{ "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.display import display, Latex\n", "from IPython.core.display import HTML\n", "css_file = './custom.css'\n", "HTML(open(css_file, \"r\").read()) " ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Python version 3.8.5 (default, Jan 27 2021, 15:41:15) \n", "[GCC 9.3.0]\n" ] } ], "source": [ "import sys #only needed to determine Python version number\n", "print('Python version ' + sys.version)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# M62_CM5 : Convergence et A-stabilité des schémas multipas linéaires\n", "$\\newcommand{\\R}{\\mathbb{R}}$ $\\newcommand{\\N}{\\mathbb{N}}$ $\\newcommand{\\dt}{\\mathrm{d}t}$ $\\newcommand{\\dx}{\\mathrm{d}x}$ $\\newcommand{\\dtau}{\\mathrm{d}\\tau}$ $\\newcommand{\\CC}[1]{\\mathscr{C}}$" ] }, { "cell_type": "markdown", "metadata": { "toc": true }, "source": [ "

Table of Contents

\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Convergence d'un schéma multipas linéaire\n", "Considérons le problème de Cauchy\n", "\n", ">trouver une fonction $y \\colon I\\subset \\mathbb{R} \\to \\mathbb{R}$ définie sur un intervalle $I=[t_0,T]$ telle que\n", "$$\\begin{cases}\n", "y'(t) = \\varphi(t,y(t)), &\\forall t \\in I=[t_0,T],\\\\\n", "y(t_0) = y_0,\n", "\\end{cases}$$\n", "avec $y_0$ une valeur donnée et supposons que l'on ait montré l'existence et l'unicité d'une solution $y$ pour $t\\in I$.\n", "\n", "\n", "
\n", "Considérons une méthode numérique à $q=p+1$ étapes (=pas) linéaire.\n", "Elle s'écrit sous la forme générale\n", "$$\n", "u_{n+1} \n", "= \n", "\\sum_{j=0}^p a_ju_{n-j}\n", "+\n", "h\\sum_{j=0}^p b_j\\varphi(t_{n-j},u_{n-j})\n", "+\n", "hb_{-1}\\varphi(t_{n+1},u_{n+1}),\n", "\\qquad\n", "n=p,p+1,\\dots,N-1\n", "$$\n", "où les $\\{a_k\\}$ et $\\{b_k\\}$ sont des coefficients donnés et $p\\ge0$ un entier.\n", "
\n", "\n", "Les données initiales $u_0, u_1, \\dots, u_p$ doivent être fournies. \n", "Mis à part $u_0$, qui est égale à $y_0$ donné, les autres valeurs, $u_1, \\dots, u_p$ peuvent être obtenues à l’aide de méthodes suffisament précises. \n", "Si $b_{-1}=0$ la méthode est explicite, sinon implicite.\n", "\n", "\n", "Les méthodes AB$_q$, AM$_q$, N$_q$, MS$_q$ et BFD$_q$ sont toutes des méthodes numériques à $q=p+1$ étapes (=pas) linéaires. \n", "En revanche, les méthodes EM et Heun ne rentrent pas dans ce cadre: elles sont des méthodes de la famille RK.\n", "\n", "**Exemples** :\n", "- Euler explicite \n", "$$\n", "u_{n+1}=u_n+h\\varphi(t_n,u_n)\n", "\\quad\\implies\\quad\n", "p=0,\\ a_0=1,\\ b_{-1}=0,\\ b_0=1;\n", "$$\n", "- Euler implicite \n", "$$\n", "u_{n+1}=u_n+h\\varphi(t_{n+1},u_{n+1})\n", "\\quad\\implies\\quad\n", "p=0,\\ a_0=1,\\ b_{-1}=1,\\ b_0=0;\n", "$$\n", "- Crank-Nicolson \n", "$$ \n", "u_{n+1}=u_n+\\frac{h}{2}\\left(\\varphi(t_n,u_n)+\\varphi(t_{n+1},u_{n+1})\\right)\n", "\\quad\\implies\\quad\n", "p=0,\\ a_0=1,\\ b_{-1}=\\frac{1}{2},\\ b_0=\\frac{1}{2}.\n", "$$\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Polynômes caractéristiques\n", "Réécrivons le schéma multistep comme suit:\n", "$$\n", "u_{n+1} \n", "-\\sum_{j=0}^p a_ju_{n-j}\n", "= \n", "h\n", "\\left(\\sum_{j=0}^p b_j\\varphi(t_{n-j},u_{n-j})\n", "+\n", "b_{-1}\\varphi(t_{n+1},u_{n+1})\n", "\\right).\n", "$$\n", "Formellement, \n", "- pour construire le premier polynômes caractéristiques on ne regarde que le LHS et les $u_{n-j}$ deviennent des $r^{p-j}$,\n", "- pour construire le second polynômes caractéristiques on ne regarde que le RHS divisé par $h$ et les $\\varphi(t_{n-j},u_{n-j})$ deviennent des $r^{p-j}$.\n", "
\n", "Définition: le polynôme\n", "$$\n", "\\varrho(r)=r^{p+1}-\\sum_{j=0}^p a_jr^{p-j}\n", "$$\n", "est appelé premier polynôme caractéristique associé à la méthode numérique. \n", "
\n", "
\n", "Définition: le polynôme\n", "$$\n", "\\sigma(r)=b_{-1}r^{p+1}+\\sum_{j=0}^p b_jr^{p-j}\n", "$$\n", "est appelé second polynôme caractéristique associé à la méthode numérique. \n", "
\n", "\n", "**Exemples** :\n", "- Euler explicite: $\\varrho(r)=r-1$ et $\\sigma(r)=1$ \n", "- Euler implicite: $\\varrho(r)=r-1$ et $\\sigma(r)=r$ \n", "- Crank-Nicolson: $\\varrho(r)=r-1$ et $\\sigma(r)=\\frac{1}{2}r+\\frac{1}{2}$\n", "- AB$_q$ ou AM$_q$: $\\varrho(r)=r^{q+1}-r^{q}$ \n", "- N$_q$ ou MS$_q$: $\\varrho(r)=r^{q+1}-r^{q-1}$\n", "- BDF$_2$: $\\varrho(r)=r^2-\\frac{4}{3}r+\\frac{1}{3}$ et $\\sigma(r)=\\frac{2}{3}$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Consistance\n", "L’erreur de troncature locale de la méthode multi-pas s'écrit\n", "$$\n", "\\tau_n(h)\n", "=\n", "\\frac{1}{h}\n", "\\left(y_{n+1}-\\sum_{j=0}^p a_jy_{n-j}\n", "-\n", "h\\sum_{j=0}^p b_j\\varphi(t_{n-j},y_{n-j})\n", "-\n", "hb_{-1}\\varphi(t_{n+1},y_{n+1})\\right).\n", "$$\n", "La méthode est dite consistante si $\\tau(h)=\\max_n |\\tau_n(h)|$ tend vers zéro quand $h$ tend vers zéro. Par un développement de Taylor assez fastidieux, on peut montrer que cette condition est équivalente à la condition suivante: \n", "
\n", "Proposition \n", "\n", "La méthode est consistante ssi \n", "$$\n", "\\begin{cases}\n", "\\displaystyle\\sum_{j=0}^p a_j=1,\n", "\\\\\n", "\\displaystyle-\\sum_{j=0}^p ja_j+\\sum_{j=-1}^p b_j=1\n", "\\end{cases}\n", "$$\n", "
\n", "Notons que la première condition de consistance équivaut à $\\varrho(1)=0$.\n", "\n", "
\n", "Proposition \n", " \n", "La méthode est d'ordre $\\omega\\ge1$ ssi elle est consistante et, de plus,\n", "$$\n", "\\sum_{j=0}^p (-j)^{i}a_j+i\\sum_{j=-1}^p (-j)^{i-1}b_j=1 \\quad i=2,\\dots,\\omega.\n", "$$\n", "
\n", "\n", "\n", "\n", "\n", "**Exemple**: schéma AB$_2$\n", "- Schéma: $u_{n+1}=u_{n}+ \\frac{h}{2} \\big(3\\varphi_{n}-\\varphi_{n-1}\\big)$\n", "- Coefficients: $q=2$, $p=1$, $a_0=1$, $a_1=0$, $b_0=\\frac{3}{2}$, $b_1=-\\frac{1}{2}$, $b_{-1}=0$\n", "- Consistance: $\\begin{cases}\\sum_{j=0}^p a_j=1+0=1\\\\-\\sum_{j=0}^p ja_j+\\sum_{j=-1}^p b_j=-(0a_0+1a_1)+(b_{-1}+b_0+b_1)=1\\end{cases}$\n", "- Ordre $\\omega$: \n", " - pour $i=2$ on a $\\sum_{j=0}^p (-j)^{i}a_j+i\\sum_{j=-1}^p (-j)^{i-1}b_j=\\sum_{j=0}^p j^2 a_j+2\\sum_{j=-1}^p j b_j=(0^2a_0+1^2a_1)+2(-1b_{-1}+0b_0+1b_1)=1$ donc $\\omega\\ge2$,\n", " - pour $i=3$ on a $\\sum_{j=0}^p (-j)^{i}a_j+i\\sum_{j=-1}^p (-j)^{i-1}b_j=\\sum_{j=0}^p (-j)^3 a_j+3\\sum_{j=-1}^p j^2 b_j=(0^3a_0-1^3a_1)+3((-1)^2b_{-1}+0^2b_0+1^2b_1)=3$ donc $\\omega<3$\n", " - donc l'ordre $\\omega$ est $2$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Zéro-stabilité\n", "\n", "\n", "
\n", "Proposition [condition des racines]\n", "\n", "Soient $r_0, r_1,\\dots, r_p$ les $p+1$ racines du polynôme $\\varrho$. On peut montrer que la méthode est **zéro-stable** ssi \n", "$$\n", "\\begin{cases}\n", "|r_j|\\le1 \\quad\\text{pour tout }j=0,\\dots,p\n", "\\\\\n", "\\varrho'(r_j)\\neq0 \\text{ si } |r_j|=1.\n", "\\end{cases}\n", "$$\n", "
\n", "\n", "En particulier:\n", "- les méthodes à un pas (EE,EI,CN) vérifient $\\varrho(r)=r-1$: le polynôme $\\varrho$ n'a qu'une racine, c'est $r=1$. Toutes ces méthodes sont donc zéro-stables. On peut donc conclure que pour les méthodes à un pas, \"consistance $=$ convergence\";\n", "- les méthodes de Adam à $q$ pas vérifient $\\varrho(r)=r^{p+1}-r^p=r^p(r-1)$: il n'y a que deux racines, la racine $1$ de multiplicité $1$ et la racine $0$ de multiplicité $p$. Toutes ces méthodes sont donc zéro-stables;\n", "- les méthodes de Nystrom et Milne-Simpson à $q$ pas vérifient $\\varrho(r)=r^{p+1}-r^{p-1}=r^{p-1}(r-1)(r+1)$: il n'y a que trois racines, les racines $\\pm1$ de multiplicité $1$ et la racine $0$ de multiplicité $p-1$. Toutes ces méthodes sont donc zéro-stables;\n", "- enfin, on peut montrer que les méthodes BDF sont zéro-stables ssi $p\\le5$ (voir les calculs `sympy` ci-dessous)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "Théorème (Dahlquist 1956). \n", " \n", "Une méthode multipas est convergente si et seulement si elle est consistante et (zero)-stable.\n", "
\n", " \n", "La zero stabilité implique une restriction significative sur l’ordre atteignable pour une méthode multipas.\n", "\n", "
\n", "Première barrière de Dahlquist \n", "\n", "L’ordre $\\omega$ d’une méthode multipas à $q=p+1$ étapes consistante et zéro-stable satisfait les inégalités suivantes:\n", "- si $b_{-1}=0$ (la méthode est explicite) alors $\\omega\\le q=p+1$\n", "- si $b_{-1}\\neq0$ (la méthode est implicite) on doit considérér deux cas \n", " - si $q=p+1$ est impair alors $\\omega\\le q+1=p+2$\n", " - si $q=p+1$ est pair alors $\\omega\\le q+2=p+3$\n", "
