyZw/yuRERERHyk4BULhevcwqkpHfyuRERERHyk4BULhes1v0tEREQUvDxXUwn7P9X8LhEREVHw8ty+T8DWKniJiIiIgpfniuqfaNRQo4iISNApeHmtcD1g3HZBIiIiEmgKXl7bswoyh0Bqut+ViIiIiM8UvLy2azn0meB3FSIiIhIHFLy8VLEfirdBn4l+VyIiIiJxQMHLS7uWu6N6vERERAQFL28peImIiEgDCl5e2rUMug+ETpl+VyIiIiJxQMHLS7uWa36XiIiIHKHgBVBbQ9eDa9v2mocPuq2CNMwoIiIiIcZa63cNLcrNzbX5+fmeXT/vL9/lrF1/47bsv7ArZUCbXHNs5XLu2n8H9/b4Gcs75rbJNb1UXFxM9+7d/S7DF0FuOwS7/Wp7MNsOwW5/kNsO0LWuhAdvvdDTDrmkPQAACXhJREFUexhjFltrG/2Xv3q8gPzsK6ikA9eVPtpm1xxSvQmAzanD2+yaIiIikthS/C4gHnzvyrPYXHIFp215in9enAwDTm39RZ97GLb248H/vKj114qBvLw8pk8/3e8yfBHktkOw26+2B7PtEOz2B7nt4NrvJ/V4hezofxl07gVv/hjaYvhVE+tFRETkOApeIbUp6TDjB7BtASyf07qLleyCoo2aWC8iIiLH0FBjQ5NuhMWPwgtfg3Xz4OzvuycTt30EnbNgwnXQvYXJ95/Mh7m3QEoajPR28p6IiIgkFs+ClzHm/7d3/zFylHUcx9+f9EeQXu0PT49aGmpRTCwEaAkiaG0tIbQqVf4gGFNraqwESSSRhEaSBv/QCIQmVIkEAwgELcG22hAaWw0BNRSF5vrLA9qaEkvPViDSVmKk9OsfMxc2y87dVbrP7M58XslmZ+d5pvd8+91n53szs3MzgIeAM4ATwL0RcZekC4B7gNOA48D1EfHndo3jpIwZC8s3wzM/gT/cmRVfAONOh7fehCd/CB9dCF9cA5OmZ21vH4eBjXBoNxz+K7y4CXrPgaUboG92ebGYmZlZx2nnEa/jwHcjYpukicDzkrYAtwPfj4hNkhbnr+e3cRwnZ9xpMO+m7OjW3i3Qd152yvDIK9D/C3jmbnhgESzbCO+bAr9aDnt/BxoDU2fBJ78FC1fB+AllR2JmZmYdpm2FV0QMAoP58lFJA8B0IID3590mAQfbNYb3ZNJ0mPv1d15POSu7BuycK+Dhq+GBxTC+B17fB59fDRcuhbHjSxuumZmZdb4kN1CVNBN4GjiXrPj6LSCyi/svjYiXW2yzAlgB0NfXN3ft2vd4wfsIjh07Rk9Pz6j6Tji2n/O3r0Jxgt2zb+ZfU85r69hSOJn4q6bOsUO943fs9Ywd6h1/nWOHNPEvWLCg8AaqbS+8JPUATwE/iIj1ktYAT0XEOknXACsi4vLh/o1237kehu5rMn/0G/z71ex5Qm9bxpPaScdfIXWOHeodv2OfX/YwSlPn+OscO6SJv7Q710saB6wDHomI9fnqZcDQ8mPAKbhbaQkm9Fam6DIzM7M02lZ4SRJwHzAQEasbmg4Cn82XPwfsadcYzMzMzDpJO7/VeBmwFNgpqT9f9z3gm8BdksYC/yG/jsvMzMys6tr5rcY/kl1A38rcdv1cMzMzs07lPxlkZmZmlogLLzMzM7NEXHiZmZmZJeLCy8zMzCwRF15mZmZmibjwMjMzM0vEhZeZmZlZIi68zMzMzBJx4WVmZmaWiAsvMzMzs0RceJmZmZkl4sLLzMzMLBFFRNljGJGkfwIvt/nH9AKvtvlndLI6x1/n2KHe8Tv2+qpz/HWOHdLEf1ZEfLBVQ1cUXilIei4iLip7HGWpc/x1jh3qHb9jr2fsUO/46xw7lB+/TzWamZmZJeLCy8zMzCwRF17vuLfsAZSszvHXOXaod/yOvb7qHH+dY4eS4/c1XmZmZmaJ+IiXmZmZWSIuvMzMzMwSqV3hJelKSS9K2itpZYt2SVqTt++QNKeMcZ5qkmZIelLSgKTdkr7Tos98SW9I6s8fq8oYa7tI2i9pZx7bcy3aq5r7jzfktF/SEUk3NvWpVO4l3S/psKRdDeumStoiaU/+PKVg22E/IzpdQex3SHohf19vkDS5YNth50g3KIj/VkmvNLy/FxdsW8XcP9oQ935J/QXbdnXui/ZxHTnvI6I2D2AMsA+YBYwHtgOfaOqzGNgECLgEeLbscZ+i2KcBc/LlicBLLWKfDzxe9ljb+H+wH+gdpr2SuW+KcQzwD7Kb+1U298A8YA6wq2Hd7cDKfHklcFvB/8+wnxGd/iiI/QpgbL58W6vY87Zh50g3PArivxW4aYTtKpn7pvY7gVVVzH3RPq4T533djnhdDOyNiL9FxH+BtcCSpj5LgIcisxWYLGla6oGeahExGBHb8uWjwAAwvdxRdZxK5r7JQmBfRLT7L0GUKiKeBl5vWr0EeDBffhD4UotNR/MZ0dFaxR4RmyPieP5yK3Bm8oElUpD70ahk7odIEnAN8Mukg0pkmH1cx837uhVe04G/N7w+wLuLj9H06WqSZgIXAs+2aP6UpO2SNkmanXRg7RfAZknPS1rRor3yuQeupfiDt8q5B+iLiEHIPqSBD7XoU4f3wHKyI7utjDRHutkN+anW+wtON1U9958BDkXEnoL2yuS+aR/XcfO+boWXWqxrvp/GaPp0LUk9wDrgxog40tS8jewU1PnAj4Ffpx5fm10WEXOARcC3Jc1raq967scDVwGPtWiueu5Hq+rvgVuA48AjBV1GmiPd6qfA2cAFwCDZKbdmlc498BWGP9pVidyPsI8r3KzFurblvm6F1wFgRsPrM4GD/0efriRpHNkb8pGIWN/cHhFHIuJYvvwEME5Sb+Jhtk1EHMyfDwMbyA4vN6ps7nOLgG0Rcai5oeq5zx0aOnWcPx9u0aey7wFJy4AvAF+N/MKWZqOYI10pIg5FxNsRcQL4Ga3jqnLuxwJXA48W9alC7gv2cR037+tWeP0F+Jikj+S//V8LbGzqsxH4Wv4Nt0uAN4YOU3az/Pz+fcBARKwu6HNG3g9JF5O9P15LN8r2kTRB0sShZbKLjXc1datk7hsU/sZb5dw32Agsy5eXAb9p0Wc0nxFdR9KVwM3AVRHxZkGf0cyRrtR0reaXaR1XJXOfuxx4ISIOtGqsQu6H2cd13rwv49sHZT7Ivrn2Etk3GG7J110HXJcvC7g7b98JXFT2mE9R3J8mO3S6A+jPH4ubYr8B2E32jY6twKVlj/sUxj8rj2t7HmNtcp/HdjpZITWpYV1lc09WYA4Cb5H9NvsN4APA74E9+fPUvO+HgScatn3XZ0Q3PQpi30t2DcvQ3L+nOfaiOdJtj4L4H87n9A6yHeq0uuQ+X//zobne0LdSuR9mH9dx895/MsjMzMwskbqdajQzMzMrjQsvMzMzs0RceJmZmZkl4sLLzMzMLBEXXmZmZmaJuPAys9qRNFnS9WWPw8zqx4WXmdXRZMCFl5kl58LLzOroR8DZkvol3VH2YMysPnwDVTOrHUkzgccj4tySh2JmNeMjXmZmZmaJuPAyMzMzS8SFl5nV0VFgYtmDMLP6ceFlZrUTEa8Bf5K0yxfXm1lKvrjezMzMLBEf8TIzMzNLxIWXmZmZWSIuvMzMzMwSceFlZmZmlogLLzMzM7NEXHiZmZmZJeLCy8zMzCyR/wGDCwh+GovPtQAAAABJRU5ErkJggg==\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": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "pphi_odeint = lambda yy,t : [ yy[1], -sin(yy[0]) ]\n", "\n", "t0 = 0\n", "yy0 = [0,1]\n", "tt = linspace(t0,10,1001)\n", "sol_1, sol_2 = odeint(pphi_odeint,yy0,tt).T\n", "\n", "figure(figsize=(18,7))\n", "\n", "subplot(1,2,1)\n", "plot(tt,sol_1,tt,sol_2)\n", "xlabel('t')\n", "ylabel('y')\n", "grid()\n", "\n", "subplot(1,2,2)\n", "plot(sol_1,sol_2)\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": 18, "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_1)+sol_2**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": 19, "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": 20, "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 " ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = sym.Symbol('x')\n", "u = sym.Function('u')\n", "left = sym.diff(u(x),x)\n", "right = 6*x**2-3*x**2*u(x)\n", "edo = sym.Eq( left , right )\n", "display(edo)" ] }, { "cell_type": "code", "execution_count": 21, "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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "solgen = sym.dsolve(edo,u(x))\n", "display(solgen)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Prise en compte des conditions initiales:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/latex": [ "$\\displaystyle \\left\\{ C_{1} : 2\\right\\}$" ], "text/plain": [ "{C₁: 2}" ] }, "execution_count": 22, "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": 23, "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": 23, "metadata": {}, "output_type": "execute_result" } ], "source": [ "solpar = solgen.subs(consts)\n", "solpar" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "On transforme le résultat en une fonction vectorisée :" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "func = sym.lambdify(x,solpar.rhs,'numpy')" ] }, { "cell_type": "code", "execution_count": 25, "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": 26, "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", "right1 = y1(t)-y2(t)\n", "right2 = y2(t)-y1(t)\n", "\n", "edo1 = sym.Eq( sym.diff(y1(t),t) , right1 )\n", "edo2 = sym.Eq( sym.diff(y2(t),t) , right2 )\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": 27, "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": 28, "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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8+HcoCAXif+VLuIew5p21evYNFAKjDERosFEnWChCmvd6QFHocqS5UJqD0qFnDpWq5ksU0pPPUae0k+6BUP59YB6lzxGMwA4Q2K18GFu3li9jEXT6mRH4bygPBSLVYTVortd37X8gP+LF9i/U9j+o87ChkvhNJQQLRLM8ebWd8ljtHog2N/YxAvMjoD7UpcSfQojlwyloOa4R2AAClyfwUBvMJXCwJHB1LUWgDNyN5H1QDBBaisOxzk3lgaSYBrv8CbMzAkYgEwJlP/xb97cjsrR8GAGekxqBNSJwigWiOBpVQoYjaP/SxZkQuMNSxKfX4veFfvnutMuRzzPlU5zCqHvz/IeQBuXEloWAxhnvqqPvVTwK4XtdYamJjbOcevhU4cFPr8t3opfZMu0LfniGN/ioKax6Z0Bl01ttcJTfppz4YxkSHrFCDLVEWD5sqlXkY0ZtyvIjH5yLyunK48ePb4kiBOUXpRBJIlBxUSQ4y6FzE5H8Ocdh0I5jpUWo/6x7UFKSaHKkvAgIfwZZ9pdwYmbtqxm9Y3m6o/tneUudPjfRjHLL1wMMehe6I+A4y+DAi56xjjEr383+F/HKciLntIxWCJWH5YPA3LNTG7D82KD8UL0y+ccIcOVqSgNvCgO9I1zJ5EFPegQIFoQhVgQEO+ntzoSA6pjBhEPDbui5a0BBsVjrzBzrSdV9rhesEVWH8KtZJKqBG32+q7quKYopfCpNTVnQu+VDCnAbjqM2YPmxA/lxmdiGaQwvKnEZWH7qEzYK43NP9jdgTUh2ZXzSHT4XTU7siFkQKOuAWTr/q9ClPFAOykPX/hfCFu3EE18TVZUD2nehsMK7Lp7DOyc8YqXbtBOPDPosTQ5xlg9DUNtoGvqQWLP8EAjCYtPyI8kCIRywCFwXGJh6WVbAfNG190FBNcenXTQkvrxIdcxsh1gtUvN3vOMIMHhi4o/ORhXGAFwdhI/nurAYZXv+VmTRnguFVXcUI5ZssECwLyKKwcLYGUvOd+I1th/pWN6WD8cQ2le45cdO5MfgPRCp/UFCCW30XopwUhwUlNe6r9U0ngrLouMJ/79F4EvdkxU5xaWeUf7Y9xKzWiyOb9HKzBsllz03hwFUzxzu89maeFkcuAkECV/LhwSc1hRFdWr5sWH5ofo97IG4nLphqjBmsgfB3Fce8YjfF8dhsyHAJtioUz1hti6cnjHxczEYrMqJdpSdYs9NyceF7lgf+DJhNYrQqkCvECuMLR8qeGzo0fJjB/IjdQljQ+3arEhoM+t+pCusebMshdk+DJgsT8XO8bhQvMJSpDiF03uxnKF7sW8g+J/rLjqi/JVhf4o2/kI9LMEEvu/IHz+UoWKJrowfO6tE0eyMwL4Q6OtfJRKWHzuRH5NbIPbVtZbPrTo/s2s+232hZyw+WIdYekChCI6va/hEl7g1Jz+UBzYhLtJSVNIc5U/hKAvvdVXpLywO8nupC4dC9aZ4+oRLNW7p7ZsR2B8Cx/pXiYjlx07khy0QO5IB6vwsMfDlxEM9h9k3CDCAHr6oYJDVdUN+7CBmIyyDbrBW8PVNmLHLezlOdCXxJ4rhiXMfAk9YW25X+EKhAiPW+lC0FsmvaLMzArMhoH6Q1L/oL7osP3YgP6xAzNb9FlEQAyOO0waxJOA4A4ENhLWvahAC8k/eRElGpzqVcU1pcv4dchJ/KhflqapA1UgvwyflvVagX4zAOhBI6l+woj5k+bGOOh1FpRWIUfCtLjGWBr5ySdrUmsqd8mPPAHlf18XM/o2uo58/Kg5CpvMkU/kPcZPwN4QQpzECG0Rgkv5l+bHelnJ1vaSb8oEIhLX9gcnbySQAwow+q2LSLinJJzt/SaU6khHYBwLZ+5flx3obzuV6STflAxBgMyBLFi2nTnz4LLMVuB6PrfO3npowpVtEYOv9a+v8ZW+TtkBkh3TRGfKZZW1tX4oD+xDwX8QnmCPR2zp/I+FxciMwCoGt96+t8zeq8rsST34SZVeh9jsfAlIY2DyJFSIc9MKGyiUsPWQBZev8ZQHJmRiBgQhsvX9tnb+B1V5LJowOJ1FagahB4xcjYASMgBEwAkYghkBVgfAeiBhK9jcCRsAIGAEjYASiCFiBiELjACNgBIyAETACRiCGgBWIGDL2NwJGwAgYASNgBKIIWIGIQuMAI2AEjIARMAJGIIaAFYgYMvY3AkbACBgBI2AEoghYgYhC4wAjYASMgBEwAkYghoAViBgy9jcCRsAIGAEjYASiCFiBiELjACNgBIyAETACRiCGgBWIGDL2NwJGwAgYASNgBKIIWIGIQuMAI2AEjIARMAJGIIaAFYgYMvY3AkbACBgBI2AEoghYgYhC4wAjYASMgBEwAkYghoAViBgy9jcCRsAIGAEjYASiCFiBiELjACNgBIyAETACRiCGgBWIGDL2NwJGwAgYASNgBKIIXK2EvNP/fFdei8fX8rvf9PS7ETACRsAIGAEjsG0ENP6/E4c3Y1yiQPyh62EkAmF2RsAIGAEjYASMwP4Q+KGP5f8DFjw1BWQMBZEAAAAASUVORK5CYII=\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", "right = sym.Rational(3,2)*y(t)*(1-y(t)/6)\n", "edo = sym.Eq( sym.diff(y(t),t) , right )\n", "display(edo)\n", "solgenLIST = sym.dsolve(edo,y(t))\n", "display(solgenLIST)" ] }, { "cell_type": "code", "execution_count": 29, "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 = solgenLIST[0]\n", "display(solgen)" ] }, { "cell_type": "code", "execution_count": 30, "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", "\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": 31, "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", "t_final = 10\n", "\n", "phi_odeint = lambda y,t : sin(t*y)\n", "tt = linspace(0,t_final,201)\n", "\n", "figure(figsize=(10,7)) # facultatif\n", "\n", "T,Y = meshgrid(linspace(0,t_final,31),linspace(-3,3,31))\n", "DT, DY = 1, phi_odeint(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_odeint,y0,tt)\n", " plot(tt,sol,lw=2,label='$y_0=$'+str(y0));\n", "legend(bbox_to_anchor=(1.04,1),loc='upper left');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 🐍 Exercice (sympy - système)\n", "> 1. Calculer la solution générale **exacte** du système \n", ">\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", ">\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": 32, "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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"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": 33, "metadata": {}, "outputs": [ { "data": { "image/png": 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"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": "iVBORw0KGgoAAAANSUhEUgAAAMEAAAAVCAYAAAD/7YqlAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAGYElEQVRoBe2b4XUUNxDHLzwXQKCCOB0YqADTgUMqgHQAj0/2N57pAKiAQAeQCojdgekgxB04v9+y0tPuaXd1u+s738Xznk5aaUYa/TUajXbtxdXV1WJqOj4+3i/po5SvpK9d4inFpZRvl7ApmcsquOR47ywm0snJyQu6OCjsZr/mL2TffbZb/Kat8Yr4OdiSDU7aBChwRKf3yT+VTAW+L/KRPy/h3zQPegrYv9elL/3uNH7XvX6r4qc+yCzZ4E8eN2OIzu4i9xf5g5x83X5G2xPK31Ienq1/TH6Z1t+0MvodotNn0jvKf8ypH/3tPH5z4tXuawg/+WueQRucchKcMs7btnLJswa0T/qe1IWicsrfaAJEvcbP5LNugHrSG8WPOR2StuJE7jCSIfwUK7LBKZvgKSC+61DQ6iekb/AseftaTnm94Y2mnP4zKbxp/MT+xuPfg/UQfooW2eCoTYBhGMs2QpyMsu7CvruC8k8zcjtfdYvftCUuxM9BimxwT0461SN4NP5KOuM5evi67T35b7QFcodVF4xQYQ6Pgxo62J+h0AF1H8m/kr8hT0l5+4ljpY3rKKOTb7XU+ZIUvOLv1D8gqb+6m3/huZp/LfO+rv+T3GNZpyA9IuXmWjUmP1uPHziIl3MXu0DOPTq+hOeiZtC+PlIfbYdy5xqETjN5Fj/56G9lG6w2AbKvEH5JcjFd4NQw9dZhkSlW9JDfpfsA8k5Og5HfmFNlu0hgVHiQ6MexiniTzs6RSzdu0hQ3/mlbR56r+J/ck8rN4MUqEs/nPFiv/vdIbvRqg5O7oDqRT6S+k3Kt+KHTrMTcdAzi8sy52jm566OBGwKLvVjoRBovRqj/bBvpDanaSOQNO+F56A6WxY+xFsiubIN7CKnsVzuAVKZ9kc3tOpVv8ykfSBmNpY+UF8xBKgBlsI8Mg0A+pO+7pNSbtTd31zw18kNk40aj7OI7lAaROhLrUlorfunAM5U1bo09en2enZMUsJQn5wxeUq+j0Fh1IiVrAFuDhvCTudgG92Cudm49hF7/dV0OmQvarlP5MNnAl+bKpAClbaGsEQXgQt3acheBpIH7HcAF8VWoi9YO2/p0+rujcWhea8OP+XSdouqwoD3ndTtPUfid2wGpgRP1rne15pRt18EF50rxB9EWHIVhp9HHmDUYws/Bim3Qk6AyZnKFnGD0YNQ5Ges0kiJCRn4B0Kj6qGQiffJztPmN4xXJ8M341vBo9m8C9FtMc+NHfzkjX1DvnP0Y2DDmAkXD6f1PD2/gqWyrg0/bkmZfA+a0kg3u/dCj+vVYd5emirsxLqk7T/gsunsdKEfKLJCJG4dyO+SQRXn7GSTku7xZn2ynN1OIPl2o7+QezybrfDnwltzUnrMsc9Fa8ZtL6bqfcNfxkttFgafLRpQzAhm7Bn342fdKNphuAhUKytuRlLsPWC9f2O0+p9SIxZioHkf+tlF5ErTHS/uJZfrIerPIMK6gJ3IO0RMyjqeA+ntfaOtL1Wy0Vvxm05qOwCc4RTFaItqPSIaVOlOxbITF1FcGSr13hrFr0Icf3TbvA+pEXacN3lGipoZB1sqqcC6s0UB8HZijaNz0oSfwyM0ZlMdgrj7X53XV+Vas7a18jqdYPXCbx2rnOZa2HT+jBte18cWZZ0PKsKaPKftBS0NPSR7fDAWMS9cg7aMPP/lWssH0JDAk8HuAShrvheMuKEtVpA+U3Mk5sh/DiQog8uhpW8xusOvw8K1hOh8vafH+8xwdA9N9Ct4LPKpdPO8Llcfj2fk+I3l6WG+7XtH61yTrw3xc2Eek+OaItpS2Gj/mJT6/MCGxMlQN3wFc98qZkhuO6ui8/Iq1JEY+B5vqXYNKIv/Th58Sq9lg199r83fXp6SznvYL2g+62vvq/Ztu0kUfz663Of9N4sfYR6QX24rzFPycM/LRBqtwiJ3pjo4fhSh7/OvJ9XBd5IkRPF8XT1e9O1X5/zNtGj+9cPDQ27gOU/BzvtEGq01AhReHD7bUVH01ZjM0LjWh0Zw2QwnjQo+4Yqr5lYuvYouFd4hx0/gxvt9JtnYNxuKnCSGrzUYbDHcCd8U9Gv0vMe8CxnYhbuOxk4x5jYl9C1BKxpBjT5DSMbaF7xa/aSs1Bj9HbNrg1Jiwjq2KYktjUPmnjrlL8rf4Tfsf91Xwq+8CSzb4Hx9lifIhxA6iAAAAAElFTkSuQmCC\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", "\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": 34, "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. On définit la fonction\n", "$$\n", "t\\mapsto E(t)=\\frac{x^2(t)}{2}+\\frac{y^2(t)}{2}.\n", "$$\n", "Calculer analytiquement $E'(t)$. Afficher ensuite $E(t)$ calculé à partir des solutions approchées." ] }, { "cell_type": "code", "execution_count": 35, "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_odeint = 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", "solx,soly = odeint(pphi_odeint,yy0,tt).T\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": [ "$$\n", "E'(t)=x'(t)x(t)+y'(t)y(t)=\\left(-y(t)+y^2(t)x(t)\\right)x(t)+\\left(x(t)-x^2(t)y(t)\\right)y(t)=0.\n", "$$" ] }, { "cell_type": "code", "execution_count": 36, "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]) # pour tracer le segment reliant (x0,y0) et (x1,y1) on peut écrire plot([x0,x1],[y0,y1])\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": 37, "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": "markdown", "metadata": {}, "source": [ "Pour une résolution graphique on affiche les deux courbes du système:" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "image/png": 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