\n", "\n", "**Exemples** :\n", "- Soit une méthode explicite à un pas, alors $q=1$, $p=0$, $b_{-1}=0$ et son ordre de consistance est au plus $\\omega=p+1=1$. \n", " (Exemple: EE qui a ordre 1)\n", "- Soit une méthode implicite à un pas, alors $q=1$, $p=0$, $b_{-1}\\neq0$ et son ordre de consistance est au plus $\\omega=p+2=2$. \n", " (Exemple: EI qui a ordre 1 et CN qui a ordre 2)\n", "- Soit une méthode explicite à deux pas, alors $q=2$, $p=1$, $b_{-1}=0$ et son ordre de consistance est au plus $\\omega=p+1=2$. \n", " (Exemple: AB$_2$ qui a ordre 2)\n", "- Soit une méthode implicite à deux pas, alors $q=2$, $p=1$, $b_{-1}\\neq0$ et son ordre de consistance est au plus $\\omega=p+3=4$. \n", " (Exemple: AM$_2$ qui a ordre 3 et MS$_2$ qui a ordre 4)" ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " EE_AB1\n", "\tq = 1\n", "\tExplicite\n", "\tConsistance: True\n", "\tOrdre 1\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r - 1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " EI_AM0_BDF1\n", "\tq = 1\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 1\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r - 1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " CN_AM1\n", "\tq = 1\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 2\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r - 1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AB2\n", "\tq = 2\n", "\tExplicite\n", "\tConsistance: True\n", "\tOrdre 2\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - r$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AB3\n", "\tq = 3\n", "\tExplicite\n", "\tConsistance: True\n", "\tOrdre 3\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{3} - r^{2}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AB4\n", "\tq = 4\n", "\tExplicite\n", "\tConsistance: True\n", "\tOrdre 4\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{4} - r^{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AB5\n", "\tq = 5\n", "\tExplicite\n", "\tConsistance: True\n", "\tOrdre 5\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{5} - r^{4}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AM2\n", "\tq = 2\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 3\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - r$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AM3\n", "\tq = 3\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 4\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{3} - r^{2}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " AM4\n", "\tq = 4\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 5\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{4} - r^{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " BDF2\n", "\tq = 2\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 2\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - \\frac{4 r}{3} + \\frac{1}{3}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 0.333333333333333, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " BDF3\n", "\tq = 3\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 3\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{3} - \\frac{18 r^{2}}{11} + \\frac{9 r}{11} - \\frac{2}{11}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0, \\ 0.426401432711221, \\ 0.426401432711221\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " BDF4\n", "\tq = 4\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 4\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{4} - \\frac{48 r^{3}}{25} + \\frac{36 r^{2}}{25} - \\frac{16 r}{25} + \\frac{3}{25}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0, \\ 0.56086151609339, \\ 0.56086151609339, \\ 0.38147840911841\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " BDF5\n", "\tq = 5\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 5\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{5} - \\frac{300 r^{4}}{137} + \\frac{300 r^{3}}{137} - \\frac{200 r^{2}}{137} + \\frac{75 r}{137} - \\frac{12}{137}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0, \\ 0.708710816266406, \\ 0.417600758175733, \\ 0.708710816266406, \\ 0.417600758175733\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " BDF6\n", "\tq = 6\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 6\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{6} - \\frac{120 r^{5}}{49} + \\frac{150 r^{4}}{49} - \\frac{400 r^{3}}{147} + \\frac{75 r^{2}}{49} - \\frac{24 r}{49} + \\frac{10}{147}$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0, \\ 0.40612326685391, \\ 0.474034857706592, \\ 0.474034857706592, \\ 0.863380267869827, \\ 0.863380267869827\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "\n", " MS2\n", "\tq = 2\n", "\tImplicite\n", "\tConsistance: True\n", "\tOrdre 4\n" ] }, { "data": { "text/latex": [ "$\\displaystyle \\varrho(r)=r^{2} - 1$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/latex": [ "$\\displaystyle \\{|r_j|\\} = \\left[ 1.0, \\ 1.0\\right]$" ], "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "%reset -f\n", "from matplotlib.pylab import *\n", "\n", "from fractions import Fraction\n", "\n", "from IPython.display import display, Math\n", "import sympy as sym\n", "sym.init_printing()\n", "r=sym.Symbol('r')\n", "\n", "\n", "sc = { \"EE_AB1\" : { \"aa\":[1], \"bb\":[ 1], \"bm1\":0 },\n", " \"EI_AM0_BDF1\" : { \"aa\":[1], \"bb\":[ 0], \"bm1\":1 },\n", " \"CN_AM1\" : { \"aa\":[1], \"bb\":[Fraction(1,2)], \"bm1\":1/2 }, \n", " \"AB2\": { \"aa\":[1,0], \"bb\":[Fraction(3,2),Fraction(-1,2)], \"bm1\":0 }, \n", " \"AB3\": { \"aa\":[1,0,0], \"bb\":[Fraction(23,12),Fraction(-16,12), Fraction(5,12)], \"bm1\":0 }, \n", " \"AB4\": { \"aa\":[1,0,0,0], \"bb\":[Fraction(55,24),Fraction(-59,24), Fraction(37,24), Fraction(-9,24)], \"bm1\":0 }, \n", " \"AB5\": { \"aa\":[1,0,0,0,0], \"bb\":[Fraction(1901,720), Fraction(-2774,720), Fraction(2616,720), Fraction(-1274,720), Fraction(251,720)], \"bm1\":0 }, \n", " \"AM2\": { \"aa\":[1,0], \"bb\":[Fraction(8,12),Fraction(-1,12)], \"bm1\":Fraction(5,12) }, \n", " \"AM3\": { \"aa\":[1,0,0], \"bb\":[Fraction(19,24),Fraction(-5,24),Fraction(1,24)], \"bm1\":Fraction(9,24) }, \n", " \"AM4\": { \"aa\":[1,0,0,0], \"bb\":[Fraction(646,720),Fraction(-264,720),Fraction(106,720),Fraction(-19,720)], \"bm1\":Fraction(251,720) }, \n", " \"BDF2\": { \"aa\":[Fraction(4,3),Fraction(-1,3)], \"bb\":[0,0], \"bm1\":Fraction(2,3) }, \n", " \"BDF3\": { \"aa\":[Fraction(18,11),Fraction(-9,11),Fraction(2,11)], \"bb\":[0,0,0], \"bm1\":Fraction(6,11) }, \n", " \"BDF4\": { \"aa\":[Fraction(48,25),Fraction(-36,25),Fraction(16,25),Fraction(-3,25)], \"bb\":[0,0,0,0], \"bm1\":Fraction(12,25) }, \n", " \"BDF5\": { \"aa\":[Fraction(300,137),Fraction(-300,137),Fraction(200,137),Fraction(-75,137),Fraction(12,137)], \"bb\":[0,0,0,0,0], \"bm1\":Fraction(60,137) }, \n", " \"BDF6\": { \"aa\":[Fraction(120,49),Fraction(-150,49),Fraction(400,147),Fraction(-75,49),Fraction(24,49),Fraction(-10,147)], \"bb\":[0,0,0,0,0,0], \"bm1\":Fraction(20,49) }, \n", " \"MS2\": { \"aa\":[0,1], \"bb\":[Fraction(4,3),Fraction(1,3)], \"bm1\":Fraction(1,3) }\n", " } \n", "\n", "\n", "for schema in sc.keys():\n", " print(\"\\n\",schema)\n", " q=len(sc[schema][\"aa\"])\n", " p=q-1\n", " print(f\"\\tq = {q}\")\n", " aa=sc[schema][\"aa\"]\n", " bb=sc[schema][\"bb\"]\n", " bm1=sc[schema][\"bm1\"]\n", " \n", " if bm1==0:\n", " print(\"\\tExplicite\")\n", " else:\n", " print(\"\\tImplicite\")\n", " print(\"\\tConsistance: \",end=\"\")\n", " \n", " ordre=[]\n", " ordre.append( sum(aa)==1 and sum([-j*aa[j] for j in range(len(aa))])+bm1+sum(bb)==1 )\n", " print(ordre[-1])\n", " i=1\n", " while ordre[-1]:\n", " i+=1\n", " ordre.append( sum([(-j)**i*aa[j]+i*(-j)**(i-1)*bb[j] for j in range(len(aa))])+i*bm1==1)\n", " print(f\"\\tOrdre {len(ordre)-1}\")\n", " \n", " rho=array([1])\n", " rho=append(rho,-array(aa))\n", " display(Math(r'\\varrho(r)='+sym.latex(sym.expand(poly1d(rho)(r)))))\n", "# print(f\"\\tZéro-stabilité: |r_j|= {abs(roots(rho))}\")\n", "# print(\"\\tRacines: \",end=\"\")\n", "# display(sym.solve(sym.expand(poly1d(rho)(r))))\n", " display( Math(r' \\{|r_j|\\} = '+sym.latex( [abs(rac).simplify().evalf() for rac in sym.solve(sym.expand(poly1d(rho)(r)))] )))\n", " \n", " \n", " \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A-stabilité\n", "\n", "\n", "Dans la section précédente, on a considéré la résolution du problème de Cauchy sur des intervalles bornés. \n", "Il existe cependant de nombreuses situations dans lesquelles le problème de Cauchy doit être intégré sur des intervalles en temps très grands ou même infini. Dans ce cas, même pour $h$ fixé, $N$ tend vers l’infini, et\n", "un résultat comme la zéro-stabilité n’a plus de sens puisque le membre de droite contient une quantité non bornée ($T-t_0$). \n", "On s’intéresse donc à des méthodes capables d’approcher la solution pour des intervalles en temps arbitrairement grands, même pour des pas de temps $h$ \"assez grands\".\n", "\n", ">Soit $\\lambda\\in\\mathbb{C}$ un nombre complexe tel que $\\Re(\\lambda)=-\\beta<0$ et considérons le problème de Cauchy\n", "$$\\begin{cases}\n", "y'(t)=\\lambda y(t), &\\text{pour }t>0,\\\\\n", "y(0)=1\n", "\\end{cases}$$\n", "Sa solution est $y(t)=e^{\\lambda t}$ et comme $\\Re(\\lambda)<0$ alors $$\\lim_{t\\to+\\infty}|y(t)|=0.$$\n", ">\n", ">Soit $h>0$ un pas de temps donné, $t_n=nh$ pour $n\\in\\mathbb{N}$ et notons $u_n\\approx y(t_n)$ une approximation de la solution $y$ au temps $t_n$.\n", ">\n", ">Si, sous d'éventuelles conditions sur $h$, on a\n", "$$\n", "\\lim_{n\\to+\\infty} |u_n| =0,\n", "$$\n", "alors on dit que le schéma est A-stable (absolument stable)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Région de stabilité absolue\n", "On appelle **région de stabilité absolue $A$** d’une méthode numérique l’ensemble des nombres complexes $z = h\\lambda$ pour lesquels la méthode est absolument stable:\n", "$$\n", "A=\\Big\\{z = h\\lambda \\in \\mathbb{C} \\ \\Big| \\ |u_n|\\xrightarrow[n\\to+\\infty]{}0 \\Big\\}\n", "$$\n", "Une méthode numérique est inconditionellement A-stable si $\\mathbb{C}^-\\subset A$ où $\\mathbb{C}^-=\\{z\\in\\mathbb{C}|\\Re(z)<0\\}$.\n", "\n", "Une méthode à $q=p+1$ pas appliquée à ce problème modèle conduit à léquation récurrente à\n", "$$\n", "u_{n+1}=\\sum_{j=0}^p a_j u_{n-j} + h\\lambda\\sum_{j=0}^p b_ju_{n-j} + h\\lambda b_{-1}u_{n+1}\n", "$$\n", "dont le polynôme caracthéristique associé\n", "$$\n", "p(r) = \\varrho(r) - (h\\lambda) \\sigma(r)\n", "$$\n", "est appelé polynôme de A-stabilité associé à la méthode numérique. \n", "
\n", "\n", "Condition des racines stricte: \n", "une méthode multipas linéaire vérifie la condition des racines stricte (éventuellement sous conditions sur $h$) si les racines du polynôme $p$ sont dans le disque unité ouvert de $\\mathbb{C}$:\n", " \n", "$$\n", "\\text{il existe $h_0>0$ tel que }\\quad |r_j(h\\lambda)|<1 \\quad\\text{pour tout }j=0,\\dots,p;\\ \\forall h\\le h_0\n", "$$\n", "
\n", "\n", "
\n", "Proposition. \n", "Une méthode multipas linéaire est absolument stable si et seulement si son polynôme de stabilité vérifie la condition des racines stricte.\n", "
" ] }, { "attachments": { "A_stab_Adams.png": { "image/png": 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} }, "cell_type": "markdown", "metadata": {}, "source": [ "Régions de A-stabilité de diverses méthodes d'Adams-Bashforth (à gauche) et d'Adams-Moulton (à droite). \n", "Source: A. Quarteroni, F. Saleri, P. Gervasio *Calcul Scientifique: Cours, exercices corrigés et illustrations en Matlab et Octave.*\n", "\n", "On remarque que les régions de stabilité absolue des méthodes d'Adams-Bashforth et d'Adams-Moulton sont bornées et diminuent quand l'ordre\n", "augmente.\n", "\n", "![A_stab_Adams.png](attachment:A_stab_Adams.png)" ] }, { "attachments": { "A_stab_BDF.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Régions de A-stabilité de diverses méthodes BDF. \n", "Source: A. Quarteroni, F. Saleri, P. Gervasio *Calcul Scientifique: Cours, exercices corrigés et illustrations en Matlab et Octave.*\n", "\n", "On remarque que les régions de stabilité absolue des méthodes BDF, pour $q\\le6$, sont non bornées. En particulier, elles contiennent toujours les réels négatifs.\n", "\n", "![A_stab_BDF.png](attachment:A_stab_BDF.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Tracer les régions de A-stabilité.** \n", "Posons $z=h\\lambda$.\n", "Il est en général difficile de déterminer la région de stabilité absolue car on doit décider pour quels $z\\in\\mathbb{C}$ les racines du polynôme de stabilité vérifient la condition de racines stricte (i.e. $|r| < 1$). \n", "Il est plus aisé de déterminer la frontière de cette région car au moins une des racines de $p$ à la frontière est de module $1$. \n", "On a donc $|r| = 1$ sur $\\partial A$. \n", "La frontière de $A$ est alors un sous ensemble des points $z\\in\\mathbb{C}$ pour lesquels $r=e^{i\\vartheta}$, $\\vartheta\\in\\mathbb{R}$. \n", "On remplace alors $r =e^{i\\vartheta}$ dans $p$ et comme $e^{i\\vartheta}$ est racine, $p(e^{i\\vartheta}) = 0$ et on résoud l’équation. On obtient $z = z(\\vartheta)$ ce qui donne une courbe dans $\\mathbb{C}$ en fonction de l’angle $\\vartheta$, ce qui décrit donc une courbe polaire.\n", "Par conséquent, pour obtenir une représentation approchée de $\\partial A$, il suffit d’évaluer le second membre pour diverses valeurs de $r$ sur le cercle unité, diverses valeurs de $\\vartheta\\in\\mathbb{R}$ et $r=e^{i\\vartheta}$. " ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "%reset -f\n", "%matplotlib inline\n", "\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "\n", "import sympy as sp\n", "sp.init_printing()\n", "def polyCar(schema):\n", " sp.var('r z')\n", " p,aa,bb,bm1=schema[\"p\"],schema[\"aa\"],schema[\"bb\"],schema[\"bm1\"] \n", " rho=r**(p+1)-sum(aa[j]*r**(p-j)for j in range(p+1)) \n", " sigma=bm1*r**(p+1)+sum(bb[j]*r**(p-j)for j in range(p+1))\n", " display(f'rho(r)={rho}')\n", " display(f'sigma(r)={sigma}')\n", " return \n", "def polyCarIMPL(schema):\n", " sp.var('r z')\n", " p,aa,bb,bm1=schema[\"p\"],schema[\"aa\"],schema[\"bb\"],schema[\"bm1\"] \n", " rho=r**(p+1)-sum(aa[j]*r**(p-j)for j in range(p)) \n", " sigma=bm1*r**(p+1)+sum(bb[j]*r**(p-j)for j in range(p))\n", " display(f'rho(r)={rho}')\n", " display(f'sigma(r)={sigma}')\n", " return \n", " \n", "\n", "# Returns > 1 if argument is not in region of absolute stability\n", "def stabilityFunction(z,schema):\n", " pol=np.array(schema[\"aa\"])+z*np.array(schema[\"bb\"])\n", " pol=np.append([1-z*schema[\"bm1\"]],-pol)\n", " return max(abs(np.roots(pol)))\n", "\n", "\n", "def Astabilite(schema):\n", " p,aa,bb,bm1=schema[\"p\"],schema[\"aa\"],schema[\"bb\"],schema[\"bm1\"]\n", " \n", " # cc liste de points sur le circle unitaire\n", " rr = np.linspace(0,2*np.pi,201)\n", " cc = np.cos(rr)+1j*np.sin(rr) \n", " ## ff fonction vectorisée qui donne zz\n", " ff = lambda cc,p,aa,bb,bm1 : (cc**(p+1)-np.polyval(aa,cc))/(bm1*cc**(p+1)+np.polyval(bb,cc)) \n", " zz = ff(cc,p,aa,bb,bm1)\n", " \n", " plt.figure(figsize=(18,7))\n", " plt.subplot(1,2,1)\n", " plt.plot(zz.real,zz.imag,'r')\n", " plt.grid(True)\n", "# plt.axis('equal')\n", " plt.xlabel(r'$\\Re(h\\beta)$')\n", " plt.ylabel(r'$\\Im(h\\beta)$');\n", " plt.title(schema[\"Nom\"])\n", " Lx,Ly = plt.xlim(),plt.ylim()\n", " \n", " plt.subplot(1,2,2)\n", " x = np.linspace(Lx[0],Lx[1], 300)\n", " y = np.linspace(Ly[0],Ly[1], 300)\n", " [X,Y] = np.meshgrid(x,y)\n", " Z = np.zeros(X.shape)\n", " for m in range(X.shape[0]):\n", " for n in range(X.shape[1]):\n", " Z[m,n] = stabilityFunction(X[m,n] + 1j * Y[m,n], schema)\n", " plt.contour(X, Y, Z, [1], colors='k')\n", " plt.contourf(X, Y, Z, [0,1], colors=[[1, 0.5, 0.8]])\n", " return None" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r - 1'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=1'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "EE = { \"Nom\":\"EE=AB1\", \"p\":0, \"aa\":[1], \"bb\":[1], \"bm1\":0 }\n", "polyCar(EE)\n", "Astabilite(EE) " ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r**2 - r'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=1.5*r - 0.5'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AB2 = { \"Nom\":\"AB2\", \"p\":1, \"aa\":[1,0], \"bb\":[3/2,-1/2], \"bm1\":0 }\n", "polyCar(AB2)\n", "Astabilite(AB2)" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r**3 - r**2'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=1.91666666666667*r**2 - 1.33333333333333*r + 0.416666666666667'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AB3 = { \"Nom\":\"AB3\", \"p\":2, \"aa\":[1,0,0], \"bb\":[23/12,-16/12, 5/12], \"bm1\":0 }\n", "polyCar(AB3)\n", "Astabilite(AB3)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r**4 - r**3'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=2.29166666666667*r**3 - 2.45833333333333*r**2 + 1.54166666666667*r - 0.375'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AB4 = { \"Nom\":\"AB4\", \"p\":3, \"aa\":[1,0,0,0], \"bb\":[55/24,-59/24, 37/24, -9/24], \"bm1\":0 }\n", "polyCar(AB4)\n", "Astabilite(AB4)" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r**5 - r**4'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=2.64027777777778*r**4 - 3.85277777777778*r**3 + 3.63333333333333*r**2 - 1.76944444444444*r + 0.348611111111111'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AB5 = { \"Nom\":\"AB5\", \"p\":4, \"aa\":[1,0,0,0,0], \"bb\":[1901/720, -2774/720, 2616/720, -1274/720, 251/720], \"bm1\":0 }\n", "polyCar(AB5)\n", "Astabilite(AB5)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r**2 - r'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=0.5*r**2 + 0.5*r'" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "AM1 = { \"Nom\":\"AM1=CN\", \"p\":1, \"aa\":[1], \"bb\":[1/2], \"bm1\":1/2 }\n", "polyCarIMPL(AM1)\n", "#Astabilite(AM1)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r**2 - r'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=0.416666666666667*r**2 + 0.666666666666667*r - 0.0833333333333333'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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UFCcaNeJ4XBxnYmKc9QDyCH2fXOnfnJOAQ4co/NNPFPrpJwr+/DNeaWmkBwVxqk4dTjRowIm4ONI8dGtWfa9cKbvPSYsWLdbZth2bbXeYx/zd65GoqKg6e/fudW1IEeDw4cN88cUXzJ8wlW93rSYl/TzBvoG0KlOXDuUa0b5cI6ILFjcdUzzYjhP7+WrHChb+XzxLdq/lfEYq+f2D6dCtM926daNjx47kz5/fdExxU5ZlXfN6xK2KiIssywoFPgXusm1787VuFxsba69duzZbH3vp0qU0vzinWwCdk/9JTXVGO8yfT8qcOQQcPeosVNioEXTtCjfcABUqmE5pjL5PrpRt5yQx0RkpsWABfPkl/P67U3K1bOmsMdK9u0ctbKrvlStl9zm53i9+yTqT1yMi17Jr1y7mzZvHp69PZeX+X7CxiQ4tTpcKTehcoQnNomtrcUnJEYmpyXy7axXzt/3Igu3LOZp4Ej9vX1qXqUePRwbTrVs3ChcubDqmuJHrXY+4zdSMy9m2fdqyrKVAe+Cav/hFctypU/DVV856D199BWfPQlAQZ2vXJuDFF50h8+HhplNKbhccDF26OIdtw4YNMGeOcwwbBsOHO4td9u7tcaWEiDvT9Yi4ix07djBnzhzmvP4RPx/eBkCtohV5tsXtdK3YjGoR5bA0/VNyWLBfIF0rNadrpeZkZGawcv8vfPrbEuZtXcLCW2/ljmG307pMfXo/fivdu3cnNDTUdGRxY25TRFiWFQ6kXfilHwi0Bl40HEvyosRE5wnetGnwww+Qnu4sNNmnjzPyoVUrtqxapVd0xQzLglq1nOO552DjxquXEv36Qc+ezloUIpJluh4Rd3HgwAFmzpzJzFc+YN2hrQDUj6zKhLb30iOmBaULRhpOKHmZt5c3jUvVpHGpmkxoey/rD/3G7C2LmbPlO4YMGcIdt91Oh3KN6DdmBJ07dyYwMNB0ZHEzblNEAMWAjy7My/QCZtu2vcBwJskrbNvZWnHSJJg50xn5UK4cPPigUz7Uq+dMwxBxJ5YFNWs6x9ixsGkTzJ4Ns2bB4MEwYgTceCPccotTTuh7WCQrdD0ixiQkJPDJJ58wbex/+WHPemxsYotXZkLbe+lVuTVRoUVNRxS5gmVZ1CkeQ53iMbzQ+i7WHvyVGb98zYzNX/N5797k9w+mV/++DBw4kCZNmmj0jgBuVETYtr0JqGU6h+Qxx47B1KnwwQewZQsEBTnD24cMcXa60A9K8RSWBTVqOMfYsRAfDx995JQSU6dCyZIwcKBz5OG1TET+iq5HxNUyMjJYvHgxkydP5vO5n5GSfp4KhaN4pvkwbqrWjvKFo0xHFMkyy7KoG1mFupFVGN/2HpbuWcfUjQuZOWU6kyZNokzBSAbddzuDBg2iZMmSpuOKQXp5TPKejAxnvYeePSEyEh54wBm+/u67cOgQfPihs02iSgjxVJYFcXHO9/ThwzBjBlSpAs8/DxUrOiXbtGmQkmI6qYhInrVz505GjRpFqYLF6dChA4vnL+LW2l1Zdetkfhs5l6ea36YSQjyat5c3rcrUY3L3Zzjy0DdM6f4spQoU46mnnqJUVCk6lo/j008/JS0tzXRUMcBtRkSI5Lhdu5yRD5MnO7sOhIXByJEwdKjzJE0kNwoMhL59nePgQaeAeP99GDAA7r3XGf1z++1QtqzppCIiuV5qaiqffvop7z72Mt/vXoOX5UWHco34T4cH6FyhiXa7kFwr2C+QATU6MaBGJ3af+p0Pfp7Phz9/QY8ePSgWEsbQe+9g2LBhGiWRh2hEhORuycnw8cfONodlyzqvCFevDp984pQRr7yiEkLyjuLF4eGH4bffYPFiaNbM+T9Qrhy0b+/sDpOebjqliEius3v3bh599FFKFCxK37592XXqd8a0uIN99y1gQb/XuLFyK5UQkmeULhjJmJbD2XPvfObf9Aq1ilXkubHPEV0qmu4xLfjuu++wbdt0TMlhGhEhudO6dc7Ck9OnQ0IClCnjzJu/5RYoUcJ0OhGzvLygdWvn+P13eO895+jWDaKi4J574NZbIX9+00lFRDyWbdssXryYN+8ay4Lty7Esiy4VmnBH7I20LdsALy0gLHmcj7cPXSo2pUvFpuw5dZB31s3jvXWf8lnr1lQJL8M9zz1K//79teNGLqWfgJJ72DYsWgRNm0JsrLPWQ+fO8P338H//B6NGqYQQ+bPISHjmGdizB+bOhehoZ92UkiWdXWP27TMcUETEsyQmJvL2229TuUgZ2rVrx6rftzCq6RD23Dufz256mfblG6mEEPmT6ILFeb71SA7cv5APuz6Nn7evM1WjcDGefPJJjhw5YjqiZDP9FBTPl5npPIGKjYUOHWD3bnj1VWfhyWnTtG2hSFb4+kKPHvDDD85Wth07wmuvOaOJbr4Z1q41nVBExK0dPHiQxx57jJJhxRk+fDghfkFM6f4s++5bwJiWwylZQFtvivyVAF9/BtXqwrrbp/HDoHdpHFWT58Y+R1RkSW677Ta2bdtmOqJkEz07E8+VluZsT1ilirMDxtmzznSMnTudRfhCQ00nFPFMdes6O23s3OlM01iwwPlYmzbw44+m04mIuJVff/2VIUOGEF2yFC+9+BItStdh+ZD3WX3bRwyo0UlrP4j8A5Zl0TS6Np/d9DLb7prL4JpdmPrhFGIqxdCzcivWrVtnOqL8SyoixPMkJ8NbbzkL7A0aBP7+MGsWbN3q7ADgp1/4ItmiVCl4+WU4cABeegl++cVZ4LJpU2exSy0kJSJ52E8//UTXSs2oUqUKM6dO5/bYHvzfXfOY22c8cVE1sbQNuEi2KF84ire7PM6++xbwWJNBfLtrNbGxsXQoH0d8fLzpePIPqYgQz3HmDLz4ojOHfeRIZ72HL7+En3+G3r3B29t0QpHcKX9+eOghZ9rTf/7jbIXbti00bOj8H1QhISJ5hG3bfP/997QsXZeGDRuyfN9Gnm52G/vu+5I3Oj5MmUJai0okpxQJKcRzrUaw974FjGs1grUHfyUuLo42ZeuzYsUK0/Hkb1IRIe7v+HF48klnNf9HH4VatZx57MuXO/PY9YqDiGsEBsLddztTNt5+Gw4fdhaEbdjQWRRWRCSXurgDRpNStWjVqhVbj+9mQtt72XvvFzzT4nbCgjUdVMRVCgSE8FiTwey59wsmtL2XTUd20LhxY9qVa8jq1atNx5MsUhEh7uvAAbjvPmd4+Nix0KoVrFlzaWcMFRAiZvj7w+23O7vRvPceHDzo/P9s3dpZ6FJEJJewbZvvvvuOxqVq0rZtW/YmHObNjg+z+575PNCoPyH+QaYjiuRZwX6BPNCoP7vu+ZyX2tzNuoNbqV+/Pt1jWrBlyxbT8eQvqIgQ97NjB9x2m7Na/xtvOAtRbtlyaWcMEXEPvr5w662wfbuzU83GjVC/PnTv7vyfFRHxYCtWrKBF6Vhat27NvoQjTOz0KDvu/pQR9XoT4OtvOp6IXBDsF8hDcQPZfe98Rre4g+93r6F6teoMHjyYfdqG3G2piBD3cfSoU0BUrAhTpzrv79jh7IxRubLpdCJyLQEBzk41u3bB6NHONI3q1Z1RE9r3W0Q8zKZNm+hcoQmNGzfmt+N7+U/7B/m/u+YxvG5P7YAh4sby+QfzZLNb2XXP59zX4GZmTJ1OhTLlefTRR0lISDAdT/5ERYSYl5YGr70GFSrA5Mlw112wZ4+zM0Z0tOFwIpJl+fI567ns2uX8P/7gAyhfHl54AVJSTKcTEbmuvXv3MnDgQGrWqMmK/Rt5vtVIdt7zGXc36KsRECIepHBQKBPa3cu2u+bSu0prXnrxJcoVj+a///0v6enppuPJBSoixKxvvoEaNZy1IBo0gE2bnFKiaFHTyUTknypc2Pl/vHkztGgBjz0GlSo52+xqhw0RcTOnT5/mkUceoWLZCsyZMZuH4gaw657PebTJIIL9Ak3HE5F/qFRoMab0GM2aYVOoEl6GO++8k5rFK/Ldd9+ZjiaoiBBTdu6Ebt2gXTtITYX58+GrryAmxnQyEckuFSvC55/Dt99CgQLQty+0aEHQ7t2mk4mIkJ6ezsSJEykfWZrxL42nT9U2bL9rLi+2uZuCgflNxxORbFKneAxLBr3D3N4vkZR2ntatW3Nj5Zbs3bvXdLQ8TUWEuNa5c/D4486aD99+6wzZ3rIFunTRLhgiuVWrVrB+vbPl56ZNxN52Gzz0EJw9azqZiORR3377LTWKV2TEiBFULVKWdbdP5aPuz1KygEZkiuRGlmXRo3JLfh0xmzEt7mDRjpXElKvIuHHjOH/+vOl4eZKKCHEN24aPP3ZeIX3+eejTx1lp/5FHnK0ARSR38/Z2Fq/cvp0j7drBhAnOCKjZszVdQ0RcZvfu3fSIaUmbNm1IST/PvD7j+f6Wt6lVrJLpaCLiAgG+/jzR7Fa2jviEjuXjGDVqFDUiK7J06VLT0fIcFRGS89atg8aNoX9/KF4c4uNhyhTnfRHJW8LC2PbQQ7ByJRQp4pSSXbrA/v2mk4lILpaSksLo0aOpXCGGr3eu5LmWd7Llztl0j2mBpRGZInlOVGhRPunzEgv7/YfUjHRatGjB4MGDOXHihOloeYaKCMk5F7fjrFvX2YZz0iRYtQoaNjSdTERMa9AA1qyBV16BJUugShWYOBEyM00nE5FcZvHixVSLrMDTTz/NDRWbsm3kXB5vOkQ7YYgIHcrHsfnOWTzWeDDTpkwlJqo8s2bNwtZozRynIkKyX1oavPrqpe0477/fmYYxZAh46VtORC7w9nZ2zNm8GerXhxEjoFkz2LbNdDIRyQUOHz7MTdXa0bZtWywsFg94i1m9nqdEgQjT0UTEjQT5BTCu9QjWDptKqdBi9O3bl+4xLTh06JDpaLmanhVK9rq4Hef99zsjHzZvduaCFyhgOpmIuKvSpZ2fHR9+6CxeW7Oms/2nRkeIyD9g2zbvv/8+MaUrMG/rEp5pPoxNw2fQumx909FExI3VKFqBlUM/YHybe/h6509UKVOJ6dOna3REDlERIdnj7FlnxEO7ds6IiC++gIULncUpRUT+imXBoEHw66/QurUzUqJVK9DWWiLyN+zYsYOWZepy2223USOiPJuGz+Dp5sM0DUNEssTH24cH4waw4Y6PqRhWin79+tGrSmuOHz9uOlquoyJC/r1Vq6BWLfjoI3jiCWcUROfO2o5TRP6+okVh/nx4/31YuxaqVXNGSujVCBG5joyMDF599VWqx1Rl/aHfeLfLKJYMeoeKYdGmo4mIB6oYFs3yIe/zQuuRzN/2I9VKV2LRokWmY+UqKiLkn8vIgLFjIS4O0tPhhx9gzBhtxyki/45lwdChsGkT1K7tjLbq2xdOnzadTETc0I4dO2hWug73338/LUvX5dcRc7itTnfthiEi/4q3lzePNB7E2mFTCQsKpUOHDtx9992kpKSYjpYrqIiQf2bPHmjeHJ580tl+b+NGZ4tOEZHsUro0fPcdPP88zJ3rrB0RH286lYi4Cdu2mThxIjUqV2PLsV181O0Zvrj5VSLzFzEdTURykepFy7PmtincU/8m3njjDepHV2fr1q2mY3k8FRHy902f7ixIuWkTTJsGH3+sxShFJGd4e8Ojj8Ly5c5IiaZNYdw4LWQpkscdPHiQ9uUbMWLECJpE1WLznbMYWLOzRkGISI4I8PXntQ4P8OXNr3Hw7DFia9Rm8uTJpmN5NBURknUJCdC/P/Tr58zb3rDBeV9EJKc1aOD8zOnZE0aNctahOXHCdCoRMWDevHlUK1eZ5fs28N9Oj/JV/9c1CkJEXKJjhcZsvGMG9SKrMHjwYAYPHkxSUpLpWB5JRYRkzfLlziiImTNh9GhYutQZNi0i4ioFCsCMGTBxojNlo3ZtWLPGdCoRcZGkpCSGDRvGjTfeSJmCkfx8+8fcUbenRkGIiEsVzx/OtwMn8mTTW/lo8kc0LFOTHTt2mI7lcVREyPWlpRH9wQfQrJkzRHr5cmddCB8f08lEJC+yLBg+3PlZBM7aNO+8YzaTiOS4TZs2EVuqKu+/9z6PxN3CiiGTqBBWynQsEcmjvL28Gd3yDhb2+w8HzhwltmotFixYYDqWR1ERIde2cyc0aUL01KkwcKAzLLpBA9OpRESgbszBC20AACAASURBVF1Yvx5atoQ77nCO1FTTqUQkm9m2zbvvvku92nU5lXKGxQPf4oU2d+Hn42s6mogI7cs3Yt2wqZQpGEmXLl0YM2YMmVrHKktURMiVbBsmT3ZWqN+2jS1PPQUffgj58plOJiJySeHCsGABPPKIMyqidWs4etR0KhHJJufOnaN/jY7cfvvtNIuuzcY7ZtCqTD3TsURE/iC6YHFWDJ3EgOodeeqpp+hdtQ2JiYmmY7k9FRHyR6dOOdtxDh4MderApk0ca9HCdCoRkavz9oYXXnB281mzBmJjnR19RMSj/frrr9QtXY2Zm79hbMvhfNXvdYqEFDIdS0TkqgJ9A/io+7O83PZePv1tKY3L1Wb//v2mY7k1FRFyycqVUL06fPqpc2H/3XdQsqTpVCIif+2mm5x1IzIynHUjFi0ynUhE/qE5c+ZQr2YsJ5PPsHjAW4xqOhQvL12yioh7syyL+xv154ubXmHnyd+pX7k269atMx3LbemnujjmzIEWLcDfH376yRnq7O1tOpWISNbVqQOrVkHZss72nm+/bTqRiPwNGRkZPPzww/Tu3ZvqEeVZf/s0WpapazqWiMjf0rFCY+KHTsLP25emDRvzxRdfmI7kllRE5HW2DRMmQO/ezpDmn35yLuZFRDxRiRLw44/Qvr2zu8aoUc7PORFxaydPnqRjxcaMHz+e4bE9WTroHSLzFzEdS0TkH6kaUY6fbv2QyuFl6Na1G2/rxZErqIjIy9LTYeRIeOgh6NULvv0WwsJMpxIR+Xfy5YPPPoPbboNx4+DOO50pGyLilrZu3Ur98jVZsnst73V5gomdH9WuGCLi8YrmC2PpoHfoWD6O4cOH8/TTT2PrxZH/URGRVyUmQvfuMHGiU0TMnAkBAaZTiYhkDx8fZyeNRx5xpmj066ftPUXc0KJFi2hQqy5nzieyZNDb3Fqnm+lIIiLZJtgvkE/7jGdora6MHj2aO++8kwy9OAKAj+kAYsDhw9ClC6xf7xQRw4ebTiQikv0sy1l4t1Ahp5A4cwY++QSCgkwnExHgrbfe4u677qZakXLMv+kVokKLmo4kIpLtfLx9eO+GJwgPLsgLb7/NqWU7mfrzl/j65u2RXyoi8pqtW6FDBzh2DD7/3FnQTUQkN3v4YaeMuP12aNsWFiyA0FDTqUTyrIyMDO6//35ef/11ulRowvQbnyPEXwWhiORelmXxfOuRFArMz8OLXyexaivmbPyGgDw8Il1FRF6ydKkzHSMgwFnMTYtSikheceutTvlw883QvDksXgzh4aZTieQ5SUlJ9KvTic9+W8q9DW5iQtt78fbSLl0ikjc8FDeQfH5BDP/yBbpWbcGnm74jKI+O1NQaEXnFtGnOK4HFi2tnDBHJm3r2dEZDbNsGbdrAyZOmE4nkKcePH6dVxQZ8/tsP/Kf9g7za/gGVECKS59xRtycfdH2KxTtX0aVqc5KSkkxHMkJFRG5n2zB2LAwYAHFxsGIFlCplOpWIiBlt2zrT0rZuhXbtICHBdCKRPGHv3r00rhTLhsPb+aT3i9zdoK/pSCIixgyudQMfdX+GJbvXckPVFiQnJ5uO5HIqInKztDRn+7onn4T+/WHRIs2LFhFp2xbmzoWNG6F9ezh71nQikVxt8+bNNKpWlyOJJ1k84C16VG5pOpKIiHEDanTio+7P8P3uNfSo3prz58+bjuRSKiJyqzNnnJ0xJk2CJ56AKVPA3990KhER99C5M8yaBWvWQKdOzpbGIpLtVq1aRdO6cdi2zY+D36NxqZqmI4mIuI0BNTrx3g2jWLQjnr4125Oenm46ksu4TRFhWVZJy7KWWJa11bKsLZZl3WM6k8c6cACaNIFvv3WKiDFjnG3sRETkku7d4eOPnSlrN9wAeXBYpFxJ1yPZ5/vvv6dVkxYUCszPiqGTqBZRznQkERG3M7R2N17v8CCf/baUoUOHkpmZaTqSS7jTrhnpwAO2ba+3LCsfsM6yrMW2bf9qOphH2bQJOnZ0RkQsXOgMQRYRkavr0wdSU2HgQOeYNQu83KajFzN0PZINFi5cSI8bulO+cEkWD3iLovnCTEcSEXFbd9Xvy+mUczw15W3CwsKYMGECVi5/IdltrrZs2z5k2/b6C++fBbYCkWZTeZhff4UWLZz3ly1TCSEikhUDBsDLL8Mnn8CDD5pOI4bpeuTf++yzz+jWpStVipRh6aB3VEKIiGTBE02Hcle9PrzyyitMmDDBdJwcZ9m2bTrDFSzLigZ+BKratn3mT383DBgGEBERUWfmzJnZ+tjnzp0jJCQkW+/TFfwPH6b2XXdBZiY/v/46KZHZd83kqeckJ+mcXEnn5Eo6J1fnlufFtin35puUmDeP/xsxgt979nTpw2f3OWnRosU627Zjs+0O86isXo9ERUXV2bt3r8vzuaO5c+fSt3cfYotX5qt+rxMamM90JBERj5GZmcnNc0cxa8tiZsyYQd++nr3DkGVZ17wecbsiwrKsEOAH4Dnbtudd77axsbH22rVrs/Xxly5dSvPmzbP1PnPckSPOmhDHjsEPP0D16tl69x55TnKYzsmVdE6upHNydW57XjIyoFcv+OwzZ3REjx4ue+jsPifX+8UvWWP6esQTzZ07lz69+lC/RBW+6vc6+QPcrHAUEfEA59NTaTt1JD8d+IVvl3xHkyZNTEf6x653PeI2UzMALMvyBeYCH//VL325ICEBOnRwFqhcsCDbSwgRkTzD29tZvLJBA+jXD+LjTScSQ3Q98vd99tln9O2tEkJE5N/y9/Hj0z7jiQ4tRvd2Xdi5c6fpSDnCbYoIy1mNYxKw1bbtV0zn8QjJyc5K77/8AnPnQlyc6UQiIp4tMBDmz4eSJZ1dNQ4cMJ1IXEzXI3/fwoUL6X1jr/9Nx1AJISLy7xQKKsCCm1/DBro0aMOZM2f+8nM8jdsUEUAcMABoaVnWhgtHR9Oh3FZamrPa+7JlMGWKMypCRET+vbAw+PxzSEqCnj3h/HnTicS1dD3yNyxZsoQeN3SnWkQ5lRAiItmofOEo5vZ+ke0n9tGvbudct62n2xQRtm0vt23bsm27um3bNS8cC03nckuZmTB0KHzxBbz5Jtx0k+lEIiK5S0yMU/KuWgV33WU6jbiQrkeybtWqVXRp14lyhUrwzYA3tTCliEg2a146lv90eIAF25fxzDPPmI6TrdymiJAssm24/36YOhVGj4Y77zSdSEQkd+reHR5/HN57D95913QaEbeyZcsWOjRvS9GQwiweOJHCQaGmI4mI5Ep31u3FoJpdGDNmDAsWLDAdJ9uoiPA0zz0H//kP3HMPPPGE6TQiIrnb6NHQvj2MHAkrV5pOI+IW9u3bR7uGLQnw8WPxwLcoli/MdCQRkVzLsiwmdnqEWkUrMqDXzezZs8d0pGyhIsKT/Pe/8OSTMGAAvPIKWJbpRCIiuZu3N0yfDiVKONPgTp82nUjEqBMnTtCuTjPOpSaxqP8blC4YaTqSiEiuF+gbwJzeL5JpZ9KncWdSU1NNR/rXVER4ihkzYMQI6NIFJk0CL/3TiYi4RMGCzs/gAwdg+HBnipxIHpScnEzXWq3Yfeog8296hepFy5uOJCKSZ5QtVIIPuz7N6t+3MGrUKNNx/jU9m/UEixbBwIHQpAnMmgW+vqYTiYjkLfXrO9M0Zs501ugRyWMyMzMZGNuF+P2bmNpjNE2ja5uOJCKS5/So3JLhsT2ZMGEC33zzjek4/4qKCHcXHw89ekC1as7e9oGBphOJiORNjzwCzZo5o9N27DCdRsSlHnvsMT759TsmtL2HXlVam44jIpJnTWh7LzFhpRl0Yz9OnDhhOs4/piLCnW3aBJ06OXOTFy2CAgVMJxIRybu8vZ3REL6+0K8fpKebTiTiEu+//z4vvfQSw2N7cl/DfqbjiIjkaUF+AUy/cSzHk04zotlNpuP8Yyoi3NWuXdCuHQQHw+LFUKSI6UQiIlKyJLz9NqxeDa+9ZjqNSI774YcfGH77HbQt24DXOzyIpYWyRUSMq1msIs80H8asLYuZPXu26Tj/iIoId5ScDF27QmoqfPMNlCplOpGIiFzUqxd06+bsYqQpGpKL7d69mxs7dKVcoZLM6vk8Pt4+piOJiMgFD8cNpG7xyowcfAfHjx83HedvUxHhjh58EDZvho8/hsqVTacREZHLWRa89Rb4+8Ott0JmpulEItkuMTGRbg3bkWFnMv+mVwgNzGc6koiIXMbH24cPuj7F6ZSz3Hfffabj/G0qItzNp5/CxInwwAPQvr3pNCIicjXFi8PLL8MPP8D775tOI5KtbNtmaP3ubD66k5k9x1G+cJTpSCIichVVI8rxaONBTJs2jcWLF5uO87eoiHAn+/fD0KFQpw6MG2c6jYiIXM+QIdCyJTz0EBw9ajqNSLZ59dVXmbVlMeNa3Um7cg1NxxERket4vMlgyheK4s6+Q0lJSTEdJ8tURLiLjAxnFfa0NJgxA/z8TCcSEZHruThFIykJRo0ynUYkWyxbtoyHH3yYHjEteDjuFtNxRETkLwT4+jOx0yPsOLmf8ePHm46TZSoi3MXYsbBsmTMto3x502lERCQrKlWCu++GSZNg3TrTaUT+lSNHjtCnYw/KFIzkw65Pa4cMEREP0bpsfXpWbsXzo59j3759puNkiYoId7BsGYweDQMGOIeIiHiOp56C8HCnkLBt02lE/pGMjAz6N7qBUyln+aT3i+QPCDEdSURE/oYJbe/FBh7tNMx0lCxREWHayZPOlIwyZZwhviIi4lkKFIDnn4f4eGdqnYgHeuGFF/h212re6PAQ1YtqZKaIiKcpFVqMBxv1Z8bmr1m1apXpOH9JRYRJtu1s/Xb4MMycCfm0NZaIiEcaNAhq1oQnn3TW+hHxIPHx8Tz95NPcVLUdQ2t3NR1HRET+oYfjBlIkuBAP97kT281HaaqIMOmdd5ztOp9/3tkpQ0REPJOXFzz3HOzaBR98YDqNSJYlJCRwc8eeRBUoytudH9O6ECIiHiyffzBPN7uNH/eu56uvvjId57pURJiyeTPcdx+0a+e8FRERz9ahAzRq5Kz5k5xsOo1IlowcOZIDZ44y/caxWhdCRCQXuLV2N8oUjOTJWx9w61ERKiJMSEqCvn2decUffeS8kiYiIp7NsmDcODh4UGv+iEeYPXs206ZN48lmQ2lQsprpOCIikg38fHx5sumtrD/0G/Pnzzcd55r0DNiEBx6ALVtgyhSIiDCdRkREskuzZtC6NUyYACkpptOIXNOhQ4cYPmgY9SKrMKrJENNxREQkG/Wv3oGyBUvw7B2PuO2oCBURrjZvHrz9Njz8MLRtazqNiIhkt8cfhyNHnBFvIm7Itm1ub96HpLQUpnR/Fh9vH9ORREQkG/l4+/B4k8H8fHgbX3/9tek4V6UiwpX27YOhQ6FuXRgzxnQaERHJCc2bOz/nx4+HjAzTaUSuMG3aNL7Yvoxxre6kYli06TgiIpID+lfvSGS+Irw4/AnTUa5KRYSrpKdDv37ORemMGeDnZzqRiIjkBMuCRx+FnTth7lzTaUT+4MiRI9wzbCSNSlbn7vp9TccREZEc4ufjy30Nb2bpnnWsXbvWdJwrqIhwlXHjYPlyZ1pG2bKm04iISE7q1g0qVIBXXjGdROQP7m41gMS0ZCbd8BTeXt6m44iISA66rXY38vkF8+qrr5qOcgUVEa6wb59TRPTtCzffbDqNiIjkNC8vGDECVq2C9etNpxEBYMGCBczespgnmw6lUni06TgiIpLD8geEMKTWDcyZOZvDhw+bjvMHKiJc4YkL83JefNFsDhERcZ2BAyEoCCZONJ1EhMTEREb0v40q4WV4OO4W03FERMRFRtTrRVpmOu+//77pKH+gIiKn/fwzTJsG994LUVGm04iIiKuEhjprA02fDqdOmU4jedyYMWPYl3CYtzs/jp+Pr+k4IiLiIuULR9G6TD3eHf8mGW60iLaKiJxk2842nYUKOQuXiYhI3nLnnZCcDB9/bDqJ5GFbt27l5fETGFyzC41L1TQdR0REXGxYnR7sP3OExYsXm47yPyoictLXX8O338KTTzqvjImISN5SsybUqAFTp5pOInmUbdvc3XkQIX5BvNjmbtNxRETEgBsqNqVwYAE+/PBD01H+R0VETsnIcEZDlCkDw4ebTiMiIqYMHAirV8Nvv5lOInnQ559/zre7VjO6xe2EBxc0HUdERAzw9/Hjpmrt+HzuZ5w+fdp0HEBFRM6ZMgV++QWefx78/EynERERU26+2dlFQ6MixMXOnz/PA0NGUiW8DMNje5qOIyIiBg2o3pHzGanMmzfPdBRARUTOSEpydsqoXx969TKdRkRETCpaFNq0gRkznLWDRFzkjTfeYNep33ml3f34ePuYjiMiIgbVjaxCuUIlmfHcO6ajACoicsZrr8HBgzB+PFiW6TQiImJaz56wezds3Gg6ieQRJ06cYOwTz9KhXCPalmtgOo6IiBhmWRa9Krdmye51HD9+3HQcFRHZ7uhReOEF6NoVmjQxnUZERNxB167O9Aw3GQ4pud9zzz3H2dQkxre9x3QUERFxEz0rtyLDzmD+/Pmmo6iIyHajRztTM1580XQSERFxF+Hh0LQpzJ1rOonkAXv37uWt199kUM3OVClS1nQcERFxE7WKVSSqQFE+f+kj01FURGSr7dvhnXdg2DCoWNF0GhERcSfdusGvv8KuXaaTSC737LPPYmHxTPNhpqOIiIgbsSyLGyo2ZfHOVSQnJxvNoiIiOz32GAQEwNNPm04iIiLupkMH5+3XX5vNIbna9u3b+WjyR9xZtyclCxQ1HUdERNxMp/KNSU4/z48//mg0h4qI7LJihTP39+GHISLCdBoREXE35ctDdDQsWmQ6ieRizz77LAE+fjzS+BbTUURExA01i65NgI8/iwxfj6iIyA62DQ89BMWKwf33m04jIiLuyLKgfXv4/ntITTWdRnKh3377jRnTZzCyXm8iQgqbjiMiIm4o0DeAxlE1WPyx2QUrVURkh3nzYOVKZ6HK4GDTaURExF21agXnzsHPP5tOIrnQuHHjCPT158FGA0xHERERN9aqdD22HNvF0aNHjWVQEfFvpabCo49ClSowaJDpNCIi4s7i4py3K1aYzSG5zq5du5g+bTp3xN5IeHBB03FERMSNtSgdC2B0nQgVEf/We+/Bjh3Odp0+PqbTiIiIOytWDMqUUREh2W7ChAl4e3nxQMP+pqOIiIibq12sEkG+ASxbtsxYBhUR/4Ztw+uvQ8OG0LGj6TQiIuIJ4uJg+XLnd4hINjh69CgfvvcBA2t0onj+cNNxRETEzfl6+1Avsgor5iw2lkFFxL+xYgVs3w7DhjmLkImIiPyVuDg4ehR27jSdRHKJN998k/PpqTzYSKMhREQkaxqWqM7GI9tJTk428vhuVURYlvWBZVlHLcvabDpLlnzwAYSEQM+eppOIiIinuLhOxMqVZnPINXnS9UhycjL/ffkNulRsQsWwaNNxRETEQ9SLrEJ6ZgYbN2408vhuVUQAk4H2pkNkydmzMHs29O3rlBEiIiJZUakS+PuDoV/8kiWT8ZDrkY8//pjjSae5r8HNpqOIiIgHiS0eA8C6deuMPL5bFRG2bf8InDSdI0tmz4bERBgyxHQSERHxJD4+ULUqbNpkOolcg6dcj9i2zRtPvET1iPI0i65jOo6IiHiQyPxFCAsK5WdDW4p73DYPlmUNA4YBREREsHTp0my9/3PnzmXpPmu9+io+UVGsSUmBbM7gbrJ6TvISnZMr6ZxcSefk6nReoGJ4OIVXrSL+wnnQOfE8l1+PREVFGcmwfPlyNh35P97r8gSW1qoSEZG/wbIsakRUYONXZqaKelwRYdv2u8C7ALGxsXbz5s2z9f6XLl3KX97n1q2wZQuMH0/zFi2y9fHdUZbOSR6jc3IlnZMr6Zxcnc4LsGEDLFpE85gYuFCq5/lz4mH+fD1iIsPEiRMJDcjHzdU8YhaJiIi4mWoRZXln7TwyMzPx8nLtZAm3mprhMT78ELy9YcAA00lERMQT1ajhvNU6EfIPHTt2jHlz5jKwRieC/AJMxxEREQ9UJbwsyenn2bNnj8sfW0XE35WWBlOmQOfOEBFhOo2IiHiiGGeBKLZvN5tDPNaUKVNIzUhjWJ3upqOIiIiHqnRht6Vt27a5/LHdqoiwLGsGsBKoaFnWAcuyhprOdIWFC+HIERjqftFERMRDRERAcDDs3Gk6iVyFu1+P2LbNBy9OpEGJalQpUtZ0HBER8VAVCjtrHJkoItxqjQjbtm8yneEvffABFC0KHTqYTiIiIp7KsqBsWRURbsrdr0fWrFnDr8d28W6XUaajiIiIBwsPLkh+/2B27Njh8sd2qxERbu/wYfjySxg40Nl+TURE5J8qWxYM/OIXzzd58mQCfPzpU6WN6SgiIuLBLMuiTMFIdu3a5fLHVhHxd0yZAhkZMGSI6SQiIuLpypaFXbsgM9N0EvEgqampzJo8nW6VmpE/IMR0HBER8XClQyPZs+Y3lz+uioissm1nWkZcHFSsaDqNiIh4utKl4fx5Z90hkSz65ptvOJmcQP/qHU1HERGRXKBUaFH2JRzGtl27E7WKiKxauRK2bdNoCBERyR7FijlvDx82m0M8yowZMygUWIA2ZeqbjiIiIrlAyfwRJKYlc/r0aZc+roqIrJo0yVnhvFcv00lERCQ3UBEhf1NycjLzP/mMG2Na4ufjazqOiIjkApH5iwDw+++/u/RxVURkxblzMGsW9OkD+fKZTiMiIrlB0aLO20OHzOYQj/H1119zLjWJXlVamY4iIiK5RPF84QAcPHjQpY+rIiIr5syBxERNyxARkexzsYjQiAjJonnz5lEwID/No2NNRxERkVyiaEhhAI64eM0qFRFZMWmSs0Blo0amk4iISG4REAChoRoRIVmSlpbGgjmf06ViE3y9tYW4iIhkj4jgQoCKCPdz4gSsWAH9+oFlmU4jIiK5SdGiGhEhWbJixQpOpZyha8VmpqOIiEguks8/GD9vX44dO+bSx1UR8VdWrnTeNtMvfhERyWZFisDRo6ZTiAdYsGABft6+tC3bwHQUERHJRSzLIiwolOPHj7v0cVVE/JUVK8DHB2I1H1NERLJZgQKQkGA6hXiAhR/No1mp2oT4B5mOIiIiuUyhwPycOnXKpY+pIuKvxMdDrVoQpF/8IiKSzVRESBbs27ePrcd3075cQ9NRREQkFyoYkJ+T6/e69DFVRFxPWhqsXq1FKkVEJGcUKABnzphOIW7um2++AaB9OV2PiIhI9gsNCCHh/DmXPqaKiOvZsAFSUlREiIhIzrg4IsK2TScRN/btt99SLCSMmPDSpqOIiEgulN8/hDPnE136mCoiric+3nmrIkJERHJC/vyQkYFXSorpJOKmbNtmyYLFtCpTF0u7d4mISA7I5x/E2fNJLn1MFRHXEx8PUVFQooTpJCIikhsVKACAT6JrX4UQz7F161aOJp6kRbQWzRYRkZwR4hfEuVQVEe4jPl6jIUREJOfkyweAd3Ky4SDirn788UcAmpaqbTiJiIjkVsG+ASSnnyczM9Nlj6ki4lr274cDB1REiIhIzvH3B8ArLc1wEHFXy5cvp2hIYcoW0uhMERHJGUG+AQAkJbluVISKiGtZscJ5qyJCRERySoDzi98rNdVwEHFX8V8uJa5kDa0PISIiOeZiEZHswhGaKiKuJT4egoKgenXTSUREJLfSiAi5jiNHjrD79O80LKlrERERyTkBPs71SIoLF89WEXEt8fFQrx74+ppOIiIiuZVGRMh1rF69GoB6kVUMJxERkdwswMcPgPPnz7vsMVVEXE1iImzYAHFxppOIiEhudmFEhKUiQq5i7dq1eFle1C5WyXQUERHJxfxVRLiJNWsgI0PrQ4iISM7SiAi5jvXr11MpLJpgv0DTUUREJBfz8/YBVESYFx/vvG3QwGwOERHJ3bRGhFzHhh/XUKtoRdMxREQkl/P1coqINBdej6iIuJr4eIiJgUKFTCcREZHcTEWEXMPJkyc5cOYINYqWNx1FRERyOV9vFRHmZWY6RYSmZYiISE7z9gbAysw0HETczebNmwGoVqSc4SQiIpLb+VwYEZGenu6yx1QR8SdB+/fDqVMqIkREJOdZlvPWts3mELezZcsWAKoUKWM4iYiI5HY+Xs4LIyoiDMp/4RUI7ZghIiI5TkWEXMPWrVsJ8QuiRP4I01FERCSXUxHhBoL37XNWMa9QwXQUERHJ7VREyDVsW7iGCoWjsC5+j4iIiOQQb8upBTIyMlz2mCoi/sTnzBkIC7t0cSgiIpJTvJxfw/qNI3+24+R+KhSOMh1DRETyAK8LRYTtwhdGVET8iW9CglNEiIiI5LSLpbcWq5TLpKWlsff0YcoWLGE6ioiI5AFeGhFhnu+ZM1C4sOkYIiKSF2hqhlzF/v37ybAzKFMw0nQUERHJA7y9VEQYpyJCRERc5kIRoakZcrm9e/cCUCq0mOEkIiKSF1gXrkQ0NcMg34QEFREiIuIaGhEhV3HgwAEAogoUNZxERETygosLI6uIMCUjA5+zZ7VGhIiIuIaKCLmKi0VEZL4ihpOIiEheYGJkpoqIy50+jWXbGhEhIiKuoSJCruLQoUPk9w8myC/AdBQREclDNCLClBMnnLcqIkRExBW0fadcxeHDhykaomsRERFxDY+YmmFZVrBlWd45Eca4i0WEpmaIiIgraPtOuYqjq3dSJLiQ6RgiIpJHuOVilZZleVmWdbNlWV9alnUU+A04ZFnWFsuyxluWVT7nY7rI8ePOW42IEBERV7A0FkKudDzpNOFBBU3HEBGRPMIycD2SlRERS4CywGNAUdu2S9q2XQRoAvwEvGBZVv8czOg6mpohIiKudHH7Tq0RIZc5mXyGQoH5TccQERHJMT5ZuE1r27bT/vxB27ZPAnOBuZZl+WZ7MhNURIiIiCtpsUq5zSqy1gAAIABJREFUioT/Z+8+o6Oq+iiMPzc9QBIg9EAwSJFeDIIIikpTQRAVECyAXRRfC3YUUewFkCLNSi9SpSkQQJASBELvvRNqID33/XBBUIoBkjkzk/1ba1ZICJntXUhu9pzzP8kJ5A0KMR1DRERyGLfamgE8ZlnWFMuyOliWFWRZ1luWZXW1LKvy2U+4WFHhkeLjyfD1hVC9CiEiIi6gIkL+JS0tjdOpSYQG5jYdRUREcgjLwNjszBQRrwJvALWApUBZ4ADwjWVZ7bMvmgGHD5MWGqo9uyIi4hr6fiP/kpCQAECegGDDSURERLJPZrZmpNi2vdqyrP8Bh4Fo27aTLcv6EZgP/JCdAV0qPp7U0FACTOcQEZGcQTMi5F9OnToFQG4VESIi4sUysyJivGVZE4G7gOds204+8/FUwLvOuYyPJzUszHQKERHJKXzOfBtWESFnJCUlARDsF2g4iYiISPb5zyLCtu33gL7AncCzlmXttCxrFjAPOGpZVnnLsjJTaPwny7KaWJa1wbKszZZlvZEVX/OKqIgQERFX0owIt2TyfiQlJQWAAF/vmAMuIiJyMZnZmoFt2zOBmQCWc8hoOaA6UA3odeb9ktcSxLIsX5zCoyGwG1hqWdYk27bXXsvXvSKHD5Na8pr+M0RERDJPWzPcjun7kdRUZ/63v2+mbtFEREQ80hV/l7OdMz3Wn3mMyMIsNwGbbdveCmBZ1kigOeCaIsK2IT7eGVYpIiLiCmeKiIDDhw0HkfMYvR9JT08HwNfydcXTiYiIGJHpIsKyrDuAdsAxYDUQB6w+b2bEtYoAdp33/m6ckzpcIykJUlNJy63jskRExEXOrIQoNmWK4SByHrP3I2foQBUREfFmV7IiYijQ6cyfqQK0ACoCpbMoy8W+5V6wVtWyrKeApwAKFy5MTExM1jy7bXOrry/px49n3df0EgkJCbom/6JrciFdkwvpmlycrst50tOpD+y57TY265q4iyu+H4mMjMzyENqtIyIi3uxKiojNtm2PP/PrMdmQZTdQ4rz3iwN7//1Jtm0PBAYCREdH2/Xr18+6BAUKkPv0abL0a3qBmJgYXZN/0TW5kK7JhXRNLk7X5TxnluGnXnedron7uKr7kax6cl9fZ0tGup2eVV9SRETE7fznaReWZf1kWdb/gD8ty3olG7MsBcpYlhVlWVYA0AaYlI3Pd6HwcPxPnHDpU4qISA6ml73dkdH7ET8/5zWitAwVESIi4r0ysyLiR6AqUARobFlWZ2DlmUecbdtZsjrCtu00y7KeB2YAvsB3tm2vyYqvnWkqIkRExAQNBHAbpu9HAgICAEhOS3HVU4qIiLjcfxYRtm3PAmadfd+yLD+gAk45UYss3KZh2/ZUYGpWfb0rFh6O3+7dxp5eRERyGK2IcEsm70eCg4MBSFIRISIiXuw/iwjLsqwzR3YCzisFOCdmxAE/X+xzPFaBAvgfP246hYiI5BRnvnXaWhEhZ+TKlQuAU6mJhpOIiIhkn/+cEQHMsSzrBcuy/jES2rKsAMuy7rAs60fgseyJ52Jnt2Z4QaciIiIinidPnjwAJKSoiBAREe+VmRkRTYCOwAjLskoBR4EgnH2TM4GvbdtekX0RXSg8HJ+0NEhIgJAQ02lERMTbqfiWf/H39yfIL5ATyadMRxERkRzCvvCU6myXmSLCAsbatt3PsqyCwJPAKWCAbdtJ2ZrO1cLDnbfx8SoiRETEdbQ1Q86TNygPx5JOmo4hIiI5jOXC+5H/3Jph23Yi0MuyrGU4Z2u3AQoAfSzLKprN+VyrQAHn7eHDZnOIiEjOoBURchH5g8M4kqiZVSIi4r0yM6yyBFAZ55SM4rZt7zjz8VxAf7xlPgT8c0WEiIiIq2hFhJwnPDiMw6dVRIiIiGuYOHciM8MqqwNbbdtOP1tCnBEKNM6eWIaoiBAREVfSigi5iEI1S3Hw1BHTMUREJIc4OyPCrbZm4BQOyy7y8aeAEVkbxzAVESIi4ko6vlMuokiRIuxP0L2IiIi4xtkVEe5WREwF1l3k44eBcVkbx7B8+ZybQc2IEBEREUOKFi3KsaSTJKUmm44iIiI5iFsVEbZtH+HihUN/YEuWJzLJz4+0PHm0IkJERFxDWzPkIiIiIgDYc/KQ4SQiIpITmLgbycyKCGzbTr/Ix2zbtvdlfSSzUkNDVUSIiIhraWuGnKd48eIA7Dy+33ASERHJCdx1a0aOkhoWpiJCRERcQysi5CJKliwJqIgQERHXcNdhlTlKWmioZkSIiIhraUWEnKdkyZJYWGw9usd0FBERyQHSMzIA8PX1ddlzqoj4F23NEBERlznzjV+nZsj5AgICiAwrwpYju01HERGRHCDDdu5HfHxcVw+oiPiX1LMrIrRcVkREsltqKgC2C1+BEM9QOn8JNsbvMB1DRERyABURbiCxRAk4fRq2bjUdRUREvF1aGgC2n5/hIOJuyja5kY3xO/8eICYiIpJd0m1tzTDueKVKzi8WLjQbREREvJ9WRMgllC9fnuPJCew7qblVIiKSvTQjwg2cKlkSQkNVRIiISPY7W0RoRYT8S8WKFQFYc2iL4SQiIuLt0jKcFZr+/v4ue04VEf/m6wu1a6uIEBGR7Hdma0aGVkTIv1Q6s0Jz9UEVESIikr1SzxQRfi58YURFxMXUqQOrVsGJE6aTiIiIN9OKCLmEQoUKUSRPOCv3bzIdRUREvFxqulZEuIc6dZxTMxYvNp1ERES8mYoIuYxqRcqxfP8G0zFERMTLpWWkAyoizKtVCywLFiwwnURERLzZ2VMztDVDLqJGq/qsPbSVxNQk01FERMSLpaQ7L4wEBAS47DlVRFxMaChUrqw5ESIikr20IkIuIzo6mrSMdG3PEBGRbJV8pogIDAx02XOqiLiUW26BRYsgPd10EhER8VZniggNq5SLuemmmwBYvGe14SQiIuLNktKSARUR7qFOHTh5EtasMZ1ERES81alTAGQEBxsOIu4oIiKC4qGFWbR7lekoIiLixRJTnSIiKCjIZc+pIuJS6tRx3mp7hoiIZJczRUS6C7/xi2ep0+Q2FuxcaTqGiIh4scQzKyKCXfjCiIqIS4mKgsKFVUSIiEj2SUgAVETIpdWtW5ddJw6w49g+01FERMRLnT4zFDlXrlwue04VEZdiWc6qCJ2cISIi2UUrIuQ/3HrrrQDM2/GX4SQiIuKtTqUkEugbgK8LZ1apiLicOnVg61bYv990EhER8UaaESH/oXLlyuQPDmPOtljTUURExEslpCQSEui61RCgIuLyzs6J+PNPszlERMQ7nV0R4cIp1eJZfHx8qH/XnczathTbtk3HERERL3Qy5RQhAbld+pwqIi7nxhshIEBzIkREJHucPAm5c4OPvh3Lpd15553sPL6fzUd2mY4iIiJe6ETyKUIDVUS4j8BAiI5WESEiItkjPh7y5zedQtxco0aNAJixWSs0RUQk6x1PSiAsKI9Ln1NFxH+pUwdiYyE52XQSERHxNvHxUKCA6RTi5kqXLs31+YozXUWEiIhkgyOJJ8hXrYRLn1NFxH+pUwdSUuAvTasWEZEsFh8P4eGmU4gHuPvh+5i9bSmJZ45YExERySpHEk+Q38UrNFVE/Jebb3bezptnNoeIiHifw4dVREimNG3alMS0ZGZtXWo6ioiIeBHbtolPPE64i+9HVET8lyJFnDkRw4eDplWLiEhW0ooIyaTbbruNkIDcTNqgF0ZERCTrJKScJiktmYIFC7r0eVVEZEbHjhAXp+0ZIiKSddLT4ehRzYiQTAkMDOTu+5oyccNc0jPSTccREREvcfDUUQAKFy7s0udVEZEZDz0EQUHw3Xemk4iIiLeIj3dW2qmIkExq2bIlB08dYcHOlaajiIiIl9ifcBhQEeGe8uaF++93tmckJppOIyIi3mD3budtCddOqRbPdffddxPkF8joNb+ZjiIiIl5i30mniChatKhLn1dFRGZ17AjHjsH48aaTiIiIN9i1y3lbvLjZHOIx8uTJwz3NmzJ27WxtzxARkSyx+8RBAIq7+H5ERURm1a8P112n7RkiIpI1zhYRWhEhV+Chhx7iwKl45myLNR1FRES8wK4TBwjyC9TxnW7Lxwc6dIBZs2D7dtNpRETE0+3aBQEB4OIp1eLZ7rnnHkIDczNs1XTTUURExAvsOLaPyLDCWJbl0udVEXEl2rcHy4LvvzedREREPN3OnRAR4RTdIpkUFBTEA+1aM3btLE6laG6ViIhcm+3H9hEVXd7lz6u7nysRGQkNGzpFRLr2ZoqIyDXYtAnKlDGdQjzQY489RkLKaX5ZN9t0FBER8XBbj+4hKirK5c+rIuJKdezoLKedrW/+IiJylWwbNmyAcuVMJxEPVK9ePa7PV5zvlk8yHUVERDxY/OljHE06QRkDL4yoiLhSLVpA/vwwZIjpJCIi4qn27YOEBChb1nQS8UCWZdHhlWeI2b6MzfG7TMcREREPtTF+JwBlDdyPuEURYVnWg5ZlrbEsK8OyrGjTeS4rMBDatXOO8TxyxHQaERHxRBs2OG+1IsKteNL9SIcOHfC1fBn81wTTUURExEOtP7wdyMFFBLAaaAnMMx0kUzp2hJQUGD7cdBIREfFEKiLclcfcjxQrVoxm5erx3fJJJKelmI4jIiIeaM3BrQT6BlCqVCmXP7dbFBG2ba+zbXuD6RyZVq0a1Kih7RkiInJ14uIgNBSKFzedRM7jafcjz/Z6k0OnjzJ27SzTUURExAOtPriF8gWvw8/Pz+XP7fpnvEaWZT0FPAVQuHBhYmJisvTrJyQkZOprFqtbl7K9exM7aBAJXj71PLPXJCfRNbmQrsmFdE0uTtcFasyZQ0ZUFCvmOS+865p4nvPvRyIjI41kaNCgAWXDI/lm8SjaVbnLSAYREfFcKw9spMkDzYw8t8uKCMuyfgeKXOS33rZte2Jmv45t2wOBgQDR0dF2/fr1sybgGTExMWTqa1atCgMGEB0XB08+maUZ3E2mr0kOomtyIV2TC+maXFyOvy6pqbBtG3Tq9Pd1yPHXxIWy634ki+JdER8fH55/71U6d+7M4t2rqVW8kokYIiLigfadPMz+hHiqVatm5PldtjXDtu0Gtm1Xusgj09/03Uq+fNCyJQwbBklJptOIiIinWLcOkpPhxhtNJ8mRvO1+pH379oQG5ubrP4eZjiIiIh5k2d51ANxo6H7ELWZEeKyOHeHoUZigidUiIpJJf/3lvK1Rw2wO8QohISE89cKzjF07m+1H95qOIyIiHmLJnjX4WD5Ur17dyPO7RRFhWdZ9lmXtBm4GfrUsa4bpTJlyxx1QsiQMGmQ6iYiIeIrFiyEkBAwclSWX56n3Iy+++CKWBV8v0mleIiKSOYt2r6JyodLkzp3byPO7RRFh2/Z427aL27YdaNt2Ydu2G5vOlCk+PtCpE8yeDXPnmk4jIiKeYO5cqFvX+R4ibsVT70eKFy9Ou0ceZvBfEzh86pjpOCIi4ubSM9JZtHs1dVreaSyD7oKu1fPPQ4kS8OqrkJFhOo2IiLizAwecGREaTClZ7PXXXycxNZlei0eYjiIiIm5u5f5NnEw5Rb169YxlUBFxrYKD4cMPITYWRo82nUZERNzZ2dVzKiIki5UvX56W5W+n9+KRHEs8aTqOiIi4sTnbYwG49dZbjWVQEZEV2rVzjvN8801nErqIiMjFxMQ48yE0qFKywTvDv+RE8imtihARkcuatXUJZcMjiYiIMJZBRURW8PWFzz+H7duhb1/TaURExF3NmQP16oGfn+kk4oWqVatG83K38fWfwzmaeMJ0HBERcUPJaSnM3fEXDds0M5pDRURWadgQGjd2tmkcPWo6jYiIuJvt22H9erjT3GAo8X7dR/fmeHICXy4cajqKiIi4oQU7V3I6NYlGjRoZzaEiIit99hkcOwYffWQ6iYiIuJspU5y3zcy+AiHerUqVKrSu2JCei0ZwMOGI6TgiIuJmft30BwG+/txxxx1Gc6iIyEpVqsBjj0Hv3s4rXyIiImdNngzlykGZMqaTiJfr/ksfktJS+HDeENNRRETEjdi2zaQN87j9umjy5MljNIuKiKz2wQfOzIh33jGdRERE3MWJE86gSq2GEBcoW7Ysjz/5ON/GjmPLkd2m44iIiJtYc3ALm4/sovkrj5iOoiIiyxUvDi+9BMOGwbJlptOIiIg7mDgRUlLgvvtMJ5Ecolu3bvj7+vHG79+YjiIiIm5i3LrZWFjc5wb3IyoissNrr0GBAtClC9i26TQiImLayJFQsiTcfLPpJJJDFC1alC5vvc7YtbNYsHOF6TgiImKYbduMXvM79UpWp0iRIqbjqIjIFmFh8N57zjFt06aZTiMiIibFx8PMmdCqFViW6TSSg3Tp0oViIQX53/SvyMjIMB1HREQMijuwibWHttL6tcdNRwFURGSfp592BpK99hqkpZlOIyIipowd63wfaN3adBLJYXLnzs2n/b4idu9aflw5xXQcEREx6OeVU/Hz8aVVq1amowAqIrKPvz98/DGsWQM//mg6jYiImPLdd1CxItSoYTqJ5EBt27bl5uJVeOP3PhxLPGk6joiIGJCWnsawVdO4u8wtFChQwHQcQEVE9mrZEurUga5d4dQp02lERMTV4uJgyRJ44gltyxAjfHx86DPxew6dOsq7c741HUdERAyYtnkh+xPi6fDJS6aj/E1FRHayLPj8c9i3D776ynQaERFxtSFDICAAHn7YdBLJwWrUqMGzzz1L36Vj+GvvetNxRETExQYuG0+RPOHcc889pqP8TUVEdqtTx1kZ8dlncOCA6TQiIuIqp0/Dzz87R3a6yTJIybl69OhBwVz5eHrKR6RnpJuOIyIiLrLj2D6mblpAx85P4+/vbzrO31REuMInn0BSkrNFQ0REcoaff4ajR+G550wnESFv3rz0HNyH2L1r+WbxKNNxRETERb6NHQfA008/bTjJP6mIcIUyZeB//4NBg2DyZNNpREQku2VkQM+ezoDKevVMpxEBoHXr1txVug7vzO7PjmP7TMcREZFsdjoliUHLxtO83G1ERkaajvMPKiJc5cMPoVo16NAB9u41nUZERLLTzJmwfj289JKGVIrbsCyL/r8Px7IsnprcA9u2TUcSEZFs9OPKKcQnHuelge+bjnIBFRGuEhgII0dCYqIztCxd+zNFRLzWl19C0aLgJmd1i5xVsmRJPv36c2ZuWcR3yyeajiMiItkkPSOdLxb+zE0RFalbt67pOBdQEeFK5cpBnz4wZw58+qnpNCIikh0WLYLff3e25AUEmE4jcoFnnnmG26+L5qXpX2uLhoiIlxqz5ne2Ht3D6727Y7nh6kwVEa7Wvj089BC8+y4sXGg6jYiIZLXu3Z1TMjSkUtyUj48PQ2aPxsam48TuZGRkmI4kIiJZKCMjgw/nDaF8gShatGhhOs5FqYhwNcuC/v0hMhLatoVjx0wnEhGRrLJkCUybBq+8AnnymE4jcklRUVF83bcXs7ctpffikabjiIhIFhq3bjZrDm2la+8e+Pi454/87pnK24WFwYgRsGcPPPUUaFiUiIh36N4d8ueHTp1MJxH5T48//jj3lruVN37vQ9z+TabjiIhIFkjPSKdbzEDKF4iilRvPqlIRYUqtWs5JGmPGwJAhptOIiMi1mjsXfv0VunSBkBDTaUT+k2VZDJ4/lrxBIbQd9zaJqUmmI4mIyDX6eeVU1h7ayvv9PsXX19d0nEtSEWFSly7QoAF07gxr15pOIyIiVysjA159FYoXhxdfNJ1GJNMKFizIT78MZ82hrbw842vTcURE5Bokpibx7pxviS5WgQceeMB0nMtSEWGSjw/89JOzj7hNG0jSKxEiIh5p1CiIjYUePSA42HQakSvSqFEjunTpwrex4xiz5nfTcURE5Cr1WjSSXScO8Pmwvm55Usb5VESYVrQo/PgjrFrlrJAQERHPkpQEb74J1arBww+bTiNyVT788ENqRVTi8YkfsDl+l+k4IiJyhfafPMxH87+nWdl61K9f33Sc/6Qiwh3cdRe8/DL06QMTJ5pOIyIiV+KLL2DHDvj8c2elm4gHCggIYNSCKfj5+PLgmNc1L0JExMO8NasvSWnJfDnFM+YP6o7JXXz0EdSoAR07wu7dptOIiEhmbN7sDB5+8EFn5o+IBytZsiRDx41gxf6NdPr1U2yd6iUi4hEW7lzJ9ysm89KrL1OmTBnTcTJFRYS7CAx0jvRMTnaW9qanm04kIiKXY9vw/PMQEABfa8ifeIe7776brl278v2KyQxc9ovpOCIi8h9S09N49tdPKB5amK5du5qOk2kqItxJ2bLQr59zBNxHH5lOIyIilzN2LMyYAR98ABERptOIZJn33nuPJqXr8MLUz1m4c6XpOCIichk9Fw0n7sAmev/Qnzx58piOk2kqItzNI49Au3bQrRv88YfpNCIicjFHjzrHdFavDp06mU4jkqV8fX0ZvmQKJfMWpeWo19h9/IDpSCIichFbjuzmvTkDaF7uNlq0aGE6zhVREeFuLMtZFREVBa1awfbtphOJiMi/vfgiHDwIAweCn5/pNCJZLl++fEycP51TqYm0GPkqp1M0vFJExJ1kZGTwxKQPCPD1p++sYW5/XOe/qYhwR6GhMH48JCZCw4ZwQK9EiIi4jfHj4eef4e23ITradBqRbFOhQgWGjx3JX/vW035CNzIyMkxHEhGRM/ouHU3M9mV82bcnER64RVRFhLuqXBl+/RX27IEmTeD4cdOJRETk4EF4+mnnlKN33jGdRiTbNWvWjM8+/4wxa3+n65z+puOIiAiw4fB2Xv/tG+4qXYeOHTuajnNVVES4szp14JdfYPVqaNbMWSEhIiJm2LZTQpw4AT/9BP7+phOJuMQrr7zCE088wUfzv+f75ZNMxxERydFS0lJ5+Jd3CfILZPDcMR63JeMsFRHurkkTZwnwH384MyNSU00nEhHJmQYNggkT4MMPoWJF02lEXMayLPr160fDUrV4anIPZm5eZDqSiEiO9V7MAGL3rmXQ0O8oVqyY6ThXTUWEJ2jTBvr2hSlToGNH0B5NERHXWrECOneGRo3g5ZdNpxFxOX9/f8Yun0mFgqW4f/Rr/LV3velIIiI5zm9bFvHpHz/y5JNPcv/995uOc01URHiKZ591zqofOhReeslZIiwiItnvxAl48EEoUMD5N9hH3zolZwoNDWXqsjnkDw7l7mEvsuXIbtORRERyjL0nDtFuXFfKF4yiZ8+epuNcM91NeZK334b//Q9693aWBouISPaybXjiCdi2DUaOhIIFTScSMSoiIoLpf84mNSONRj93Yt/Jw6YjiYh4vdT0NNqMfYtTqYmMnTuFXLlymY50zVREeBLLgi+/hMceg3ffhX79TCcSEfFuffvCmDHQowfUrWs6jYhbKF++PFPnzOBAwhGaDH2Bo4knTEcSEfFqr/3Wi/k7lzPohyGUL1/edJwsoSLC0/j4wODBcO+98PzzMGKE6UQiIt5pzhxnK9w990CXLqbTiLiVWrVqMWHqJNYf3s5dQztzMvmU6UgiIl5pWNw0ei4awQsvvEDbtm1Nx8kyKiI8kZ+fs0S4Xj149FGYNs10IhER77JpE9x/P5QpA8OGaS6EyEU0aNCAUWNHE7t3HfeOeJnTKUmmI4mIeJWle9bwxKQPubVkDb788kvTcbKU7qw8VXAwTJoElSs7N8sLFphOJCLiHY4dg2bNnPJh8mQICzOdSMRttWjRgp+G/sTc7X/RYuQrJKUmm44kIuIV9pw4SIuRr1I4d37GLp2Ov7+/6UhZyi2KCMuyPrcsa71lWXGWZY23LCuv6UweISwMpk+HEiWgaVOIizOdSETEs6WlQatWsHUr/PILXH+96UTiQrofuTpt27blu++/47eti2k5qovKCBGRa3QqJZFmw1/iZPJpJs+fQUEvHJbtFkUE8BtQybbtKsBG4E3DeTxHoUIwcybkyeOcb79li+lEIiKeybadk4l++w3694dbbzWdSFxP9yNXqX379gwaNIhpmxeqjBARuQZpZ07IWHlgEyPHj6Zy5cqmI2ULtygibNueadt22pl3FwHFTebxOCVLOmVEWho0bAj79plOJCLieT7+2Dkl4+WX4fHHTacRA3Q/cm2eeOKJv8uI5iNfITFVMyNERK6Ebds8P/UzpmycT5++fbj77rtNR8o2lm3bpjP8g2VZk4FRtm0PvcTvPwU8BVC4cOEbR44cmaXPn5CQQJ48ebL0a7pKyLp1VHv5ZZILFiTuk09IKlYsS76uJ1+T7KJrciFdkwvpmlycO16XopMmUe7rrznQoAHr3nzT5cMps/qa3H777cts247Osi+YA13J/UhkZOSNO3bscGU8t/b999/zeMfHqX/djUx66CvyBHr+efciIq7wfsxAusUM5PXXX+eTTz4xHeeaWZZ1yfsRlxURlmX9DhS5yG+9bdv2xDOf8zYQDbS0MxEsOjrajo2NzdKcMTEx1K9fP0u/pkstWOAc7enr6wxZq1Xrmr+kx1+TbKBrciFdkwvpmlyc212X0aOhTRu4+24YPx4MDIPK6mtyuW/8OZ2n3I94umHDhvHYI49xU0RFprbrRd7gENORRETcWr8lY+g09VPat2/Pd999h2VZpiNds8vdj/i5KoRt2w0u9/uWZT0GNAXuzMw3fbmEW26BP/+Eu+6C22+H4cOhRQvTqURE3NPMmfDww86/naNHGykhxLV0P+Ia7dq1Izg4mDYPtqb+D08z45FvKJwn3HQsERG3NHTlVDpN/ZRmZesxcOBArygh/otbzIiwLKsJ8Dpwr23bp03n8Xhly8KiRVClCrRsCb16mU4kIuJ+Fi2C++6DChWcFWS5tHw8p9P9SNZq2bIlU6b9yqYjO6n73RNsO7rHdCQREbczbu0s2k94n/rX3cjolTO97pjOS3GLIgLoA4QAv1mWtcKyrG9NB/J4BQvC7NlSsA9yAAAgAElEQVTOaoj//c95pKebTiUi4h7+/BMaN4ZixWDGDMirUxoF0P1IlmvUqBG/z51N/Onj3DLkceL2bzIdSUTEbUzeMI82Y9/ipoiKTF4VQ1BQkOlILuMWRYRt26Vt2y5h23a1M49nTGfyCrlywZgxTgnRqxc8+CCc1gs8IpLDzZ/vHHdcuDDMmeO8FUH3I9nl5ptvZn7sQnx9fKn3/RPM2aZ5GiIikzfM4/5Rr1G9SDmmrZ7ndoO8s5tbFBGSjXx94euvnSJiwgS44w44eNB0KhERM+bMgSZNoHhxiIlx3opItqtYsSILVy+lRGhhGv/8PMPjppuOJCJizPh1c7h/1GtULVKWmWsWEBYWZjqSy6mIyCk6d4ZffoG4OLj5ZtiwwXQiERHXmjnTORkjKsopIbLoiGMRyZwSJUowf0Mst0RWpd0v79Bj3hA0D1REcppRq2fy4Og3uLFYeX5bs4C8OXR7qIqInKRFC+fVwJMnoU4d+OMP04lERFxj6lTnaOOyZbUdQ8SgfPnyMX39AtpVvot3Zven48TupKSlmo4lIuISQ/6awENj36ZOiSrMXJtzSwhQEZHz1KrlTIovWBAaNIBRo0wnEhHJXiNHOkVsxYrOEN+CBU0nEsnRAgMD+Xnlr3Tr1o0fVkymwU/PcfjUMdOxRESy1ZcLh/LEpA9pdH1tpq/7g5CQENORjFIRkROVKgULF8JNN0GbNvDpp6ClkSLibWwbPvsMHnrI2ZL2++8QHm46lYgAlmXx3nvvMWLECJbsWUPNQY+y6sBm07FERLJcRkYGr//Wm1dn9qRVxYZMXDOHXDoyXEVEjpU/v7Nfuk0beOMNeO45SEsznUpEJGukp8MLL8Drr0Pr1s6/d/nymU4lIv/Spk0b5i2cT3JaCjcP7sD4dXNMRxIRyTIpaam0n9CNzxb8xLPPPsvwldMIDAw0HcstqIjIyYKCYNgw50b922+heXNISDCdSkTk2pw+DfffD337QpcuMHw46Ju+iNu66aabWLp+BRULlaLlqC68N2cAGRkZpmOJiFyT40kJ3D3sRX6Om8oHH3xA37598fX1NR3LbaiIyOl8fOCTT5wiYvp0qFcPNm40nUpE5OocOuQcUzxpEnzzjbM1w0ff6kTcXUREBHM3x9KhQwe6zx1EsxEvceT0cdOxRESuyvaje7llSEfm7ljGjz/+yDvvvINlWaZjuRXdnYnj6adhyhTYuROqV4fBgzU3QkQ8y8aNzolAK1fCuHHw/POmE4nIFQgKCmLIkCH079+f37Ys5saBj/DX3vWmY4mIXJGFO1dSa3B79pw8xIzfZvLoo4+ajuSWVETIOXfdBXFxzlC3J590ljbHx5tOJSLy36ZPdwbwHjvmnIxx332mE4nIVbAsi2eeeYb5C/8gLSOdOkM6MiB2HLZeHBERD/Djiinc/uMzhAbm5s/lS7jjjjtMR3JbKiLknyIinKFuX3zhrJCoUoV8y5aZTiUicnG2DZ9/DvfcA9ddB0uXOmWqiHi0WrVqsXzLam6PiuaZKR/TdtzbnEjSHCsRcU9p6Wm8NP1L2k/oRt3IaizetIIbbrjBdCy3piJCLuTjA6+8AosXQ2goVV99FV59FZKTTScTETnn1Cl4+GF47TVnBdeCBU4ZISJeoUCBAvy6YT49evRg9JrfuXHgIyzbu850LBGRfzh06iiNfn6enotG0LlzZ2ZsXEj+/PlNx3J7KiLk0qpXh2XL2HPvvfDll1CrFqxdazqViAisX+9sxRgxAnr0gFGjIHdu06lEJIv5+Pjw1ltvETM3hqQzR3x+uXCoTtUQEbewaNcqagx4mD93r+LHH3+kV69e+Pn5mY7lEVREyOXlysWml15yJtDv2QM33gj9+mmQpYiYM3o01KwJBw86W8neegs0iVrEq9WrV48VW9fQtGw9Xp3ZkyZDX2DviUOmY4lIDmXbNr0XjeTW75/E38ePhUv+1FDKK6QiQjKnWTNYtQpuuw06dXLeP3jQdCoRyUmSkuCFF6B1a6hcGZYvhwYNTKcSERcJDw9n3NpZDBgwgAW7VlK5fxvGrPnddCwRyWGOJZ7kgdGv8eL0L2hS+maWbV1F9erVTcfyOCoiJPOKFIGpU6FXL/j9d+cHgWnTTKcSkZxg3Tpne1ifPvDSSxATA8WLm04lIi5mWRZPPfUUy1ev5Pp8EbQa8wYPj+vK0cQTpqOJSA7w5644qg9ox6QN8/j888+ZuH4u+fLlMx3LI6mIkCvj4wOdOzuT6QsVgrvvdt5PTDSdTES8kW3D4MHOtrB9++DXX+GrryAgwHQyETGobNmyLNi+gm7dujFqzUwq9WvN1I1/mI4lIl4qLT2ND+YOpt53TwLwx8IFvPrqq1jaGnrVVETI1alc2SkjXnwRvvnGGRq3apXpVCLiTQ4dck7DePJJuOUWWLnSKT9FRAB/f3/ee+89Fi9dQr6gEO4Z/j/aj++m1REikqW2Hd1D/R+e5t0539KqYgNWbF9LrVq1TMfyeCoi5OoFBUHPnjB9Ohw+7AyP69kTNMlaRK7VxIlQsaKzAuKzz2DGDCha1HQqEXFDNWrUYNmutbz99tsMjZtGhb4P8sva2aZjiYiHs22bIX9NoEr/h1h1cDNDhw5l+KrphIWFmY7mFVREyLVr3Bji4py3L73krI5YuNB0KhHxRMePQ/v20KIFRETAsmXQpYuzLUxE5BICAwP58MMPWRK7hCJ5wrl/9GvcP6qLTtYQkauy98Qhmg1/iScmfUh0sfKs2riWdu3amY7lVXRnJ1mjYEGYMAGGDnX2cd9yCzzyCOzdazqZiHiKKVOgUiX4+Wd45x1YvNh5X0Qkk2rUqMGSnav5+OOPmbppIeX7PkDfJaNJz0g3HU1EPIBt2/ywfDIV+7Vi9ral9OrVi1lblhAZGWk6mtdRESFZx7KgXTvYsAHeegtGj4ayZeGTTyA52XQ6EXFXBw/CQw85xwLnzeusqPrgAw2kFJGr4u/vzxtvvMGqdau5KaIiz0/9jJsHd2DZ3nWmo4mIG9t2dA9Nhr5Ah4nvU7lQaeLWraZz5874aFVmttBVlayXJw/06OEct9ewIbz5prPXe9IkZwK+iAg4/x78/DOULw/jxsH77ztbMTQASkSyQOnSpZm5eRHDhg1j5/ED1Bz4KM9N+YQjp4+bjiYibiQtPY2vFg6lUr/WLNwVR9++fYnZFkvp0qVNR/NqKiIk+5QqBePHw8yZziubzZtDkyZOQSEiOdu6dXDnnfDoo1CuHKxYAe++q1UQIpKlLMuibdu2rN+9medfeJ4By36h7DctGRj7i7ZriAhLdq+m5qBHeWVmT+6Iqsnazet57rnntArCBXSFJfs1bOgcu9ezp7Pnu0oVZ6jlsWOmk4mIqyUkUGrAAOffgeXLoV8/+OMPqFDBdDIR8WJ58+ald+/e/LX8LyoULMXTUz6i5sBHmb9jueloImJA/OljPDP5I2oP7sDBU0cZO3Ysk9bPpUSJEqaj5RgqIsQ1/P3hxRdh0ybo2BF69XLmRwweDOl6RULE69m2s/2iQgUiR450htlu3AjPPqsTMUTEZapWrcrc7csYMWIEh04f49bvn+TB0a+z9chu09FExAXSM9IZEDuOst/cz+C/JvK/l/7H+j1buP/++7Esy3S8HEV3f+JaBQvCgAEQG+sUEU8+6Rz3uWCB6WQikl1WrHC2YTzwAOTLx1+9e8N33zn/HoiIuJhlWbRp04YN+7bSvXt3pm5awA19HuCVGV9rfoSIF5u7fRnRAx/hmSkfU6nQ9ayIW8FXX31FSEiI6Wg5kooIMaNGDZg/H4YPhwMHoG5dePhh2LPHdDIRySr79sHjjzv/v8fFQZ8+sGwZJypXNp1MRIRcuXLRtWtXNm3fwiPtH+XrP4dzfe8WfL7gJxJTk0zHE5EssuXIbh4Y9Rr1f3ia+NPHGTlyJDHbYqmkI8KNUhEh5liWc2Tfhg3wzjswdqwztK5HDzh50nQ6Eblap0/Dhx9CmTLOqRivvAKbN0OnTuDnZzqdiMg/FCtWjCFDhrBi5QpuLl6Z137r7SzbXjaBtPQ00/FE5CodOX2cl6d/Rfk+DzBt80K6d+/O+n1bad26tbZhuAEVEWJe7tzwwQfOFP1GjZxSomRJeO89iI83nU5EMislBfr3h9KloWtXaNzY+f/6888hb17T6URELqtKlSpM3bSAOXPmUDy0EE9O/pAKfVsxPG66TtgQ8SCnU5L4ZP4PlOrVnF6LR/Joh8fYtH0LXbt2JVeuXKbjyRkqIsR9REXBL7/AkiVQvz507+4UEq+8Anv3mk4nIpeSng5Dh0L58vDcc3D99c7Wq3HjnF+LiHiQ+vXrs3DnSiZMmECQXwDtfnmHqv0fYsya38nIyDAdT0QuISUtlf5Lx1K6dwvenNWHeiWrszJuJYMHD6ZYsWKm48m/qIgQ91OzplNIrF4NLVs6J2xERcHTT8OWLabTichZtg0TJ0K1as4pGKGhMHUqzJvnzH0REfFQlmXRvHlzVuzbwMiRI0m3M2g15g2qfvsQo1bP1AoJETeSlp7G98sncUOfB3ju108olS+CefPmMXnDPM2BcGMqIsR9VawIP/3kHPn5+OPw44/OSRvt2sGqVabTieRcGRnOTJfq1aFFC0hOhpEjYdkyuOsuZ/6LiIgX8PHxoXXr1qzev5nhw4eTnpFBm7FvUbFvK35cMYVUzZAQMSY1PY0flk/mhj4P0HFid/IHhzJt2jTm71hOvXr1TMeT/6AiQtxfVBT06wfbtjnbNCZNgipVoHlzWLzYdDqRnCMtzTnppnJlePBBSEyE77+HtWuhdWvw0bcUEfFOvr6+PPTQQ6zav4lRo0YR6BdA+wndKNP7PvosHsXpFJ2yIeIqyWkpDFo2nnLf3E+Hie8TGpibCRMmsHTPGpo0aaJBlB5Cd43iOYoWhc8+gx074P334Y8/oHZtuPNOmDXLWSYuIlkvJcUpHMqXd1YkWRaMGOEUEO3b6yQMEckxfH19adWqFSv2bWDy5MlEhBbkhWmfU7JnU96PGcihU0dNRxTxWgnJp/lq4VCu79WCpyb3oECuMCZNmsSyveto3ry5CggPoyJCPE/+/PDuu04h8eWXzlT+Bg2cUmLiRGfZuIhcuyNH4OOP4brroGNHCAlxBlDGxUGbNuDrazqhiIgRlmXRtGlT/tixgvnz51O7eGW6xQwk8uumPDP5I9Yf2m46oojXOJAQT9fZ/Yn8uimvzOxJmfASzJw5k8W7V9OsWTMVEB5KRYR4rjx54OWXYetWGDAADh929qtXqeJM8E9ONp1QxDNt2QIvvAAlSsBbb0GlSjB9ujMDomVLbcEQETnDsizq1q3L5A3zWLt2LY90eJQfVkyhfN8HuGtoZ6ZtWqCTNkSu0uoDm3li4gdEft2UHvO+o/51N/Lnn38yZ1ssDRs2VAHh4XQ3KZ4vKAieego2bHAKCHAm+BcrBi++6Lx6KyKXZ9vOaRf33w9lyjjl3oMPwsqVMHMmNG6sIZQiIpdRvnx5Bg4cyK59u+nevTsr9m/g7mEvckOfB+j553COJZ40HVHE7aVnpDNlw3wa/vQclfu3Yfiq6XR4oiPrN6znl3WzqV27tumIkkVURIj38PNz9q/HxcGMGc52jW+/hapVnSNBv/0Wjh0znVLEvRw/Dn36OAMob7sN5syBN96A7dvhhx+cFUYiIpJpBQsWpGvXruyI38uwYcMokCsvL834ioiv7uKJiR+wbO860xFF3M6R08f5cuFQyn7TkmYjXmLdoe306NGDXfv38O2331K2bFnTESWLqYgQ7+PjA40awahRsHcv9OzpbNN49lln4OUjj0BMjIZbSs62fLmzkigiwtmGERQEgwfDrl3w0UfOiiIREblqAQEBtG3bloW7VrJs2TLaPvYwI1bPIHrgI9w44GEGxI7jRFKC6Zgixti2zZ+74mg/vhsRX93NqzN7EhFSiFGjRrEtfjdvvfUW4eHhpmNKNlERId4tPNzZnrFyJSxd6kz4nzQJbr/dWX7eowfs2WM6pYhrnDgB333nDHatUcPZytSqFSxZArGx8PjjkDu36ZQiIl6nRo0aDBo0iD0H99GnTx/SMtJ5ZsrHFPmiMY+Nf4+525dploTkGPGnj9F70Uiq9G9DnSEdGbduNh2e7MjKlSuZt+MvWrVqhb+/v+mYks1UREjOYFkQHQ39+8O+ffDTT1C8OLzzDkRGwj33wC+/OMcUiniT9HT47Td4+GEoUsQpG44dg6+/dkq4775zti6JiEi2y5s3L506dWLFvg0sWbKERzo+xoT1MdT/4WlK976PbnMGsOXIbtMxRbJcWnoa0zYtoPWYNyn25V28OP0Lgv0CGThwIPviD9CvXz+qaDtojqLD3yXnyZXL2Z7xyCOwebPzg9gPPzhD+goWhEcfdY4qrFDBdFKRq7dhA/z4I/z8M+zeDWFhzt/t9u2hVi0NnhQRMciyLGrWrEnNmjX5+uuvGT9+PN937U33uYN5f+4gbi5ehYer3EWrig0pkDuv6bgiV8W2bVbu38jQuGkMWzWN/QnxhAeH8ezzz9GxY0cVDzmcigjJ2UqXdvbDd+/uDLgcMgR69YIvv3R+WHvgAWje3NnGIeLudu2CsWOd+SiLFzvzUpo0cf4+33uvMwdCRETcSq5cuWjXrh3t2rVj165dDBs2jKFfDaLT1E/pPO0LGl5fizaVGtHihvqEBeUxHVfkP205sptRq2cyfNV01hzaip+PL03L1uORHi/QtGlTAgICTEcUN6AiQgScEzfuucd5HDjgvIr888/QpYvzKF/e+UGueXOnoBBxFzt3OuXDmDGwaJHzsWrV4PPPnVNkihY1m09ERDKtRIkSvPHGG7z++uvExcUxcuRIRn77E+0ndCPA159G19fmgQp3cm+5W8kXHGo6rsjfth/dy9i1sxi15jdi964F4JYSVenXrx+tWrXS0Em5gFsUEZZlfQA0BzKAg0B727b3mk0lOVbhwvDqq85j2zaYPBkmToQvvoBPP4VChSgXHQ0nTzpHhAYHm04sOc2lyoePPnJW8WgFj8hV0f2IuAvLsqhatSpVq1blo48+YvHixYwZM4axQ4YzZeN8/Hx8qX/djdx3w+00v+E2IkILmY4sOdD6Q9sZv34Ov6yb83f5EF2sAp9++imtW7emZMmShhOKO3OLIgL43LbtrgCWZXUG3gWeMRtJBIiKgs6dncfRozBtGkyaRMEpU2DqVKeEaNTIWSlxzz1QSDcCkg3S052tFr/+ClOmQFyc8/Hq1Z3y4cEHnW1GInKtdD8ibseyLGrXrk3t2rX54osviI2NZdy4cfwyaASdpn5Kp6mfEl2sAs3K1qNp2XpUL1oOS3OAJBukZ6SzaPcqJm2Yx8T1c9kQvwOAWhGV+PTTT3nggQcoVaqU4ZTiKdyiiLBt+8R57+YGbFNZRC4pXz5o2xbatmXBb79xGzgrJSZNct5aFtSpc24LR7lyphOLJzt61JlbMmUKTJ8O8fHg6wu33OKszGnZUuWDSBbT/Yi4u/OHXH788cesW7eOSZMmMbHvcLrFDOS9mAEUzVOAu8rU4a7SdWhQqhZ5g0NMxxYPFn/6GDM2L2LqpgVM37yQ+MTjf6/Ieb7bq7Ro0YLixYubjikeyLJt9/gea1lWD+BR4Dhwu23bhy7xeU8BTwEULlz4xpEjR2ZpjoSEBPLk0SCg8+maXOgf18S2ybN5MwUWLCB84UJCNm0C4HSJEsTffDPHqlbleKVKpIV6915O/T250JVcEystjZCNG8m7fDn5lywhbPVqrIwMUsLCOHLTTcTXrs3RmjVJC/H8G0r9XblQVl+T22+/fZlt29FZ9gVzkKu5H4mMjLxxx44drgspchEHDx5k2rRp/Prrr8ycNI3jyQn4Wr7UKl6RhqVq0fD6WtwUUQl/X7d4HVLcVGp6Got3r2bmlkXM2PInS/esxcamQK683HV/M5o2bUrjxo0JCwszHVU8gGVZl7wfcVkRYVnW70CRi/zW27ZtTzzv894Egmzbfu+/vmZ0dLQdGxubhSkhJiaG+vXrZ+nX9HS6Jhe67DXZufPcXImYGEhNdT5esSLUrQv16jlvvWzfnP6eXOiy1yQ9HZYvhzlznMf8+ZCQ4PxetWrnhqfedJOzEsKL6O/KhbL6mlzuG39O5yn3IyLXIi0tjUWLFjFjxgxmfj/+7x8mc/sHc2vJ6tweFU39626kepFy+KmYyNHSM9JZuX8Tc7bHMnvbUubtWE5Cyml8LB9qRVSi8RMtadKkCdHR0fh62f2IZL/L3Y+47F8e27YbZPJThwO/Av/5jV/ELUVGQqdOziMxEZYuhT/+cH7QHDECBgxwPq9EiX8WExUrOsctindKS3NmO8TEOMXDvHlw4swq8PLl4dFH4fbb4bbboGBBo1FFvJnuRyQn8PPzo27dutStW5cPPviAI0eOEBMTw6xZs5g9eirTfusNQEhAbuqUqMKtJatTN7IaNSMqEOyvo569WXJaCn/tW8/8HcuZv3MF83cs53iy80JIufCSPPL4YzRo0IA77riDvHnzGk4r3swtKlDLssrYtr3pzLv3AutN5hHJMsHBcOutzgOcV8FXrTpXTMTEOOUEODMobrnlXDlx440QGGgsulwD24adOyk4Z44z42HxYli2zCmmwDnVok0bp3ioXx+KXOzFWRFxNd2PiLfKnz8/LVu2pGXLltAX9u3bx7x585g7dy5zx87g7dn9APDz8aV6kXLcXKIKtYtXolZEJaLyRWj4pQfbe+IQi/esZtHuVSzcFcfSPWtJTk8BoGx4JK0efYjbbruN+vXrExERYTit5CRuUUQAn1iWVQ7nuKwdaEK1eCtfX2fZfbVq8Pzzzg+s27adKyb++MP5wRUgKAhq1oQaNaByZahUCSpUAC+YEeB1jh1zVr4sWeKUDkuWwIEDVASnTKpRA556CmrVckomDXUScVe6H5EcoWjRorRu3ZrWrVtDP4iPj2fhwoUsWLCAP0f+xqBl4+m92JnDFh4cRnSxCtSMqECNojdQo+gNRIYVUTnhhg6dOspf+9azbO86YveuY8meNew5eRAAfx8/ahS9gec6d+KWW26hbt26FC5c2HBiycncooiwbft+0xlEjLAsKFXKeTz6qPOxQ4dgwQKnlPjjDxg0CE6fPvdnrrvOKSXOlhOVKjkndGj1RPZLTIR162D1auexapXzdvfuc59zww3QuDHUqkWsry/RHTpAQIC5zCKSabofkZwqPDycZs2a0axZM/jkE1JTU1m9ejVLlixhyZIlLJ0yj4/n/0C6nQ5AvqBQqhYpQ9XCZalSuDSVC5emfIEo8gTmMvxfkjOkpqexKX4ncQc2sergZlbs38jK/Zv+Lh0ASucvwW3NGlCzZk1q1apF9erVCQrSthtxH25RRIjIeQoWhBYtnAdARgZs337hD7/TpztzB8BZaVG27D/LiUqVnIJDg4Wu3PHjzkqVjRvPXffVq2HzZmcVCzjFT/nyztaKihWdrTQ1a8J5+ykTYmJUQoiIiMfx9/enevXqVK9enaeffhqAxMREVq5cyfLly1mxYgUrfl3AoL/Gczo16e8/d13eYlQoGEX5AlGUK1CScuElKRseSeE84VpBcRVOJp9iU/wu1h/ezob4Haw7tI21h7ayMX4nqRnOPaCfjy83FLiO+vc2pHr16tSoUYPq1atrvoO4PRURIu7Ox+fcqol77z338ZQU2LTpn+XEsmUwZsy5H5aDgpyhmOc/IiP/+b6XHyt6UUlJsGOHUzb8+7F1Kxw9eu5zfXycmQ5VqkDbtufKnuuvBz/9EyoiIjlDcHAwtWvXpnbt2n9/LD09na1bt7J69WrWrFnDmjVrWDtnGbO3xZKUlvz35+UJyEXp/MW5Pl9xSuWLICpfBNflLUpkWBFKhhXNsSspUtPT2HPiIDuO72PHsX1sO7aXrUf3sOXIbjYf2c2BU/F/f66P5UNU3mJUqFudZhVbUbFiRSpXrswNN9xAoFbFigfSXbSIpwoIcF6Jr1gRWrc+9/FTp5ztA6tWwdq1znGiu3bBrFmwd6+zwuJ8oaEXlhNnH+HhEBbmvMofEuLeqyvS0yE+Hg4e/Ofj0KFzvz5wwCkg9u79558NCHC2vERFOasaoqKcR+nSzqoHLWUUERG5gK+vL2XKlKFMmTLcd999f388IyODHTt2sHHjRjZt2sSmTZvYvHkzqxevYfLG+aSkp/7j6+QNCqF4aCEiQgoREVqQonkKUDSkAEXyhFMod34K5c5HwVz5yBsUgo8HnDB2OiWJQ6ePcujUUQ6cOsKBhHj2J8SzL+Ewe08eYs+JQ+w6cYD9CfFk2OfuyywsIkILUSpfBE3btKB06dKUKVOGcuXKUaZMGRUO4lVURIh4m9y5ITraefxbWprzQ/iuXeceZ4uKXbsgNtb5wf1SQkLOFRNhYf/4ddTx486gxrAwyJXLKS18fM49Lve+r68zLyMlxZmHcanHqVMXvn/4sFMyxMefWwlyPh8fZ7tLoULO24YNndUlZ8uGqCgoWlRHp4qIiGQRHx8foqKiiIqKonHjxv/4vYyMDPbt28eOHTvYvn07O3fuZPfu3ezatYs9S52ZB//+Af3vr2v5kC8ohPzBYeQLDiFvUAhhgXkIC8pDSEAu8gTkIndAELn9gwn2DyTYL4hAP38CfQMI8PXH39cPX8sHXx8ffC1fLMvCAmwgPSOdDNsmLSONtIx0UjPSSElPJSkthaS0FBJTkziVmsSplEROpSZyIvkUJ5NPcyI5gWNJCRxNOsHRxJPEJx7/x2qQ84UF5qFYSEEiql1Po+LRlChRgsjISEqWLPn3Q2WD5BQqIkRyEj8/Z/VDZOSlPycx0Rm+uHs3HDnizEs4ftw5GeLsr8++v38/bNgAx49T4uhRGD48e3L7+DjlRq5cTtFy9te5cjnDIW+91Skazg7i0MQAAAliSURBVD7OFg+FCkH+/CoZRERE3ISPjw8RERFERERQp06di35Oeno6hw8fZv/+/Rw4cIBDhw5x6NAhDh8+zJEjRzhy5AjHjh3j2Oo97Dy+n+NJCSSkJJKQchqbi7wokcUCfP0JDcz99yNvUAil61QmX758hIeHU6BAAcLDwylUqBCFChWicOHCFClShODg4GzPJuIpVESIyD8FBzszEcqUuaI/Nm/OnP+3d68xdhRkGMf/D9vuumwwosWCQrhELkFsi1ogURJRFLykggZvqCR8UDH1g4Qo2KBENBLA8EGNCUaCGtFo5GIAI2AIGBO8QqFEimBALkHBSPzQuqXt64czbbc7291W25lD9/9LTtqZM2f2PW/O7nn32Zk5vOXEEwchxbp1g1NAttw2bdrx8tT/j41tHzJsuY2ODo6YkCRJe72RkREWL168yx8vWVWsW7eO9evXb/13cnKSyclJNmzYwMaNG7feNm/eTE05knJkZGTrbcGCBYyOjrJw4ULGxsYYHx9nfHycfffdl4mJCRZ4jSjp/+Z3kaTdI9kWHEiSJHUsCRMTE0xMTPRdiqQ5eLyyJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqjEGEJEmSJEnqTKqq7xr+Z0meBR7fzbtdBDy3m/f5YmdP2uxJmz1psyczsy9tu7snh1bVAbtxf5qF80hn7EmbPWmzJ232pM2ezKyzeeRFHUTsCUn+UFVv7LuOYWJP2uxJmz1psyczsy9t9kTT+Zposydt9qTNnrTZkzZ7MrMu++KpGZIkSZIkqTMGEZIkSZIkqTMGEW1X913AELInbfakzZ602ZOZ2Zc2e6LpfE202ZM2e9JmT9rsSZs9mVlnffEaEZIkSZIkqTMeESFJkiRJkjpjECFJkiRJkjpjEDGDJJ9JsjbJg0ku77ueYZDkkiRPJbmvub2r75qGRZILklSSRX3X0rcklya5v3mN3JbkVX3X1LckVyR5qOnLDUle1ndNfUtyVvPzdXOSef3RWUlOb95vHklyYd/1aLg4j2zPWWR2ziPbOI+0OY+0OY9s08c8YhAxTZJTgPcCS6rqtcCVPZc0TK6qqmXN7da+ixkGSQ4B3g78re9ahsQVVbWkqpYBNwNf7LugIXA7cFxVLQEeBi7quZ5hsAZ4H3B334X0KckI8C3gncCxwIeTHNtvVRoWziM75CwyA+eRFueRNueRNucR+ptHDCLazgMuq6pJgKr6R8/1aLhdBXwO8KqvQFX9e8riBPaFqrqtqjY2i/cAB/dZzzCoqj9X1dq+6xgCJwCPVNVfq2oD8GMGv3hK4DyiXeM8MoXzSJvzSJvzyFa9zCMGEW1HAScn+W2Su5Is77ugIbKyOZzrmiT7911M35KsAJ6qqtV91zJMknw1yRPA2fgXiOnOBX7RdxEaGq8Gnpiy/GSzTgLnkR1xFpnGeWRmziOzch7RVL3MIwv29BcYRknuAA6c4a5VDHqyP3ASsBz4SZIjah58zukcffk2cCmDRPlS4OsMfojt1eboyReAd3RbUf9m60lV3VRVq4BVSS4CVgJf6rTAHszVk2abVcBG4Idd1taXnemJyAzr9vr3Gm3jPNLmLDIz55E255E255E255Gd0ss8Mi+DiKo6dUf3JTkPuL55o/9dks3AIuDZrurry2x9mSrJdxicb7fX21FPkrwOOBxYnQQGh7f9KckJVfVMhyV2bmdfJ8B1wC3Mgzf+uXqS5BzgPcDb9vZfIrbYhdfJfPYkcMiU5YOBp3uqRT1wHmlzFpmZ80ib80ib80ib88hO6WUe8dSMthuBtwIkOQoYBZ7rtaIhkOSgKYtnMri4y7xVVQ9U1Sur6rCqOozBN/Dr9/Y3/bkkOXLK4grgob5qGRZJTgc+D6yoqnV916Oh8nvgyCSHJxkFPgT8vOeaNDycR6ZxFmlzHpmZ80ib84hm0cs8Mi+PiJjDNcA1SdYAG4Bz5ktiOIfLkyxjcJjOY8An+y1HQ+qyJEcDm4HHgU/1XM8w+CYwBtze/LXqnqqa131JcibwDeAA4JYk91XVaT2X1bmq2phkJfBLYAS4pqoe7LksDQ/nkTZnEe0s55E255FpnEcG+ppH4nuaJEmSJEnqiqdmSJIkSZKkzhhESJIkSZKkzhhESJIkSZKkzhhESJIkSZKkzhhESJIkSZKkzhhESJIkSZKkzhhESJIkSZKkzhhESNpOkn2SfCXJDUmOSbIkydVJvp9kQbPNeJK7kow0y6cm+cEO9vflJA8keTjJJ5KMJrl7y74kSZIkzS8GEZKm+wDwK+CnwJ3AScDFwBnAYc025wLXV9WmZnkpcO/0HSU5DTgeWAa8HzijqjY0+//gnnsKkiRJkoaVQYSk6RZX1Z0MgoiXVtXVVfV34DHg8Wabs4GbpjxmKXBgkl8neSbJqc36FcC1wEJgJfCzZv2NzT4kSZIkzTMGEZKmezTJKVX1AjAGkOSjwMVV9UKSUeCIqnpsymOWAs9V1cnAp9kWMrwB2A/4J/Bm4EfN+jXA8j3+TCRJkiQNHYMISdupqpuBI5KMA0lyCfA14Kxmk0XA81u2T7IQeDlwZbNqAfB8kn2Ag6vq2uYxfwTOb77GJmBDkv32+BOSJEmSNFQMIiS1VNV3q2o9UAxCiI8Db2ruXg+8ZMrmxwKrq2pzs7yEwREPRwN/afa3HvgNMDLlcWPAf/bUc5AkSZI0nAwiJG0nybuTHJLkNQxOt5gE1gKHJlleVf8CRpJsCSOWAqun7GIJcD+Di1SOJRlJMgZ8hMG1IUjyCuDZ5vQPSZIkSfOIQYSk6e4ALgCuAy4EqKqnGVzf4aBmm9sYXPMBBkHE/VMefxyDIyKWAePAowyOhvheVW0JLE4Bbt1zT0GSJEnSsEpV9V2DpBeZJMcD51fVx2bZ5nbgs1W1Zob7rgcuqqq1e7BMSZIkSUPIIyIk7bKquhe4M8nILJsdAzw0fWXzqRs3GkJIkiRJ85NHREiSJEmSpM54RIQkSZIkSeqMQYQkSZIkSeqMQYQkSZIkSeqMQYQkSZIkSeqMQYQkSZIkSeqMQYQkSZIkSeqMQYQkSZIkSerMfwFKpFMicANUxgAAAABJRU5ErkJggg==\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AM2 = { \"Nom\":\"AM2\", \"p\":1, \"aa\":[1,0], \"bb\":[8/12,-1/12], \"bm1\":5/12 }\n", "polyCar(AM2)\n", "Astabilite(AM2)" ] }, { "cell_type": "code", "execution_count": 41, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r**3 - r**2'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=0.375*r**3 + 0.791666666666667*r**2 - 0.208333333333333*r + 0.0416666666666667'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AM3 = { \"Nom\":\"AM3\", \"p\":2, \"aa\":[1,0,0], \"bb\":[19/24,-5/24,1/24], \"bm1\":9/24 }\n", "polyCar(AM3)\n", "Astabilite(AM3)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r**4 - r**3'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=0.348611111111111*r**4 + 0.897222222222222*r**3 - 0.366666666666667*r**2 + 0.147222222222222*r - 0.0263888888888889'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "AM4 = { \"Nom\":\"AM4\", \"p\":3, \"aa\":[1,0,0,0], \"bb\":[646/720,-264/720,106/720,-19/720], \"bm1\":251/720 }\n", "polyCar(AM4)\n", "Astabilite(AM4)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r**2 - 1'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=0.333333333333333*r**2 + 1.33333333333333*r + 0.333333333333333'" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "MS2 = { \"Nom\":\"MS2\", \"p\":1, \"aa\":[0,1], \"bb\":[4/3,1/3], \"bm1\":1/3 }\n", "polyCar(MS2)\n", "#Astabilite(MS2)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r**2 - r'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=r**2'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BDF1 = { \"Nom\":\"BDF1=EI\", \"p\":1, \"aa\":[1], \"bb\":[0], \"bm1\":1 }\n", "polyCarIMPL(BDF1)\n", "Astabilite(BDF1)" ] }, { "cell_type": "code", "execution_count": 45, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "'rho(r)=r**2 - 1.33333333333333*r'" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "'sigma(r)=0.666666666666667*r**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": [ "BDF2 = { \"Nom\":\"BDF2\", \"p\":1, \"aa\":[4/3,-1/3], \"bb\":[0], \"bm1\":2/3 }\n", "polyCarIMPL(BDF2)\n", "Astabilite(BDF2)" ] }, { "cell_type": "code", "execution_count": 46, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BDF3 = { \"Nom\":\"BDF3\", \"p\":2, \"aa\":[18/11,-9/11,2/11], \"bb\":[0], \"bm1\":6/11 }\n", "# polyCarIMPL(BDF3)\n", "Astabilite(BDF3)" ] }, { "cell_type": "code", "execution_count": 47, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BDF4 = { \"Nom\":\"BDF4\", \"p\":3, \"aa\":[48/25,-36/25,16/25,-3/25], \"bb\":[0], \"bm1\":12/25 }\n", "# polyCarIMPL(BDF4)\n", "Astabilite(BDF4)" ] }, { "cell_type": "code", "execution_count": 48, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BDF5 = { \"Nom\":\"BDF5\", \"p\":4, \"aa\":[300/137,-300/137,200/137,-75/137,12/137], \"bb\":[0], \"bm1\":60/137 }\n", "# polyCar(BDF5)\n", "Astabilite(BDF5)" ] }, { "cell_type": "code", "execution_count": 49, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "BDF6 = { \"Nom\":\"BDF6\", \"p\":5, \"aa\":[120/49,-150/49,400/147,-75/49,24/49,-10/147], \"bb\":[0], \"bm1\":20/49 }\n", "# polyCar(BDF6)\n", "Astabilite(BDF6)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercice\n", ">Pour les méthodes d'Euler explicite et implicite:\n", ">1. Trouver les coefficients $p\\ge0$, $\\{a_k\\}$ et $\\{b_k\\}$ tels que $$\n", "u_{n+1} \n", "= \n", "\\sum_{j=0}^p a_ju_{n-j}\n", "+\n", "h\\sum_{j=0}^p b_j\\varphi(t_{n-j},u_{n-j})\n", "+\n", "hb_{-1}\\varphi(t_{n+1},u_{n+1}),\n", "\\qquad\n", "n=p,p+1,\\dots,N-1\n", "$$\n", ">1. Écrire le premier polynôme caractéristique \n", "$$\n", "\\varrho(r)=r^{p+1}-\\sum_{j=0}^p a_jr^{p-j}\n", "$$\n", "et en calculer les racines.\n", ">1. Montrer que la méthode est zéro-stable, i.e. que\n", "$$\n", "\\begin{cases}\n", "|r_j|\\le1 \\quad\\text{pour tout }j=0,\\dots,p\n", "\\\\\n", "\\varrho'(r_j)\\neq0 \\text{ si } |r_j|=1.\n", "\\end{cases}\n", "$$\n", ">1. Montrer que la méthode est consistante, i.e.\n", "$$\n", "\\begin{cases}\n", "\\displaystyle\\sum_{j=0}^p a_j=1,\n", "\\\\\n", "\\displaystyle-\\sum_{j=0}^p ja_j+\\sum_{j=-1}^p b_j=1\n", "\\end{cases}\n", "$$\n", ">1. Étudier l'ordre de consistance $\\omega\\ge2$ \n", "$$\n", "\\sum_{j=0}^p (-j)^{i}a_j+i\\sum_{j=-1}^p (-j)^{i-1}b_j=1 \\quad i=2,\\dots,\\omega.\n", "$$\n", ">5. Étudier la A-stabilité" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Euler explicite\n", "\n", "1. $u_{n+1}=u_n+h\\varphi(t_n,u_n)$ donc $p=0$, $a_0=1$, $b_{-1}=0$, $b_0=1$\n", "2. $\\varrho(r)=r-1$ donc il n'y a qu'une racine: $r_0=1$\n", "3. $|r_0|=1$ et $\\varrho'(1)=1$\n", "4. $a_0=1$ et $-0a_0+b_{-1}+b_0=1$\n", "4. Pour $i=2$ on a $(-0^2a_0)+2((+1)^{1}b_{-1}+0^{1}b_0)=0\\neq1$ donc $\\omega0$ et $\\Re(\\beta)<0$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "colab": { "collapsed_sections": [], "default_view": {}, "name": "EdoExplicites.ipynb", "provenance": [], "version": "0.3.2", "views": {} }, "hide_input": false, "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.5" }, "latex_envs": { "LaTeX_envs_menu_present": true, "autoclose": true, "autocomplete": true, "bibliofile": "biblio.bib", "cite_by": "apalike", "current_citInitial": 1, "eqLabelWithNumbers": true, "eqNumInitial": 1, "hotkeys": { "equation": "Ctrl-E", "itemize": "Ctrl-I" }, "labels_anchors": true, "latex_user_defs": false, "report_style_numbering": true, "user_envs_cfg": true }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": true, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": true, "toc_position": { "height": "calc(100% - 180px)", "left": "10px", "top": "150px", "width": "307px" }, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }