{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"data": {
"text/html": [
"\n",
"\n",
"\n",
"\n",
"\n",
"\n"
],
"text/plain": [
""
]
},
"execution_count": 2,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"%reset -f\n",
"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": "markdown",
"metadata": {
"toc": true
},
"source": [
"Table of Contents
\n",
""
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# M62-CM8 : Correction Contrôle Continu 2019\n",
"\n",
"Soit le schéma de Runge-Kutta dont la *matrice de Butcher* est\n",
"$$\n",
"\\begin{array}{c|cc}\n",
"0 & 0 & 0\\\\\n",
"\\alpha & \\alpha & 0\\\\\n",
"\\hline\n",
" & \\frac{2\\alpha-1}{2\\alpha} & \\frac{1}{2\\alpha}\n",
"\\end{array}\n",
"$$\n",
"\n",
"Chaque sujet correspond à une valeur de $\\alpha$ choisie parmi les suivantes:\n",
"$$\n",
"\\left\\{\\frac{1}{6},\\frac{1}{4},\\frac{1}{3},\\frac{5}{12},\\frac{7}{12},\\frac{2}{3},\\frac{3}{4},\\frac{5}{6},\\frac{11}{12}\\right\\}\n",
"$$"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"c_2=a_{21}= 1/6 \tb_1= -2 \tb_2= 3\n",
"c_2=a_{21}= 1/4 \tb_1= -1 \tb_2= 2\n",
"c_2=a_{21}= 1/3 \tb_1= -1/2 \tb_2= 3/2\n",
"c_2=a_{21}= 5/12 \tb_1= -1/5 \tb_2= 6/5\n",
"c_2=a_{21}= 7/12 \tb_1= 1/7 \tb_2= 6/7\n",
"c_2=a_{21}= 2/3 \tb_1= 1/4 \tb_2= 3/4\n",
"c_2=a_{21}= 3/4 \tb_1= 1/3 \tb_2= 2/3\n",
"c_2=a_{21}= 5/6 \tb_1= 2/5 \tb_2= 3/5\n",
"c_2=a_{21}= 11/12 \tb_1= 5/11 \tb_2= 6/11\n"
]
}
],
"source": [
"from fractions import Fraction\n",
"ALPHA=[Fraction(2,12),Fraction(3,12),Fraction(4,12),Fraction(5,12),\n",
" Fraction(7,12),Fraction(8,12),Fraction(9,12),Fraction(10,12),Fraction(11,12)]\n",
"for alpha in ALPHA:\n",
" print(\"c_2=a_{21}=\",alpha,\"\\tb_1=\",1-Fraction(1,2*alpha),\"\\tb_2=\",Fraction(1,2*alpha))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercice: écriture schéma\n",
"\n",
"Écrire le schéma sous la forme d'une suite définie par récurrence."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Correction : écriture schéma\n",
"\n",
"Considérons le problème de Cauchy\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",
"Pour $h>0$ soit $t_n\\stackrel{\\text{déf.}}{=} t_0+nh$ avec $n=0,1,2,\\dots,N$ une suite de $N+1$ nœuds de $I$ induisant une discrétisation de $I$ en $N$ sous-intervalles $I_n=[t_n;t_{n+1}]$ chacun de longueur $h>0$ (appelé le *pas de discrétisation*).\n",
"\n",
"Pour chaque nœud $t_n$, on cherche la valeur inconnue $u_n$ qui approche la valeur exacte $y_n\\equiv y(t_n)$. \n",
"- L'ensemble de $N+1$ valeurs $\\{t_0, t_1=t_0+h,... , t_{N}=T \\}$ représente les points de la discrétisation. \n",
"- L'ensemble de $N+1$ valeurs $\\{y_0, y_1,... , y_{N} \\}$ représente la solution exacte. \n",
"- L'ensemble de $N+1$ valeurs $\\{u_0 = y_0, u_1,... , u_{N} \\}$ représente la solution numérique. Cette solution approchée sera obtenue en construisant une suite récurrente.\n",
"\n",
"Le schéma qu'on va construire permet de calculer explicitement $u_{n+1}$ à partir de $u_n$ et il est donc possible de calculer successivement $u_1$, $u_2$,..., en partant de $u_0$ par la formule de récurrence\n",
"$$\\begin{cases}\n",
"u_0\t = y_0 \\\\\n",
"K_1 = \\varphi\\left(t_n,u_n\\right)\\\\\n",
"K_2 = \\varphi\\left(t_n+\\alpha h,u_n+\\alpha hK_1\\right)\\\\\n",
"u_{n+1} = u_n + \\frac{h}{2\\alpha} \\left((2\\alpha-1)K_1+K_2\\right) & n=0,1,\\dots N-1\n",
"\\end{cases}$$\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercice : étude de la A-stabilité\n",
"Étudier théoriquement la A-stabilité."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Correction : étude de la A-stabilité"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"**Définition de A-stabilité**\n",
">Soit $\\beta>0$ un nombre réel positif et considérons le problème de Cauchy\n",
"$$\\begin{cases}\n",
"y'(t)=-\\beta y(t), &\\text{pour }t>0,\\\\\n",
"y(0)=y_0\n",
"\\end{cases}$$\n",
"où $y_0\\neq0$ est une valeur donnée. Sa solution est $y(t)=y_0e^{-\\beta t}$ donc $$\\lim_{t\\to+\\infty}y(t)=0.$$\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.**"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Le schéma donné appliqué à cette équation devient"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle - \\beta u_{n}$"
],
"text/plain": [
"-β⋅uₙ"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle \\beta u_{n} \\left(A \\beta h - 1\\right)$"
],
"text/plain": [
"β⋅uₙ⋅(Α⋅β⋅h - 1)"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle u_{np1} = \\frac{u_{n} \\left(\\beta^{2} h^{2} - 2 \\beta h + 2\\right)}{2}$"
],
"text/plain": [
" ⎛ 2 2 ⎞\n",
" uₙ⋅⎝β ⋅h - 2⋅β⋅h + 2⎠\n",
"uₙₚ₁ = ──────────────────────\n",
" 2 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"import sympy as sym\n",
"sym.init_printing()\n",
"sym.var('h,Alpha,beta,u_n,u_np1')\n",
"\n",
"Phi=lambda y : -beta*y\n",
"\n",
"K_1=Phi(u_n)\n",
"display(K_1)\n",
"K_2=Phi(u_n+Alpha*h*K_1)\n",
"display(K_2.expand().factor(u_n))\n",
"display(sym.Eq(u_np1,(u_n+h/(2*Alpha)*((2*Alpha-1)*K_1+K_2 )).factor()))"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"c'est-à-dire\n",
"$$\\begin{cases}\n",
"u_0\t = y_0 \\\\\n",
"u_{n+1} = \\dfrac{2 - 2(\\beta h) + (\\beta h)^2}{2}u_n & n=0,1,\\dots N-1\n",
"\\end{cases}$$\n",
"Par induction on obtient\n",
"$$\n",
"u_{n}=\\left(1 - (\\beta h) + \\frac{1}{2}(\\beta h)^2 \\right)^nu_0.\n",
"$$\n",
"Notons que $u_n$ ne dépend pas du choix de $\\alpha$.\n",
"\n",
"Étant une suite géométrique, $\\lim\\limits_{n\\to+\\infty}u_n=0$ si et seulement si \n",
"$$\n",
"\\left|1 - (\\beta h) + \\frac{1}{2}(\\beta h)^2\\right|<1.\n",
"$$\n",
"Notons $x$ le produit $\\beta h$ et $q$ le polynôme $q(x)=\\frac{1}{2}x^2-x+1$. "
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"|q(x)|<1 ssi "
]
},
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle x < 2$"
],
"text/plain": [
"x < 2"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"q'(x)=\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAC4AAAAOCAYAAABQFS4BAAAACXBIWXMAAA7EAAAOxAGVKw4bAAABSElEQVRIDdWV203DQBBFE5QCEHSQEgh0EDogUAHQAYgv+w+FFiiBdABUkJAOoIQoHZhzrPVqsYTkL3tzpeuZfSR7ZzyzHldVNcodZVmeofENzvD36p34yBEIPEbXK9zBcziFETkLN7MLlRLEA8asRxxF78CcgxUeSyXU1F1I/AX2FlpXN2FuzZ5V8Ac3acaXCHuRqFpDG2PO+BFroyxhNqgzjjgznQqzMa6gWRcnMF2vJ4d8NKWyQfxPImSGv2XOAEbYuruT9T8u676RT6jtigW/23bd3N7XZLz9B9dsfG5v/m+MAAM02N6Q1nh9KCLmOGYuNqIZlb2p6nDQJAjyc2pzfmDv4R4/LZ0nxjZpNjDjZljuQhB+YiOYc81bZkichsO9JGqMi6KwBLwxvp1BqFeiN8ol/IIGFMuGcW/gXCtBNOVrL1oJ77+zk16agmP5dQAAAABJRU5ErkJggg==\n",
"text/latex": [
"$\\displaystyle x - 1$"
],
"text/plain": [
"x - 1"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"q'(x)=0 ssi x=\n"
]
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAAgAAAAOCAYAAAASVl2WAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAAZElEQVQYGWP8//8/Aww0NDQYAdmrgdgYyP4AEmcBMgSA9GwgfgfEJkCsBMRwAFIAUhkKEgGyy4AUyBQ4YIKzcDBGFUACBj0chKHhJQQLN0ZQZAGDGBRBIOACxKC4OQfE94B4NwDm+hiAOyllRAAAAABJRU5ErkJggg==\n",
"text/latex": [
"$\\displaystyle 1$"
],
"text/plain": [
"1"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"Comme q(x_sommet)=\n"
]
},
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle \\frac{1}{2}$"
],
"text/plain": [
"1/2"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stdout",
"output_type": "stream",
"text": [
"donc q(x)>0 pour tout x et q(x)<1 ssi x< 2\n"
]
},
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"import sympy as sym\n",
"from sympy.plotting import plot\n",
"sym.init_printing()\n",
"sym.var('x',positive=True)\n",
"\n",
"q=1-1*x+x**2/2\n",
"print(\"|q(x)|<1 ssi\", end=' ')\n",
"display(sym.solve(abs(q)<1))\n",
"print(\"q'(x)=\")\n",
"dq=sym.diff(q,x)\n",
"display(dq)\n",
"print(\"q'(x)=0 ssi x=\")\n",
"x_sommet=sym.solve(dq)[0]\n",
"display(x_sommet)\n",
"print(\"Comme q(x_sommet)=\")\n",
"y_sommet=q.subs(x,x_sommet)\n",
"display(y_sommet)\n",
"print(\"donc q(x)>0 pour tout x et q(x)<1 ssi x<\",x_sommet*2)\n",
"sym.plot(q,1,-1,(x,0,x_sommet*2));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Il s'agit de la parabole convexe de sommet $\\left(1,\\frac{1}{2}\\right)$. \n",
"Nous avons $|q(x)|<1$ si et seulement si $x<2$. La relation $\\lim\\limits_{n\\to+\\infty}u_n=0$ est donc satisfaite si et seulement si\n",
"$$\n",
" h <\\frac{2}{\\beta}.\n",
"$$\n",
"Cette condition de stabilité limite le pas $h$ d'avance en $t$ lorsqu'on utilise le schéma.\n",
"\n",
"Nous avons $q(x)>0$ pour tout $x$ donc cette convergence est monotone."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercice : implémentation et test\n",
"Implémenter le schéma et le tester avec le problème de Cauchy utilisé pour la A-stabilité sur l'intervalle $[0;1]$. \n",
"On choisira le nombre minimal de points pour avoir A-stabilité.\n",
"\n",
"Chaque sujet correspond à une valeur de $\\beta$ choisie parmi les suivantes:\n",
"$$\n",
"\\left\\{50,60,70,80,90,100\\right\\}\n",
"$$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Correction : implémentation et test\n",
"$h<\\frac{2}{\\beta}$ sur l'intervalle $[0;1]$ impose $N>\\frac{\\beta}{2}$."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"def RKalpha(phi,tt):\n",
" uu = [y0]\n",
" for i in range(len(tt)-1):\n",
" k1 = phi( tt[i], uu[i] )\n",
" k2 = phi( tt[i]+h*alpha , uu[i]+h*alpha*k1 )\n",
" uu.append( uu[i] + h*((2*alpha-1)*k1+k2 )/(2*alpha))\n",
" return uu"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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kSZKklzA8StmM+okAPJOlodmSJEmSJA1SbPOSNbwT+XdpeJSymZNz4dGzWZt7VGgdHbBsmfOTJEmSJKnI1NTUsGfPHgOkEhBjZM+ePdTU1Izq65x5lLKB8KjUdx6tWwdbtsDatT65TZIkSZKKyJFH2T/77LNpl5I5XV1dow5i0lZTU8PcuXNH9TWGRykr+fCotha6uo6+3rAh91FTAwcPpleXJEmSJCkvVVVVnHHGGWmXkUktLS2cffbZaZeRONvWUjazvsTDo9ZWWLkS6upyr+vqYNUqaGtLty5JkiRJkpQXw6OUlfzMozlzoKEht/uopiZ3bGiA2bPTrkySJEmSJOXB8ChlJd+2BrBrF6xZA1u35o4OzZYkSZIkqWg48yhlJ/eHR7tLOTxqbj76+fr16dUhSZIkSZJGzZ1HKZtZn5vKXtI7jyRJkiRJUtEyPEpZQ20l1RUT2H+oh4PdvWmXUxw6OmDZMtvfJEmSJEkaB4ZHKQshDMw92l2qQ7MLbd062LIF1q5NuxJJkiRJkkqe4VEGzOgPj56xde3l1dZCCLBhA/T15Y4h5M5LkiRJkqREGB5lwMz6MnjiWiG0tsLKlVBXl3tdVwerVkFbW7p1SZIkSZJUwgyPMuBI29qztq29vDlzoKEBurqgpiZ3bGiA2bPTrkySJEmSpJJleJQBA+GRO49GtmsXrFkDW7fmjg7NliRJkiQpUZVpFyDDo1Fpbj76+fr16dUhSZIkSVKZcOdRBjjzSJIkSZIkZZXhUQY48yhlHR2wbJktcJIkSZIkDcHwKANO7g+PdrvzKB3r1sGWLbB2bdqVSJIkSZKUOYZHGTBjUNtajDHlaspIbS2EABs2QF9f7hhC7rwkSZIkSQIMjzKhtrqCyRMr6e7t44WDPWmXUz5aW2HlSqiry72uq4NVq6CtLd26JEmSJEnKEMOjjDg696gr5UrKyJw50NAAXV1QU5M7NjTA7NlpVyZJkiRJUmYkGh6FEM4PITwWQtgZQrhiiPenhBD+LYTw8xDCoyGEDyVZT5bN6A+PnnHu0fjatQvWrIGtW3NHh2ZLkiRJknSMyqRuHEKoANYD5wHtwLYQwuYY4y8GXXYp8IsY4wUhhJnAYyGEm2OM3UnVlVUDO48Mj8ZXc/PRz9evT68OSZIkSZIyKsmdR+cCO2OMrf1h0C3AhcddE4HJIYQA1AN7gbIc+jOz3vBIkiRJkiRlT5Lh0anAU4Net/efG+ybwGuAp4GHgY/HGPsSrCmzjs48Mjwqeh0dsGyZLXCSJEmSpJKQWNsaEIY4d/xz6N8ObAfeCpwJ/CiEcE+M8YVjbhTCamA1wKxZs2hpaSl8tSno7Owc+Fn2/vYwAI88/iQttbtSrEpjteDaaznlnnt4+uKLefyTn0y7nJIweK1IGp5rRcqPa0XKj2tFGlm5rJMkw6N24LRBr+eS22E02IeAq2OMEdgZQmgDXg3cP/iiGONGYCNAY2NjbGpqSqrmcdXS0sKRnyU+9gzffmQbEyZNpanpDekWphNTW5t7Ylu/Uzdv5tTNm3NPcjt4MMXCit/gtSJpeK4VKT+uFSk/rhVpZOWyTpJsW9sGLAghnBFCqAZWAJuPu+ZJ4G0AIYRZwFlAa4I1ZZYzj0pAayusXAl1dbnXdXWwahW0taVblyRJkiRJY5DYzqMYY08I4TLgTqACuCHG+GgIYU3/+9cD64AbQwgPk2tzuzzGuDupmrLs5P6ZR7udeVS85syBhobc7qOamtyxoQFmz067MkmSJEmSTliSbWvEGG8Hbj/u3PWDPn8a+KMkaygW0yZVEwLsOdBNT28flRVJbgpTYnbtgjVrYPVq2LgxNzxbkiRJkqQilmh4pPxVVkxg+qRqdnd2s/fFbk6eXJN2SToRzc1HP1+/Pr06JEmSJEkqELe3ZMgM5x5JkiRJkqSMMTzKkJmTDY80hI4OWLYMfve7tCuRJEmSJJUhw6MMMTzSkNatgy1bYO3atCuRJEmSJJUhw6MMGQiPfOKaAGprIQTYsAH6+nLHEHLnJUmSJEkaJ4ZHGTLTmUcarLUVVq6Eurrc67o6WLUK2trSrUuSJEmSVFYMjzLEtjUdY84caGiAri6oqckdGxpg9uy0K5MkSZIklRHDowwxPNJL7NoFa9bA1q25o0OzJUmSJEnjrDLtAnTUyc480vGam49+vn59enVIkiRJksqWO48yZGZ9DeDOIyWsowOWLXMXkyRJkiQpL4ZHGdJQW0l1xQT2d/XQdbg37XJUqtatgy1bYO3atCuRJEmSJBUBw6MMCSE490jJqa2FEGDDBujryx1DyJ2XJEmSJGkYhkcZM8O5R0pKayusXAl1dbnXdXWwahW0taVblyRJkiQp0wyPMmZmvTuPlJA5c6ChAbq6oKYmd2xogNmz065MkiRJkpRhhkcZM3NyNWB4pITs2gVr1sDWrbmjQ7MlSZIkSSOoTLsAHcudR0pUc/PRz9evT68OSZIkSVLRcOdRxsx05pGKTUcHLFvmLiZJkiRJKlGGRxnj09ZUdNatgy1bYO3atCuRJEmSJCXA8ChjDI9UNGprIQTYsAH6+nLHEHLnJUmSJEklw/AoY2bW1wCGRyoCra2wciXU1eVe19XBqlXQ1pZuXZIkSZKkgjI8ypgZR5621nmIGGPK1UgvY84caGiAri6oqckdGxpg9uy0K5MkSZIkFZDhUcbUVVdSP7GS7p4+XujqSbsc6eXt2gVr1sDWrbmjQ7MlSZIkqeRUpl2AXmrm5Il0Hurh2f2HmFJblXY50vCam49+vn59Ye7Z0QErVsCmTe5ikiRJkqQMcOdRBs2sd2i2yphPb5MkSZKkTDE8yqCBJ651Gh6pjPj0NkmSJEnKJMOjDBoIj9x5pHLi09skSZIkKZMMjzLI8Ehlyae3SZIkSVImGR5lkDOPVLZ8epskSZIkZY5PW8sgZx6pbCXx9DZJkiRJ0pi48yiDbFuTCqijA5YtcxeTJEmSJJ0gw6MMMjySCmjdOtiyBdauTbsSSZIkSSpKhkcZNG1SNSHA3gOH6O2LaZcjFafaWggBNmyAvr7cMYTceUmSJElS3gyPMqiqYgLT6qrpi7DngLuPpBPS2gorV0JdXe51XR2sWgVtbenWJUmSJElFxvAoo2xdk8ZozhxoaICuLqipyR0bGmD27LQrkyRJkqSiYniUUYZHUgHs2gVr1sDWrbmjQ7MlSZIkadQq0y5AQ5tZb3gkjVlz89HP168vzD07OmDFCti0yV1MkiRJksqCO48yamDnUafhkZQpPr1NkiRJUpkxPMoo29akjPHpbZIkSZLKlOFRRhkeSRnj09skSZIklSnDo4xy5pGUMT69TZIkSVKZSjQ8CiGcH0J4LISwM4RwxTDXNIUQtocQHg0h/FeS9RQTZx5JGeTT2yRJkiSVocSethZCqADWA+cB7cC2EMLmGOMvBl0zFbgOOD/G+GQI4eSk6ik2tq1JGeTT2yRJkiSVoSR3Hp0L7IwxtsYYu4FbgAuPu2Yl0BxjfBIgxvhMgvUUlSm1VVRVBPZ39dB1uDftciQlxae3SZIkScq4JMOjU4GnBr1u7z832KuAk0IILSGEB0MIH0ywnqISQnDukVTKfHqbJEmSpCKRWNsaEIY4F4f4/ucAbwNqgftCCFtjjL865kYhrAZWA8yaNYuWlpbCV5uCzs7Ol/1ZJtINwJ1338f8qRXjVJWUPSOtlWJU/a//ypkbNjBjyxYqDh2id+JEdr/lLfz6kkvoLrGfVeOnFNeKlATXipQf14o0snJZJ0mGR+3AaYNezwWeHuKa3THGA8CBEMLdwGLgmPAoxrgR2AjQ2NgYm5qakqp5XLW0tPByP8u/PrGNtn3PcNqChTQtdBaKytdIa6Vo3XUX/Od/Qk0NFd3dzFqwgFnvfW/aVamIlexakQrMtSLlx7Uijaxc1kmSbWvbgAUhhDNCCNXACmDzcdd8H3hLCKEyhFAHvAHYkWBNRcWh2VKJ8+ltkiRJkopAYjuPYow9IYTLgDuBCuCGGOOjIYQ1/e9fH2PcEUK4A3gI6AO+FWN8JKmaio0zj6QSV+int/nkNkmSJEkJSLJtjRjj7cDtx527/rjXXwG+kmQdxWpg51Gn4ZGkPAx+ctt116VdjSRJkqQSkWTbmsbItjVJefHJbZIkSZISZHiUYYZHkvLS2gorV0JdXe51XR2sWgVtbenWJUmSJKkkGB5l2Mz6GsDwSNII5syBhgbo6oKamtyxocG5R5IkSZIKwvAow2ZMrgZyM49ijClXIynTknhyW0cHLFvmU+AkSZKkMpfowGyNTV11JfUTK+k81MMLXT1Mqa1KuyRJWVXoJ7eBA7glSZIkAe48yjznHkkadw7gliRJkjSI4VHGzaw3PJI0zhzALUmSJGkQw6OMG9h51Gl4JGmcOIBbkiRJ0iCGRxln25qkVDiAW5IkSVI/B2ZnnOGRpFQ4gFuSJElSP3ceZZwzjyQVPQdwS5IkSUXN8CjjnHkkqeg5gFuSJEkqaoZHGWfbmqSi5wBuSZIkqagZHmWc4ZGkkpDEAG5JkiRJ48KB2Rk3bVI1IcDeA4fo7YtUTAhplyRJo5fEAO6ODlixAjZtcheTJEmSlCB3HmVcVcUEptVV0xdhzwF3H0nSgMFPb5MkSZKUGMOjImDrmiQN4tPbJEmSpHFleFQEDI8kaRCf3iZJkiSNqxHDoxDCthDCt0MInwghvDWEMHM8CtNRM+sNjyRpQFJPb+vogGXLHOYtSZIkHSefnUcXAt8BqoE1wG9CCE8kWpWOMbDzqNPwSJKAZJ7e5gwlSZIkaUgjPm0txvg08DRwB0AI4TXA+xOuS4PYtiZJxynk09tqa3O7l47YsCH3UVMDBw+O7d6SJElSCcinbe0Vg1/HGHcACxOrSC9heCRJCXKGkiRJkvSyRtx5BGwKIZwGtAEPA13AqxOtSsdw5pEkJSipGUqSJElSiRhx51GM8X/EGOcCHwJ+BDwKvCvpwnSUM48kKWFJzFByALckSZJKRD47jwCIMe4EdiZYi4Zh25okJayQM5SOGDyA+7rrCnNPSZIkKQX5PG1NKZtSW0VVRWB/Vw9dh3vTLkeS9HJqayGE3NDtvr7cMYTceUmSJKkIGR4VgRCCc48kqVg4gFuSJEklxvCoSDj3SJKKhAO4JUmSVGIMj4rEDHceSVLxcAC3JEmSSkjeA7OVLodmS1IRcQC3JEmSSog7j4qE4ZEklSkHcEuSJCllhkdFwplHklSmHMAtSZKklBkeFQmftiZJZSqpAdzOUJIkSVKeDI+KhG1rklTGkhjAPXiGkiRJkvQyHJhdJAyPJKmMFXIAd21tbvfSERs25D5qauDgwbHdW5IkSSXJnUdFYkb90ZlHMcaUq5EkFS1nKEmSJGmUDI+KxKSJlUyqrqC7p48XunrSLkeSVKycoSRJkqRRMjwqIrauSZIKwhlKkiRJGgVnHhWRmZMn8ps9L/Ls/kPMP7k+7XIkScXKGUqSJEkaBXceFZGBnUed7jySJGWEM5QkSZJKnuFREZnZPzR7t21rkqSsSGKGkvOTJEmSMiXR8CiEcH4I4bEQws4QwhUvc93SEEJvCOH9SdZT7Nx5JEnKpELPUHJ+kiRJUqYkNvMohFABrAfOA9qBbSGEzTHGXwxx3ZeAO5OqpVQ4MFuSlEmFmqHk/CRJkqRMSnLn0bnAzhhja4yxG7gFuHCI6z4GfBd4JsFaSoLhkSSppDk/SZIkKZOSDI9OBZ4a9Lq9/9yAEMKpwHuA6xOso2TMrK8BDI8kSSUqiflJ4AwlSZKkMUqsbQ0IQ5yLx73+n8DlMcbeEIa6vP9GIawGVgPMmjWLlpaWQtWYqs7OzlH9LM919QHw2737S+afgZSP0a4VqVyVwlpZ+OijdF9wAU+/612c8oMfUP3IIzw6xp9pwbXXcso99/D0xRfz+Cc/WZhCVdRKYa1I48G1Io2sXNZJiPH4PKdANw7hfwB/F2N8e//rvwGIMf7DoGvaOBoyzQBeBFbHGG8b7r6NjY3xgQceSKTm8dbS0kJTU1Pe1x/u7WPB//NDJgR4/AvvpGLC8IGbVEpGu1akcuVaOc7xM5SOcIZS2XOtSPlxrUgjK6V1EkJ4MMbYONR7SbatbUas2GcAABTcSURBVAMWhBDOCCFUAyuAzYMviDGeEWOcF2OcB9wKfPTlgqNyV1UxgWmTqumLsPdAd9rlSJKUbc5QkiRJKojEwqMYYw9wGbmnqO0A/neM8dEQwpoQwpqkvm+pm1nv0GxJkvLiDCVJkqSCSHLnETHG22OMr4oxnhlj/EL/uetjjC8ZkB1j/KsY461J1lMKBp641ml4JEnSiHbtgjVrYOvW3LEQgc+6dbBlC6xdO/Z7SZIkFYEkB2YrAQPhkTuPJEkaWXPz0c/Xrx/bvY6fobRhQ+7DGUqSJKnEJbrzSIVneCRJUkqSmqFkG5wkSco4w6Mi48wjSZJSktQMJdvgJElSxhkeFRlnHkmSlKJCzlCqrYUQcq1vfX25Ywi585IkSRnizKMic7RtrWuEKyVJUsEVcoZSayt85jNw223w4ou5Nrj3vAeuuWZs95UkSSowdx4VGWceSZJUIpJqg3OGkiRJKjDDoyLjzCNJkkpIIdvgjnCGkiRJKjDb1orMlNoqqioCL3T10HW4l5qqirRLkiRJJ6qQbXC1tbndS0ds2JD7qKmBgwfHdm9JklTW3HlUZCZMCMzo332026HZkiTpiNZWWLkyNzsJcsdVq6CtbWz3tQ1OkqSyZ3hUhJx7JEmSXiKpGUq2wUmSVPYMj4qQc48kSdKQCjlDqbYWQsi1vvX15Y4h5M5LkqSyYnhUhAZ2Htm2JkmSBmtuzs1OWrw4dxw8U2m0bIOTJEn9DI+KkG1rkiQpcbbBSZKkfoZHRcjwSJIkjQvb4CRJEoZHRcmZR5IkaVzYBidJkjA8KkrOPJIkSUXHNjhJkoqW4VERsm1NkiQVJdvgJEkqSoZHRWjGoLa1GGPK1UiSJOXJNjhJkoqS4VERmjSxkknVFRzq6WP/oZ60y5EkSRp/tsFJkjRuDI+KlK1rkiSp7NkGJ0nSuDA8KlKGR5IkqezZBidJ0rgwPCpShkeSJEkFZBucJEnDMjwqUjPrDY8kSZIKyjY4SZKGZHhUpAZ2HnUaHkmSJBVE1tvgbIGTJKXE8KhI2bYmSZKUYUm0wdkCJ0lKieFRkTI8kiRJyrhCtcEl1QLnTiZJUp4Mj4rUzPoawPBIkiQpswrVBpfUk+DcySRJypPhUZFy5pEkSVKZKHQLnMO8JUmjZHhUpKbXVwOwp/MQvX0x5WokSZKUqEI+CS6pnUy2wUlSyapMuwCdmKqKCUybVM3eA93sPdA9sBNJkiRJJWhwy9v69WO7VxLDvOHYNrjrrhvbvSRJmeLOoyI2s96h2ZIkSToBhdzJ5EBvSSp5hkdFzLlHkiRJOiGFGuYNDvSWpDJgeFTEBsIjdx5JkiQpLQ70lqSSZ3hUxAyPJEmSlAkO9JakkubA7CLmzCNJkiRlggO9JamkufOoiDnzSJIkSSXJgd6SlCmGR0XsaNtaV8qVSJIkSQXkQG9JyhTDoyLmzCNJkiRpBMUy0NudTJIyzPCoiDnzSJIkScpDMQz0dieTpAxzYHYRm1JbRVVF4IWuHroO91JTVZF2SZIkSVL2ZHmgd21t7h5HbNiQ+6ipgYMHT7zOjg5YsQI2bRr7sHFJZS/RnUchhPNDCI+FEHaGEK4Y4v1VIYSH+j9+EkJYnGQ9pWbChMCM/t1Hux2aLUmSJI0PdzJJKjOJ7TwKIVQA64HzgHZgWwhhc4zxF4MuawOWxRifCyG8A9gIvCGpmkrRjPqJdOzr4tn9h5h7Ul3a5UiSJEmlz51MJ34fSUUpyZ1H5wI7Y4ytMcZu4BbgwsEXxBh/EmN8rv/lVmBugvWUJIdmS5IkSUXOnUySMi7JmUenAk8Net3Oy+8q+jDwwwTrKUkDQ7NtW5MkSZKKU7ntZHIXk1R0kgyPwhDn4pAXhrCcXHj05mHeXw2sBpg1axYtLS0FKjFdnZ2dY/5ZXtzbDcC2hx/j1INj/L8JUkYVYq1I5cC1IuXHtaJSt/DRR+m+4AKefte7OOUHP6D6kUd49AT+zHd2dvKTf/1XztywgRlbtlBx6BC9Eyey+y1v4deXXEL3Ca6jBddeyyn33MPTF1/M45/85AndQ8qKcvk7JcnwqB04bdDrucDTx18UQlgEfAt4R4xxz1A3ijFuJDcPicbGxtjU1FTwYtPQ0tLCWH+WJ6p/w7+1Psqk6XNoanpdYQqTMqYQa0UqB64VKT+uFZW8u+8Gcq0gfOQjADSdwG1aWlr4/Xe9C+66C/7zP6GmhorubmYtWMCs97539Dc8bhfTqZs3c+rmzc5jUlErl79Tkpx5tA1YEEI4I4RQDawANg++IITwCqAZ+IsY468SrKVkOfNIkiRJUqIKNZOpWOYxdXTAsmVjmz0llZjEdh7FGHtCCJcBdwIVwA0xxkdDCGv6378e+BwwHbguhADQE2NsTKqmUjQQHjnzSJIkSVISCjWTqRjmMcGxYdR11534faQSkuTOI2KMt8cYXxVjPDPG+IX+c9f3B0fEGD8SYzwpxrik/8PgaJQGBma780iSJElS1mX5yXK1tRBCLoDq68sdQ8idHwt3MqkEJBoeKXmD29ZiHHIeuSRJkiRlQ3NzbvfS4sW54+BdTaNV6J1MxdJWJ6XA8KjITZpYSV11BYd6+th/qCftciRJkiRp/BRyJ1MSbXXuZFKJMDwqAQ7NliRJklSWCrmTCbLdVneEA8KVgsQGZmv8zKyfyBN7XuTZ/Yc4c2Z92uVIkiRJUnEq1HBwcEC4Soo7j0qAO48kSZIkKYOyvJPJtjqNguFRCTA8kiRJkqQMckD42BlGZYLhUQmYWd8fHnUaHkmSJElSySrHAeE+rS4TDI9KgDuPJEmSJKkMlNOAcNvqMsXwqAQYHkmSJEmSRs22urHp6GDJxz9eFkGU4VEJmNVQA8COjhc4cKgn5WokSZIkSWWp3Nrq1q1jysMPl0VLneFRCXj17Mm8dk4Dz+w/xJfv+GXa5UiSJEmSylG5tNUNCqJCjIVrqcsww6MSUFkxga/86SIqJwRuuu8J7vv1nrRLkiRJkiRpbLLaVpdUS12GGR6ViIWnTOHS5fMB+Ox3f86L3bavSZIkSZI0oFA7mQYFUb3V1WNvqSsClWkXoMK5dPl8/uMXu9jR8QJfvuMx/u5PFqZdkiRJkiRJ2TB459L69WO7V38Q9dOzz2bpz36We4pbCXPnUQmprpzANf3tazf+5DdsbbV9TZIkSZKkgutvqTswf35h5jtlnOFRiTmmfe3Wh2xfkyRJkiRJY2J4VIIuXT6f18xp4Mm9L/LlOx5LuxxJkiRJklTEDI9KkO1rkiRJkiSpUAyPStTCU6bwUdvXJEmSJEnSGBkelbDLls/n1bMn274mSZIkSZJOmOFRCcu1ry2mor997b9tX5MkSZIkSaNkeFTifu/UKVzadCYAn/2u7WuSJEmSJGl0DI/KwGVvXcCrZ0/miT0v8pU7bV+TJEmSJEn5MzwqA8e3r93ftjftkiRJkiRJUpEwPCoTR9rXYoS/vvXnHOzuTbskSZIkSZJUBAyPysjg9rUv3/nLtMuRJEmSJElFwPCojFRXTuAr77d9TZIkSZIk5c/wqMy8bu4UPtrfvvZZ29ckSZIkSdIIDI/K0GVvnc9ZsybzG5++JkmSJEmSRmB4VIYmVlYMPH3tn3/Sxrbf2L4mSZIkSZKGZnhUpl43dwqXLOt/+tp3bF+TJEmSJElDMzwqYx9729H2tWv+w/Y1SZIkSZL0UoZHZWxiZQVf+dNFVEwI3HCv7WuSJEmSJOmlDI/K3KK5U1mz7JX9T197yPY1SZIkSZJ0DMMj8X+/bQGvmlVP2+4DfNX2NUmSJEmSNIjhkY55+tq3723jAdvXJEmSJElSP8MjAce2r/31rQ/Rddj2NUmSJEmSZHikQQa3r11zp+1rkiRJkiTJ8EiDHN++9p0HnuKZF7rSLkuSJEmSJKWoMu0ClC2L5k7l4j94Jde1/Jq/vvUhAOZMqWHJaVNZfNpUFs+dyuvmTqF+on90JEmSJEkqByYAeolP/OGrqK+p5N6du3noqX107OuiY9/v+OEjvwMgBFhwcj2L5+YCpSWnTeWs2ZOpqnAjmyRJkiRJpSbR8CiEcD7w/wIVwLdijFcf937of/+dwIvAX8UYf5pkTRpZdeUEPto0n482zaevL9K6u5PtT+3j5089z8/bn2dHxwv8alcnv9rVyXcebAdgYuUEfu/UKf2B0hSWnDaVV0yrI/evWJIkSZIkFavEwqMQQgWwHjgPaAe2hRA2xxh/MeiydwAL+j/eAGzoPyojJkwIzD95MvNPnsz7z5kLQNfhXnZ0vMD2p57vD5T20bb7AA8+8RwPPvHcwNdOrasa2J206NQpnDSpmomVE/o/KphYNYHqiglMrMq9rphg0CRJkiRJUtYkufPoXGBnjLEVIIRwC3AhMDg8uhD4lxhjBLaGEKaGEObEGDsSrEtjVFNVwdmvOImzX3HSwLnnX+zmofaju5O2P/U8uzu7+a9fPct//erZvO5bMSEMhEvV/QFT9UDYdPTcxMoJVFVOYEIIBHJtdAGY0P9JIAycC4NfBwjHfM3g614+uBru7dzdRvc1Gr32pw5xT+cvRr5QKnOuFSk/rhUpP64VaWTtTx2i8tTdvHnBjLRLSVSS4dGpwFODXrfz0l1FQ11zKnBMeBRCWA2sBpg1axYtLS2FrjUVnZ2dJfOzHPG6Cnjd6bDqFZXs6aqgdV8frc/38eT+Xrp64HAfHO6L9PT1f9579PPevsiL3b282N2b9o+hLHqiLe0KpOLgWpHy41qR8uNakUY0+e6f0vPb6rTLSFSS4dFQ+y7iCVxDjHEjsBGgsbExNjU1jbm4LGhpaaFUfpaxijHS0xc51NPHocO9dPf2cehw36BjL4cO9+Xe7+njUE9v/9dBJOaOEfpizP0BGnz+JdfFo+cGfT5sbS9Ts8bHzp2/Zv78M9MuQ8o814qUH9eKlB/XijSynTt/zYo/XMqS06amXUqikgyP2oHTBr2eCzx9AteoDIQQqKoIVFVMoH6iDwHUsVp6n6TpLa9Muwwp81wrUn5cK1J+XCvSyFp6nyz54AggyWerbwMWhBDOCCFUAyuAzcddsxn4YMh5I7DPeUeSJEmSJEnZkdgWjxhjTwjhMuBOoAK4Icb4aAhhTf/71wO3A+8EdgIvAh9Kqh5JkiRJkiSNXqL9QTHG28kFRIPPXT/o8whcmmQNkiRJkiRJOnFJtq1JkiRJkiSpyBkeSZIkSZIkaViGR5IkSZIkSRqW4ZEkSZIkSZKGZXgkSZIkSZKkYRkeSZIkSZIkaViGR5IkSZIkSRpWiDGmXcOohBCeBZ5Iu44CmQHsTrsIqQi4VqT8uFak/LhWpPy4VqSRldI6OT3GOHOoN4ouPColIYQHYoyNadchZZ1rRcqPa0XKj2tFyo9rRRpZuawT29YkSZIkSZI0LMMjSZIkSZIkDcvwKF0b0y5AKhKuFSk/rhUpP64VKT+uFWlkZbFOnHkkSZIkSZKkYbnzSJIkSZIkScMyPBoHIYTzQwiPhRB2hhCuGOL9EEL4ev/7D4UQXp9GnVKa8lgnq/rXx0MhhJ+EEBanUaeUtpHWyqDrloYQekMI7x/P+qSsyGethBCaQgjbQwiPhhD+a7xrlLIgj/8GmxJC+LcQws/718qH0qhTSlsI4YYQwjMhhEeGeb+kf683PEpYCKECWA+8A3gt8OchhNced9k7gAX9H6uBDeNapJSyPNdJG7AsxrgIWEeZ9BZLg+W5Vo5c9yXgzvGtUMqGfNZKCGEqcB3wJzHGhcCfjnuhUsry/HvlUuAXMcbFQBPw1RBC9bgWKmXDjcD5L/N+Sf9eb3iUvHOBnTHG1hhjN3ALcOFx11wI/EvM2QpMDSHMGe9CpRSNuE5ijD+JMT7X/3IrMHeca5SyIJ+/UwA+BnwXeGY8i5MyJJ+1shJojjE+CRBjdL2oHOWzViIwOYQQgHpgL9AzvmVK6Ysx3k3uz/9wSvr3esOj5J0KPDXodXv/udFeI5Wy0a6BDwM/TLQiKZtGXCshhFOB9wDXj2NdUtbk8/fKq4CTQggtIYQHQwgfHLfqpOzIZ618E3gN8DTwMPDxGGPf+JQnFZWS/r2+Mu0CykAY4tzxj7jL5xqplOW9BkIIy8mFR29OtCIpm/JZK/8TuDzG2Jv7n8RSWcpnrVQC5wBvA2qB+0IIW2OMv0q6OClD8lkrbwe2A28FzgR+FEK4J8b4QtLFSUWmpH+vNzxKXjtw2qDXc8ml9qO9Riplea2BEMIi4FvAO2KMe8apNilL8lkrjcAt/cHRDOCdIYSeGONt41OilAn5/vfX7hjjAeBACOFuYDFgeKRyks9a+RBwdYwxAjtDCG3Aq4H7x6dEqWiU9O/1tq0lbxuwIIRwRv9guRXA5uOu2Qx8sH86+xuBfTHGjvEuVErRiOskhPAKoBn4C/+vsMrYiGslxnhGjHFejHEecCvwUYMjlaF8/vvr+8BbQgiVIYQ64A3AjnGuU0pbPmvlSXI79AghzALOAlrHtUqpOJT07/XuPEpYjLEnhHAZuSfeVAA3xBgfDSGs6X//euB24J3ATuBFcum+VDbyXCefA6YD1/XvqOiJMTamVbOUhjzXilT28lkrMcYdIYQ7gIeAPuBbMcYhH78slao8/15ZB9wYQniYXFvO5THG3akVLaUkhPC/yD1xcEYIoR34PFAF5fF7fcjtPpQkSZIkSZJeyrY1SZIkSZIkDcvwSJIkSZIkScMyPJIkSZIkSdKwDI8kSZIkSZI0LMMjSZIkSZIkDcvwSJIkSZIkScMyPJIkSZIkSdKwDI8kSZISEEKYG0L4QNp1SJIkjZXhkSRJUjLeBrw+7SIkSZLGKsQY065BkiSppIQQ3gx8H3ge2A+8J8bYlm5VkiRJJ8bwSJIkKQEhhDuAz8QYH0m7FkmSpLGwbU2SJCkZZwGPpV2EJEnSWBkeSZIkFVgIYTqwL8Z4OO1aJEmSxsrwSJIkqfDOAJ5OuwhJkqRCMDySJEkqvF8CM0IIj4QQfj/tYiRJksbCgdmSJEmSJEkaljuPJEmSJEmSNCzDI0mSJEmSJA3L8EiSJEmSJEnDMjySJEmSJEnSsAyPJEmSJEmSNCzDI0mSJEmSJA3L8EiSJEmSJEnDMjySJEmSJEnSsP5/PEdGIXDtco8AAAAASUVORK5CYII=\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"from matplotlib.pylab import *\n",
"\n",
"BETA=arange(50,101,10)\n",
"\n",
"t0, y0, tfinal = 0, 1, 1\n",
"\n",
"sol_exacte = lambda t : y0*exp(-beta*t)\n",
"phi = lambda t,y : -beta*y\n",
"\n",
"i=0\n",
"\n",
"\n",
"for beta in BETA:\n",
" N=(int(beta/2)+1)\n",
" tt = linspace(t0,tfinal,N+1)\n",
" h = tt[1]-tt[0]\n",
" yy = [sol_exacte(t) for t in tt]\n",
" alpha=ALPHA[0]\n",
" uu = RKalpha(phi,tt) \n",
" i+=1\n",
" figure(i,figsize=(20,5))\n",
" plot(tt,yy,lw=2,label=(\"Exacte\"))\n",
" plot(tt,uu,'r*',label=(\"N=\"+str(N)+\" beta=\"+str(beta)))\n",
" xlabel('$t$')\n",
" ylabel('$u$')\n",
" legend() \n",
" grid(True)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercice : étude de l'ordre\n",
"Étudier théoriquement l'ordre du schéma."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Correction : étude de l'ordre"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"+ C'est un schéma explicite à deux étage: l'ordre est au plus 2.\n",
"+ $c_1=a_{11}+a_{12}$, $c_2=a_{21}+a_{22}$ et $1=b_1+b_2$ $\\implies$ il est consistante\n",
"+ $c_1 b_1 + c_2b_2=\\frac{1}{2}$ $\\implies$ il est d'ordre $2$"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"alpha= 1/6\n",
"{True}\n",
"---------------------\n",
"alpha= 1/4\n",
"{True}\n",
"---------------------\n",
"alpha= 1/3\n",
"{True}\n",
"---------------------\n",
"alpha= 5/12\n",
"{True}\n",
"---------------------\n",
"alpha= 7/12\n",
"{True}\n",
"---------------------\n",
"alpha= 2/3\n",
"{True}\n",
"---------------------\n",
"alpha= 3/4\n",
"{True}\n",
"---------------------\n",
"alpha= 5/6\n",
"{True}\n",
"---------------------\n",
"alpha= 11/12\n",
"{True}\n",
"---------------------\n"
]
}
],
"source": [
"for alpha in ALPHA:\n",
" print(\"alpha=\",alpha)\n",
" c=[0,alpha]\n",
" b=[1-1/(2*alpha),1/(2*alpha)]\n",
" A=[[0,0],[alpha,0]]\n",
" s=len(c)\n",
" ordre=[]\n",
" ordre.append(sum(b)==1)\n",
" for i in range(s):\n",
" ordre.append(sum(A[i])==c[i])\n",
" ordre.append(sum([b[i]*c[i] for i in range(s)])==Fraction(1,2))\n",
" print(set(ordre))\n",
" print(\"---------------------\")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercice : solution exacte\n",
"Calculer la solution exacte du problème de Cauchy\n",
" $$\n",
" \\begin{cases}\n",
" y'(t)=-2t\\left(y(t)\\right)^2, & t\\in[0;3]\\\\\n",
" y(0)=2\n",
" \\end{cases}\n",
" $$"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Correction : solution exacte"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On peut soit calculer la solution \"à la main\" soit utiliser `sympy`.\n",
"\n",
"Il s'agit d'une EDO à variables séparables. La fonction $y(t)=0$ pour tout $t$ est solution de l'EDO mais elle ne vérifie pas la CI. Toute autre solution de l'EDO sera non nulle et se trouve formellement comme suit:\n",
"$$\n",
"y'(t)=-2ty^2(t)\n",
"\\quad\\implies\\quad\n",
"\\frac{y'(t)}{y^2(t)}=-2t\n",
"\\quad\\implies\\quad\n",
"\\int y^{-2}\\mathrm{d}y=-2\\int t\\mathrm{d}t\n",
"\\quad\\implies\\quad\n",
"y(t)=\\frac{1}{t^2+c}, \\ c\\in\\mathbb{R}.\n",
"$$\n",
"En imposant la CI on obtient $2=1/C$ d'où l'unique solution du problème de Cauchy: $y(t)=\\frac{2}{2t^2+1}$."
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [],
"source": [
"import sympy as sym\n",
"sym.init_printing()"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle \\frac{d}{d t} u{\\left(t \\right)} = - 2 t u^{2}{\\left(t \\right)}$"
],
"text/plain": [
"d 2 \n",
"──(u(t)) = -2⋅t⋅u (t)\n",
"dt "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"sym.var('t,C1')\n",
"u=sym.Function('u')\n",
"f=-2*t*(u(t))**2\n",
"edo=sym.Eq(sym.diff(u(t),t),f)\n",
"display(edo)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle u{\\left(t \\right)} = \\frac{1}{C_{1} + t^{2}}$"
],
"text/plain": [
" 1 \n",
"u(t) = ───────\n",
" 2\n",
" C₁ + t "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"solgen=sym.dsolve(edo,u(t))\n",
"display(solgen)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle \\left\\{ C_{1} : \\frac{1}{2}\\right\\}$"
],
"text/plain": [
"{C₁: 1/2}"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"t0=0\n",
"u0=2\n",
"consts = sym.solve( [solgen.rhs.subs(t,t0)-u0 ], dict=True)[0]\n",
"display(consts)"
]
},
{
"cell_type": "code",
"execution_count": 13,
"metadata": {},
"outputs": [
{
"data": {
"image/png": "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\n",
"text/latex": [
"$\\displaystyle u{\\left(t \\right)} = \\frac{1}{t^{2} + \\frac{1}{2}}$"
],
"text/plain": [
" 1 \n",
"u(t) = ──────\n",
" 2 1\n",
" t + ─\n",
" 2"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"solpar=solgen.subs(consts)\n",
"display(solpar)"
]
},
{
"cell_type": "code",
"execution_count": 14,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"%matplotlib inline\n",
"sym.plot(solpar.rhs,(t,0,3));"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Exercice : convergence\n",
"Vérifier empiriquement l'ordre de convergence en affichant la courbe de convergence et en estimant la pente sur ce problème de Cauchy. "
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"### Correction : étude empirique de l'ordre de convergence"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"On calcule la solution approchée avec différentes valeurs de $h_k=1/N_k$, à savoir $N_k=2^3$, ... $2^{10}$. On sauvegarde les valeurs de $h_k$ dans le vecteur `H`. \n",
"\n",
"Pour chaque valeur de $h_k$, on calcule le maximum de la valeur absolue de l'erreur et on sauvegarde toutes ces erreurs dans le vecteur `err` de sort que `err[k]` contient $e_k=\\max_{i=0,...,N_k}|y(t_i)-u_{i}|$ avec $N_k=2^{k+1}$.\n",
"\n",
"Pour afficher l'ordre de convergence on utilise une échelle logarithmique : on représente $\\ln(h)$ sur l'axe des abscisses et $\\ln(\\text{err})$ sur l'axe des ordonnées ainsi, si $\\text{err}=Ch^p$, alors $\\ln(\\text{err})=\\ln(C)+p\\ln(h)$. En échelle logarithmique, $p$ représente donc la pente de la ligne droite $\\ln(\\text{err})$.\n",
"\n",
"Pour estimer l'ordre de convergence on estime la pente de la droite qui relie l'erreur au pas $k$ à l'erreur au pas $k+1$ en echelle logarithmique en utilisant la fonction `polyfit` basée sur la régression linéaire. \t"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
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},
"output_type": "display_data"
},
{
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xxhQo3XADjByZa5nKR0EFTJIkSZIkqZXs3Jm2utUHSi+/nMYHDYKKCvjqV1OgdPnlEEKelaoDMGCSJEmSJEmwbx9UV2eNuVevTlvh+vZNvZPuuy/1UbrmGigqyrtadTAGTJIkSZIkdUWHD8OiRVkPpSVL4Ngx6NkTJk+Gxx9PgdL48WlMOomCCphs8i1JkiRJUjOOHYOVK7MtbzU1cOgQdOsGpaXwla+kLW9Tp6ZVS9IpKKiAySbfkiRJkiTVqa2FNWuyLW8LFsA776S50aPhP/2nFChNmwYDB+Zbqzq9ggqYJEmSJEnqsmKE3/0uC5R+8xvYvj3NjRoFd96ZtrxVVMCQIbmWqsJjwCRJkiRJUme1eXPWQ+mZZ2DDhjR+/vlw001phdINN8CIEfnWqYJnwCRJkiRJUmfx9ttpZVJ9oPTKK2n87LNh+nR45JEUKF12GYSQb63qUgyYJEmSJEnqqPbuherqrDH3c8+lrXD9+qXeSbNmpUDpmmtSs24pJwUVMHmKnCRJkiSpUzt0CBYtyvooLV0Kx49Dz54wZQo88UTqozR+PPTokXe10u8VVMDkKXKSJEmSpE7l2DFYvjwLlBYuhMOH02qk8ePha19LgdKUKdCnT97VSs0qqIBJkiRJkqQOrbYWXngh66G0YEHaBgcwZgw88EDa8jZtGhQX51urdAoMmCRJkiRJaisxwrp1WQ+l3/wGduxIcyUlcNddKVCqqIDzzsu1VOlMGDBJkiRJktSaNm3Ktrw980y6DzBsGHzwg2nL2/TpMHx4vnVKrciASZIkSZKkM7F9O1RWZqHSb3+bxs85JwVJN9yQQqVLL4UQci1VaisGTJIkSZIknWjePJgzBzZsSCuN5s6FmTPT3DvvQFVV1kfpuefSeP/+cP31cP/9KVQaMyY165a6gIIKmEIIM4AZJSUleZciSZIkSeqs5s2D2bPhwIF0f/16+Mxn4Oc/h23bYNkyOH4cevVKp7v96Z+mQKm0FHr0yLd2KScFFTDFGOcD80tLS2flXYskSZIkqZP6+tezcKne4cPwi1/ApEnwyCNpy9vkydCnTz41Sh1MQQVMkiRJkiSdsgMHYPFiWLAg/Wzc2PTjQoBFi9q3NqmTMGCSJEmSJHUt+/bBs89mgdLSpXD0aOqXNHYsDBgAe/e++3me+iY1y4BJkiRJklTY3nkHamqyQGnFCjh2DIqK4Lrr4EtfSs25y8qguPjdPZgA+vZNjb4lNcmASZIkSZJUWHbtgurqLFBatQpqa1MD7vHj4atfTYHSlClptdKJ6k+La+4UOUnvYsAkSZIkSercduyAqqosUHr+eYgRevZMTbnnzEmB0uTJaSVSS8ycaaAknQIDJkmSJElS5/LWWylQqqxMgdKaNWm8d++0Kunxx1OgNHFiGpPU5gyYJEmSJEkd25Yt2eqkBQvg5ZfTeL9+KVD65CdToDR+PPTqlW+tUhdlwCRJkiRJ6lg2bGgcKK1bl8YHDEiNuO+9NwVK112X+ipJyl1BBUwhhBnAjJKSkrxLkSRJkiS1RIzw+uuNA6U33khzAwdCeTncf38KlMaOhe4F9c9YqWAU1O/MGON8YH5paemsvGuRJEmSJDUhRvjtbxsHSps2pblzzoFp0+BLX0qB0tVXQ1FRvvVKapGCCpgkSZIkSR1MjLB2bRYmVVXB1q1p7rzzUpBU/3PlldCtW771SjotBkySJEmSpNZTW5tOdWu4Qmn79jQ3bBhUVGSB0mWXQQi5liupdRgwSZIkSZJO3/Hj8PzzjVco7dyZ5i66CG66KYVJFRUwapSBklSgDJgkSZIkSS137BisWpUFStXVsGdPmrv4YrjttmyF0siRBkpSF2HAJEmSJElq3tGjsHx5FigtXAh796a5Sy+FO+7IAqWLLsq3Vkm5MWCSJEmSJGUOH4alS7NA6dln4cCBNHfFFTBzZgqTpk1LPZUkCQMmSZIkSeraDh6ExYuzQGnxYjh0KM1dfTXcd18WKJ13Xr61SuqwDJgkSZIkqSvZvx8WLcoCpSVL4MiR1Ctp7Fi4//4UKJWXwznn5F2tpE7CgEmSJEmSCtnevalvUn2gtGxZatTdrRtcey18/vMpUCorg0GD8q5WUidlwCRJkiRJhWT3bqipyQKllSvh+HHo3h1KS+Hhh1OgNHUqnHVW3tVKKhAGTJIkSZLUme3cCVVVWaC0ejXECD17woQJ8OijKVCaMgX69cu7WkkFyoBJkiRJkjqTbdsaB0ovvJDGe/eGSZPgT/4kBUqTJkGfPvnWKqnL6BQBUwjhduBDwHnA92KM/5ZzSZIkSZLUPt58MwVJlZXpdu3aNN63b1qV9PGPp0BpwgTo1SvXUiV1XW0eMIUQngJuBbbFGEc3GL8Z+A5QBPwgxvjt5q4RY/wn4J9CCIOAvwQMmCRJkiQVpk2bstVJCxbAq6+m8f79UyPuu+9OgdJ116VtcJLUAbTHCqYfAd8Fflw/EEIoAr4H3AhsApaFEH5BCpu+dcLz74sxbqv79R/XPU+SJEmSCsMbbzQOlF57LY0XF0N5OcyalQKlceNSo25J6oDa/E+nGGNVCGHkCcMTgHUxxtcAQgg/Az4cY/wWabVTIyGEAHwb+GWMcWVTrxNCmA3MBhgyZAiVlZWt9RYkKRf79u3zzzJJknLSZt/DMdJnyxaKV69m4HPPMfD55+n91lsAHB0wgD1jxrD75pvZPXYs+y65BIqK0vP2708nw0lSB5VX/H0BsLHB/U3AxJM8/vPAB4DiEEJJjPGvT3xAjPFJ4EmA0tLSWFFR0XrVSlIOKisr8c8ySZLy0WrfwzHCK680XqG0ZUuaO/dcmDYtrU66/np6jB7N4G7dGHzmrypJ7S6vgCk0MRabe3CM8a+Av3rPi4YwA5hRUlJyBqVJkiRJ0mmqrYWXXsrCpKoqqFuhxNChvw+TuP56uOIKCE3900iSOp+8AqZNwEUN7l8IbDnTi8YY5wPzS0tLZ53ptSRJkiTpPdXWwgsvNA6UduxIcxdeCB/4QBYoXXqpgZKkgpVXwLQMuDSEcDGwGfgEcFdOtUiSJElSyxw/DqtXZ4FSdTXs2pXmRo6ED30oC5QuvthASVKX0eYBUwjhp0AFMDiEsAl4LMb4wxDCg8CvSCfHPRVjXNMKr+UWOUmSJEmt5+hRWLkyC5RqauCdd9JcSQl89KNZoDR8eL61SlKOQozNtj7qtEpLS+Py5cvzLkOSzohNviVJysGRI7BsGa/97d9yycaNsHBhOsEN4LLLGvdQuuCCfGuVpHYWQlgRYyxtai6vLXKSJEmSlL9Dh2DJkmyF0qJFcPAglwBcdRXcc08Kk6ZNS026JUlNMmCSJEmSVHjmzYM5c2DDhrR1be5cmDkTDhyAxYuzQGnxYjh8OPVKGjMGZs2C669nYVERUz/84bzfhSR1GgUVMNmDSZIkSRLz5sHs2SlMAli/Hu69F554At54I/VV6tYNxo2DP/qjtEKpvBwGDfr9JY5WVuZRuSR1WgUVMMUY5wPzS0tLZ+VdiyRJkqQc7N4NDz2UhUv1jh1LQdNDD6VAaepUKC7Op0ZJKkAFFTBJkiRJ6mK2b4fqaqiqSlvennsOmjvI6OhR+PM/b9/6JKmLMGCSJEmS1Hls2ZKFSVVV8NJLabxPH5g8GR57DL7/fXjrrXc/d/jw9q1VkrqQggqY7MEkSZIkFZAY07a2+jCpqgrWrUtzAwakbW6f+lQ64a20FHr2THMlJY17MAH07ZsafUuS2kRBBUz2YJIkSZI6sRjht7/NAqUFC2DjxjQ3aFAKkh54IN2OHQvdm/nnzMyZ6bapU+QkSW2ioAImSZIkSZ1IbS2sWdN4y1v91rYhQ1KQ9LWvpabcV12VTn5rqZkzDZQkqR0ZMEmSJElqH8eOpSbc9WFSdTXs3JnmLrwQPvCBFCZNmwbvex+EkG+9kqQWK6iAyR5MkiRJUgdy5AgsX571T6qpgb1709yoUXD77SlMuv56GDHCQEmSOrGCCpjswSRJkiTl6OBBWLIkW6G0aFEaA7jyyrRl7frrobwcLrgg31olSa2qoAImSZIkSe1o794UItUHSkuXplVLIcA118CsWVmgdO65eVcrSWpDBkySJEmSWmbXrrTNrb4p98qVcPw4FBXBddfBF7+YtryVlcHAgXlXK0lqRwZMkiRJkpq2bVtqxF2/Qun55yFG6NkTJk6ERx9NK5QmT4b+/fOuVpKUIwMmSZIkScnmzdnqpKoqWLs2jffpA1OmwBNPpBVKEyakMUmS6hRUwOQpcpIkSVILxQhvvJGFSQsWwGuvpbmzzkrb3O65JwVK112XVi1JktSMggqYPEVOkiRJakaM8MorjVcobdqU5s4+OwVJDz6Ytrxdc03qqyRJUgsVVMAkSZIkqU5tLbz4YuNAadu2NDd0aAqUrr8+3V55JXTrlm+9kqROzYBJkiRJKgTHjsHq1VmYVF2dTn0DGD4cbropC5VKSiCEfOuVJBUUAyZJkiSpMzpyBJYty1YoLVwI+/aluUsvhY9+NAuURozIt1ZJUsEzYJIkSZI6gwMHYMmSbIXSokVw6FCau+oquPvuFCiVl8OwYfnWKknqcgyYJEmSpI5o7960KqmqKv0sXQpHj6ZeSWPHwv33Z4HS4MF5VytJ6uIKKmAKIcwAZpSUlORdiiRJknRqdu6Emppsy9vKlalRd/fuUFoKDz2UtrtNnQrFxXlXK0lSIwUVMMUY5wPzS0tLZ+VdiyRJknRSb72VGnHXb3l74QWIEXr1gokTYc6ctEJp8mTo1y/vaiVJOqmCCpgkSZKkDmvTpixMWrAAXnkljfftm1Yl3XFHCpQmTIDevfOtVZKkU2TAJEmSJLW2GOG117L+SQsWwOuvp7mzzkp9k+67L215u/Za6NEj33olSTpDBkySJEnSmYoRXn45C5OqqmDz5jR3zjlpZdIXv5hux4yBoqJ865UkqZUZMEmSJEmnqrY29UyqD5OqqmD79jR3/vlpZdK0aenniivSyW+SJBUwAyZJkiTpvRw7lk51qw+Tqqth9+40N3IkfPCDWag0ahSEkGu5kiS1NwMmSZIk6USHD8OyZdmWt2efhX370tz73gd/8AdZoDR8eL61SpLUARgwSZIkSQcOwOLF2Za3xYvh0KE0N3o03HNPtuVt6NB8a5UkqQMyYJIkSVLX8847sHBhtkJp+XI4ejT1Sho3Dh54IK1QKitLTbolSdJJFVTAFEKYAcwoKSnJuxRJkiR1JG+/DTU12QqlVatSo+7u3WH8ePjyl1OgNGUKFBfnXa0kSZ1OQQVMMcb5wPzS0tJZedciSZKkHL35ZtaQu6oqnfgG0Ls3TJoEf/zHabvbpEnQr1++tUqSVAAKKmCSJElSF7VxY7Y6acECePXVNN6vH0ydCnfemVYojR8PvXrlW6skSQXIgEmSJEkdz7x5MGcObNiQTmmbOxdmzkxzMcLvfpeFSVVV8MYbaa64GMrLYdastEJp3Djo0SO3tyFJUldhwCRJkqSOZd48mD07newGsH49fPaz8B//kU52q6qCLVvS3LnnpiDpoYfSCqXRo6GoKL/aJUnqogyYJEmS1LF84xtZuFTv0CH40Y9g2LAUJE2blm4vvxxCyKVMSZKUMWCSJElSvg4fhuXLobo6rU7asKHpx4UAmzYZKEmS1AEZMEmSJKl97d8PixalMKm6GhYvTiuUAK68Evr3h3373v284cMNlyRJ6qAMmCRJktS2du2CmposUFqxAo4dg27dUhPuBx5IW97KymDw4Hf3YALo2zc1+pYkSR2SAZMkSZJa19at2Xa3qip48cV08lvPnjBxInztaylQmjwZzjrr3c+vPy2uuVPkJElSh2PAJEmSpNMXI7z+euNAad26NNevH0ydCh//eAqUJkyA3r1bdt2ZMw2UJEnqRAyYJEmS1HK1tbB2bbbdraoKNm9Oc2efDeXlactbeXna/tbdv25KktQV+I0vSZKk5h07BqtXZ4FSdTW8/XaaGzYsrUyaNi0FSldemfoqSZKkLseASZIkSZlDh2DZsmy727PPZie6lZTAbbdlodLFF3uqmyRJAjpBwBRCuAL4IjAY+HWM8fs5lyRJklQ49u6FRYuyQGnpUjh8OM1dfTXcfXW1ZfMAAB4eSURBVHe2QmnYsHxrlSRJHVabBkwhhKeAW4FtMcbRDcZvBr4DFAE/iDF+u7lrxBjXAveHELoBf9OW9UqSJBW8t9+GmposUFq1Co4fh6IiuO46+PznU5hUVpZ6KkmSJLVAW69g+hHwXeDH9QMhhCLge8CNwCZgWQjhF6Sw6VsnPP++GOO2EMJtwKN115IkSVJLbd7cuCH3mjVpvFcvmDQJvvGNFChNngz9++dbqyRJ6rRCjLFtXyCEkcC/1K9gCiFMBh6PMd5Ud//rADHGE8Olpq71rzHGDzUzNxuYDTBkyJDrfvazn7VK/ZKUl3379tHff+xJOhUx0mfLFoqfe47iF15g4PPP02fLFgCO9e3LntGj2TNmDLvHjGHvZZcRe/bMuWCp4/J7WJLebfr06StijKVNzeXRg+kCYGOD+5uAic09OIRQAXwU6AU83dzjYoxPAk8ClJaWxoqKilYoVZLyU1lZiX+WSTqp2tq0Iql+u1t1NWzdmuYGD04rk+oacncfM4ZzunfnnHwrljoNv4cl6dTkETA1ddRIs8uoYoyVQGVbFSNJktRpHD2aeibVB0o1NbBrV5q78EKYPj074e3yyz3hTZIktZv3DJhCCJcCXwcOxhj/qBVecxNwUYP7FwJbWuG6hBBmADNKSkpa43KSJEn5OngQlizJ+ic9+ywcOJDm3vc++NjHslVKI0YYKEmSpNy0ZAXT/ws8Afw5QAhhNPC1GOPdp/may4BLQwgXA5uBTwB3nea1Gokxzgfml5aWzmqN60mSJLWrPXtSiFQfKC1dmlYthQBjxsBnPpPCpLIyGDo072olSZJ+ryUBU7cY4y9DCH8GEGN8sS5kek8hhJ8CFcDgEMIm4LEY4w9DCA8CvyKdHPdUjHHN6ZUvSZLUiW3fnoVJ1dWwenXqq9S9O5SWwkMPpUBp6lQYODDvaiVJkprVkoBpS91qowgQQghAn5ZcPMb4yWbGn+YkDbtPl1vkJElSh7ZxY+OG3GvXpvE+fWDSJPjmN1OgNHEi9OuXb62SJEmnoCUB05eAHwBDQwifBm4GXmzTqk6TW+QkSVKHESP89rdZoFRVBevXp7ni4rTN7Z57UqB03XXQs2e+9UqSJJ2B9wyYYoxvhBBuBm4HrgEWAE+1dWGSJEmdyvHj8MIL2Za3qirYti3NnXdeCpK+/OV0e/XVUFSUb72SJEmtqCUrmIgxHgP+vu6nw3KLnCRJajdHjsCKFdl2t5qa1KQb0oluN92UwqTy8nTimye8SZKkAtaigKmzcIucJElqMwcOwOLFWaC0aBEcPJjmLr8c7rwzC5SGD8+3VkmSpHZWUAGTJElSq9m9GxYuzLa7LV8Ox45Bt25wzTUwe3YKlMrK0hY4SZKkLsyASZIkCeCttxr3T3r++dSou0cPmDABvvKVFChNmZKadEuSJOn3CipgsgeTJElqkRjTiW4NA6VXX01zffumEOmJJ9J2t4kToU+ffOuVJEnq4AoqYLIHkyRJalKM8PLLWf+kqirYuDHNDRyYgqRZs9LttdemVUuSJElqsYIKmCRJkgA4fhyeey4LlKqrYfv2NDd0aNrq9sgj6faqq1JfJUmSJJ02AyZJktT5HT6cmnDXb3d79ll45500d8klcMstKUyaNg1GjYIQ8q1XkiSpwBRUwGQPJkmSuoh9+2Dx4ixQWrIEDh1Kc1ddBXfdlcKk8nK48MJ8a5UkSeoCCipgsgeTJEkFaudOqKnJ+ietWJG2wXXrlnomfe5zKUwqK4PBg/OuVpIkqcspqIBJkiQViC1bst5JVVXwwgtpvGfPdKrbo4+mQGnKFBgwIN9aJUmSZMAkSZJyFiO8/nq23a26GtatS3P9+6cQ6c4705a38eOhd+9865UkSdK7GDBJkqTWN28ezJkDGzbA8OEwdy7MnJnmamth7drGgdLmzWnu7LPTyqQHHkiB0tix0N2/rkiSJHV0/o1NkiS1rnnzYPZsOHAg3V+/Hj77WXj6adi/PwVKO3emuWHD4PrrU6g0bRpccUXqqyRJkqROpaACJk+RkySpA/j617Nwqd6hQ/CTn0BJCdx+exYoXXwxhJBPnZIkSWo1BRUweYqcJEk52LMHFi7MmnJv3Nj040KA3/62fWuTJElSuyiogEmSJLWDN99sfMLb88+nRt3du0NpKZx1FrzzzrufN3x4+9cqSZKkdmHAJEmSmhcjvPZa1oy74QlvffvC5Mnw+ONpy9vEiWnsxB5M9Y+dOzeXtyBJkqS2Z8AkSZIytbXwwgtZmFRdDVu3prlzzoGyMrj//hQojRsHPXq8+xr1p8U1d4qcJEmSCo4BkyRJXdmRI7B8eRYmLVwIu3enuYsugunTU5hUXn5qJ7zNnGmgJEmS1IUYMEmS1JXs2weLFmWB0uLF6YQ3gMsvhzvuyE54GzEi31olSZLUaRRUwBRCmAHMKCkpybsUSZI6hh07oKYma8i9ahUcP55WIo0bl213KyuD887Lu1pJkiR1UgUVMMUY5wPzS0tLZ+VdiyRJudiwIQuTqqth7do03qtXasL96KNpddLkyTBgQL61SpIkqWAUVMAkSVKXEmMKkBo25N6wIc2ddRZMnQp3351WKJWWppBJkiRJagMGTJIkdRbHjqUtbvVhUk1N2gIHMGRIWpn0la+kQOnqq6GoKN96JUmS1GUYMEmS1FEdPAhLlmSB0rPPwv79aW7UKLj11uyEt5ISCCHfeiVJktRlGTBJktRR7N4NCxdmPZSWL4ejR1NwdPXVcO+9WaA0bFje1UqSJEm/Z8AkSVJetm5t3JD7hRdSX6UePVLPpIceSmHS1KkwaFDe1UqSJEnNMmCSJKk9xAjr1jVuyP2736W5fv3SqW6PP576KE2YAH375lquJEmSdCoMmCRJagvHj6cVSQ0DpTffTHPnnANlZfC5z6UVSmPHplVLkiRJUidlwCRJUms4fDj1TKoPkxYuhD170txFF8H735/1T7r8cujWLd96JUmSpFZUUAFTCGEGMKOkpCTvUiRJhW7vXli0KOuhtHQpHDqU5q64Au68MwuURozIt1ZJkiSpjRVUwBRjnA/MLy0tnZV3LZKkArN9O9TUZA25V69O2+CKimDcOHjggRQmlZXBuefmXa0kSZLUrgoqYJIkqdWsX5+FSdXV8PLLabx3b5g4Eb7+9dSQe9IkGDAg31olSZKknBkwSZJUWwtr1zZuyL1xY5orLoapU+Gee1KgdN110KtXvvVKkiRJHYwBkySp6zl6FFatysKkmhp4++00N3Ro2ur2ta+l29Gj0zY4SZIkSc0yYJIkFb4DB2DJkqwh9+LFsH9/mhs1Cm67LWvIPWoUhJBvvZIkSVInY8AkSSo8u3bBwoVZD6UVK9KqpRBgzBj49KezQOn88/OuVpIkSer0DJgkSZ3f5s2N+ye9+CLECD16wPjx8OUvpzBp6lQYODDvaiVJkqSCY8AkSepcYoR16xqf8Pbaa2muXz+YMgXuuCMFShMnQp8++dYrSZIkdQEGTJKkju34cXj++cYrlN56K80NHgxlZfBHf5ROeBs7Frr71SZJkiS1N/8WLknqWA4fhmXLsjBp4UJ45500N3w4fOADKUwqL4fLL7chtyRJktQBGDBJkvK1dy88+2x2wtvSpSlkArjiCvjkJ7OG3MOH51urJEmSpCYZMEmS2te2bVBTk/VQWr0aamuhqAiuvTZtdysvT1vfBg/Ou1pJkiRJLWDAJElqOzHC+vWNG3K/8kqa690bJk2COXNSoDR5MvTvn2+9kiRJkk5LpwiYQgj9gCrgsRjjv+RdjySpGbW18NJLjRtyb9qU5oqL06qkT386BUqlpdCzZ771SpIkSWoVbRowhRCeAm4FtsUYRzcYvxn4DlAE/CDG+O33uNQjwM/brFBJ0uk5ehRWrszCpJoa2LkzzZ1/ftY7qbwcRo9O2+AkSZIkFZy2XsH0I+C7wI/rB0IIRcD3gBuBTcCyEMIvSGHTt054/n3AGOAloHcb1ypJamjevLR9bcOG1Fx77lz4yEdg8eKsIffixXDgQHp8SQl8+MPZCW+XXOIJb5IkSVIXEWKMbfsCIYwE/qV+BVMIYTLweIzxprr7XweIMZ4YLtU/fy7QD7gSOAh8JMZY28TjZgOzAYYMGXLdz372s1Z/L5LUnvbt20f/nHoSnfcf/8Flf/mXFNWf5gbEEIhAtxiJIbD/kkvYPWYMe8aMYc/VV3PknHNyqVWSpLaQ5/ewJHVU06dPXxFjLG1qLo8eTBcAGxvc3wRMbO7BMcY5ACGEe4EdTYVLdY97EngSoLS0NFZUVLRSuZKUj8rKStr9z7KNG9PqpO98BxqESwAhRsJZZ8FPf0qYMoX+AwfSH7iwfSuUJKld5PI9LEmdWB4BU1P7Jd5zGVWM8UetX4okdWExwssvN27IvX79yZ+zdy/cckv71CdJkiSp08gjYNoEXNTg/oXAlta4cAhhBjCjpKSkNS4nSYXl2DFYtapxQ+4dO9Lcueemvklf+lK6/ehHU++lEw0f3r41S5IkSeoU8giYlgGXhhAuBjYDnwDuao0LxxjnA/NLS0tntcb1JKlTO3AAlizJAqVFi2D//jR3ySXwoQ9lJ7xdemnjhtx/9mcwe3bWwBugb9/U6FuSJEmSTtCmAVMI4adABTA4hLAJeCzG+MMQwoPAr0gnxz0VY1zTlnVIUpewc2dalVQfKK1YkVYthQBXXw333pvCpLIyuOCCk19r5sx0e+IpcvXjkiRJktRAmwZMMcZPNjP+NPB0a7+eW+QkdSn1Dbnrf9bUZfU9esD48fDwwylQmjIFBg069evPnGmgJEmSJKlF8tgi12bcIiepYJ2sIXf//ilE+sQnUqA0YQL06ZNvvZIkSZK6lIIKmCSpYBw9yoC1a9M2t/qG3G+/nebOOy8FSQ89lG7HjIHu/nEuSZIkKT8F9S8St8hJ6rQOHIDFi7PVSYsXc13Dhty33tp8Q25JkiRJyllBBUxukZPUabSgIfeas8/mqvvvh2HD8q5WkiRJkk6qoAImSeqwNmxoHCjVN+Tu2TM15P7KV7KG3AMHArC9stJwSZIkSVKnYMAkSa0tRli7tnFD7g0b0tyAASlE+uQnU6A0frwNuSVJkiR1egUVMNmDSVIujh6FVauyMKmphtxf/rINuSVJkiQVrIL6V449mCS1i/37YcmSLFBatCg16QYYNQpmzEhhUlmZDbklSZIkdQkFFTBJUpt4++3G/ZNWrswaco8ZA/fdlwVK9kySJEmS1AUZMEnSiTZsaNw/6aWX0vhJGnJLkiRJUldWUAGTPZgknbKWNOS+664UKE2YAL1751uvJEmSJHVABRUw2YNJ0ns6WUPuIUNSkPTww1lD7qKifOuVJEmSpE6goAImSXqX/fth8eIsUFq8uOmG3OXlUFJiQ25JkiRJOg0GTJIKS0sbcpeXw/nn512tJEmSJBUEAyZJndvJGnJPmABf/WoKkyZPtiG3JEmSJLURAyZJnUdtbWrI3XCFUsOG3FOnwsyZKVAaP96G3JIkSZLUTgoqYPIUOanAHD2atrjVh0kLF9qQW5IkSZI6oIIKmDxFTurkTtaQu6QEbrsNyspsyC1JkiRJHUxBBUySOpkdO9KqpKYacl9zDXzmMylMKiuzIbckSZIkdWAGTJLaz/r1jRtyr12bxk9syD1lChQX51urJEmSJKnFDJgktY36htwNA6WNG9PcWWelEOkP/9CG3JIkSZJUAAyYJLWOExty19TAzp1pbujQFCTVr1C6+mobckuSJElSATFgknR69u+HRYtSkNRUQ+4PfziFSeXlMGqUDbklSZIkqYAVVMAUQpgBzCgpKcm7FKnw7NiRhUn1DbmPH7chtyRJkiSpsAKmGON8YH5paemsvGuROr3mGnL36pUacj/ySAqTbMgtSZIkSV1eQQVMkk5TbS289FLjFUoNG3JPnQqf+lRaoVRaakNuSZIkSVIjBkxSoZo3D+bMgQ0bYPhwmDsXZs5Mc0ePwooVWZi0cKENuSVJkiRJp82ASSpE8+bB7NlZ0+3161OPpH/4B9i9OzXkPngwzV16Kdx+e9ruZkNuSZIkSdJpMGCSCtGjj2bhUr3Dh+F//S8YNw5mzcoacg8dmk+NkiRJkqSCYcAkdXYxvrsh96ZNTT82hHT6myRJkiRJrciASepsamthzZosTKqpyQKl4uLUkPvNN9NWuBMNH96+tUqSJEmSugQDJqmjO3Lk3Q25d+1Kc+efn7a61f+MHp0acp/Ygwmgb9/U6FuSJEmSpFZmwCR1NHv3wqJFWaC0ZAkcOpTm3vc++OhHs0Dp4oubbshdf1pcc6fISZIkSZLUigoqYAohzABmlJSU5F2K1HJvvZW2udUHSqtXp21w3bqlhtz335/CpKlTYciQll935kwDJUmSJElSuyiogCnGOB+YX1paOivvWqQmxQivvZb1TqquhldfTXO9e8OkSWnVUVkZTJ4MAwbkW68kSZIkSS1QUAGT1OEcPw4vvtj4hLetW9PcoEEpSPrMZ9IKpeuug549861XkiRJkqTTYMAktabDh2HZsixMevZZ2LMnzV14IVRUZP2TrrwybYOTJEmSJKmTM2CSzsSePSlEqt/ytnRpCpkArrgC7rwzhUllZTBiRNMNuSVJkiRJ6uQMmKRTsXVr44bczz+fGnIXFaUtbg8+mMKksjIYPDjvaiVJkiRJahcGTFJzYoR16xr3T/rd79Jc376pIfc3v5lWKE2aBP365VuvJEmSJEk5MWCS6h0/Ds89l4VJNTXw1ltp7pxz0qqkBx5IgdK4cdCjR771SpIkSZLUQRgwqes6eDD1TKrf8vbss7B3b5obMQJuvDHrn3T55TbkliRJkiSpGQZM6jp274aFC7MVSsuXw5EjaW70aPjDP0xhUnk5XHRRvrVKkiRJktSJGDCpcG3e3Lh/0osvpr5K3btDaSl88YspTJo6Fc4+O+9qJUmSJEnqtAyYVBhihFdeyXonVVfD66+nuf79YfJkuOOOFChNmJCadEuSJEmSpFZhwKTO6dgxWLUqC5NqamD79jR37rkpSPrCF9KWt7Fj06olSZIkSZLUJvxXtzqHAwdgyZJsu9uiRbB/f5q75BK45Zasf9L73gch5FuvJEmSJEldSIcPmEIIFcB/AdYAP4sxVuZakNrHzp2NVyetWAFHj6bg6Oqr4d57sxPeLrgg72olSZIkSerS2jRgCiE8BdwKbIsxjm4wfjPwHaAI+EGM8dsnuUwE9gG9gU1tWK7ytGFD4/5Ja9ak8Z49Yfx4ePjhFChNmQIDB+ZbqyRJkiRJaqStVzD9CPgu8OP6gRBCEfA94EZSYLQshPALUtj0rROefx9QHWNcEEIYAvxXYGYb16y2FiOsXdv4hLcNG9LcgAHpVLe77kqrkyZMgN69861XkiRJkiSdVJsGTDHGqhDCyBOGJwDrYoyvAYQQfgZ8OMb4LdJqp+bsAno1NxlCmA3MBhgyZAiVlZWnX7haVTh2jP6vvsrAF16g+PnnKX7xRXq88w4ARwYNYveYMey57Tb2jBnDvksugaKi9MTaWli8OMfKpXzt27fPP8skScqJ38OSdGry6MF0AbCxwf1NwMTmHhxC+ChwEzCQtBqqSTHGJ4EnAUpLS2NFRUVr1KrTsW9fCobqt7wtXpyadAOUlMDHPpa2u5WX03PUKM4LgfPyrVjqkCorK/HPMkmS8uH3sCSdmjwCpqaO94rNPTjG+I/AP7ZdOTpjO3ZkvZOqq2HlSjh+HLp1g2uugc9+NmvIPXRo3tVKkiRJkqRWlkfAtAm4qMH9C4EtrXHhEMIMYEZJSUlrXE5NiRHWr2/cP+nll9Ncr14wcSI8+mgKk6ZMgbPOyrdeSZIkSZLU5vIImJYBl4YQLgY2A58A7mqNC8cY5wPzS0tLZ7XG9UTqg7RmTRYm1dTAprrD/IqLU0Pue+5JK5RKS1PIJEmSJEmSupQ2DZhCCD8FKoDBIYRNwGMxxh+GEB4EfkU6Oe6pGOOatqxDp+DIEVixIguUFi6EXbvS3LBhv++dRHk5jB6dtsFJkiRJkqQura1PkftkM+NPA0+39uu5Re407N0LixZlgdKSJXDoUJq77LJGDbkZORJCUy20JEmSJElSV5bHFrk24xa5FnjrrcYNuVevTtvgiopg3Dh44IHUP6msDM7zbDdJkiRJkvTeCipg0glihNdey3onVVfDq6+muT59UkPuOXPS6qRJk2DAgHzrlSRJkiRJnVJBBUxdfovc8ePw4ouNT3jbujXNDRqUViV99rMpULr2WujZM996JUmSJElSQSiogKnLbZE7fBiWLcvCpGefhT170txFF8H06SlMKiuDK6+0IbckSZIkSWoTBRUwFZR589L2tQ0bYPhwmDsXbr01hUj1W96WLk0hE6QA6c47s4bcI0bkW78kSZIkSeoyDJg6onnzYPZsOHAg3V+/Hj71qdRTCaB797TF7cEHU5g0dSoMHpxfvZIkSZIkqUsrqICpYHowzZmThUv1YoTiYvjHf0zNufv1y6c2SZIkSZKkExRUU54Y4/wY4+zi4uK8SzkzGzY0Pf7OO3DDDYZLkiRJkiSpQymogKlgDB9+auOSJEmSJEk5MmDqiObOhb59G4/17ZvGJUmSJEmSOpiCCphCCDNCCE/u2bMn71LOzMyZ8OST6SS4ENLtk0+mcUmSJEmSpA6moAKmgunBBClMeuMNqK1Nt4ZLkiRJkiSpgyqogEmSJEmSJEntz4BJkiRJkiRJZ8SASZIkSZIkSWfEgEmSJEmSJElnpKACpoI5RU6SJEmSJKkTKaiAqaBOkZMkSZIkSeokCipgkiRJkiRJUvsLMca8a2h1IYTtwPq862hDxUBX2gfYWd9vR64779ra+/Xb+vXa6vqDgR1tcF11HXn/Xi9EXe0z7czvt6PWnnddhfYd3Jav4fewzlTev98LUVf7TDvi+x0RYzy3qYmCDJgKXQjhyRjj7LzraC+d9f125Lrzrq29X7+tX6+trh9CWB5jLG3t66rryPv3eiHqap9pZ36/HbX2vOsqtO/gtnwNv4d1pvL+/V6Iutpn2tner1vkOqf5eRfQzjrr++3IdeddW3u/flu/Xt6fp9Qc/9tsfV3tM+3M77ej1p53XYX2HdxeryGdDv/bbH1d7TPtVO/XFUyS1EH5/5xKkpQfv4cl6dS4gkmSOq4n8y5AkqQuzO9hSToFrmCSJEmSJEnSGXEFkyRJkiRJks6IAZMkSZIkSZLOiAGTJEmSJEmSzogBkyRJkiRJks6IAZMkdUIhhNtDCH8TQvjnEML/kXc9kiR1JSGES0IIPwwh/H3etUhSR2HAJEntLITwVAhhWwjhxRPGbw4hvBJCWBdCePRk14gx/lOMcRZwL3BnG5ar/92+HavKWUVRAF6bJD6ANoIRtBBBQgabdLG6doJNCsXONCL6AD5BLGKTKrVBFLGyEVstLAJKRBFE0ngREQMpLMVtM8XN1YsmZ2bOTOb7unNgfla3Yc0+ADxUVjSHb3f35fUmBdgt1d2zMwDslap6IckfSd7v7nPLu1NJfkzyYpLDJDeTvJrkVJIrxz7xenf/tvzde0k+6O6vNxQfAHbaiufwJ919aVPZAbbZ6dkBAPZNd39RVU8du76Q5Kfuvp0kVfVRkpe7+0qSl45/o6oqybtJPlMuAcD/t4o5DMA/eSIHsB2eSPLzkfPh8u4kbyc5SHKpqt5YZzAA2AP3NYer6rGqup7k+ap6Z93hAHaBDSaA7VD/cnfiG+buvpbk2vriAMBeud85fCeJP3gAjrDBBLAdDpM8eeR8Nskvk7IAwL4xhwEGKZgAtsPNJM9U1dNV9UiSV5J8OjkTAOwLcxhgkIIJYMOq6sMkXyV5tqoOq+pyd/+Z5K0knyf5IcnH3f39zJwA8DAyhwHWo7pPfFoMAAAAAP/JBhMAAAAAQxRMAAAAAAxRMAEAAAAwRMEEAAAAwBAFEwAAAABDFEwAAAAADFEwAQAAADBEwQQAAADAEAUTAMAEVXVQVTdm5wAAWAUFEwDAHIsk38wOAQCwCgomAIA5Fkker6ovq+rXqjqYHQgA4EEpmAAA5lgk+b27LyZ5M8lrk/MAADwwBRMAwIZV1Zkkjya5urw6neTuvEQAAGMUTAAAm/dcklvd/dfyfD7JdxPzAAAMUTABAGzeIsmtI+fzSb6dlAUAYJiCCQBg8xa5t1A6FxtMAMAOq+6enQEAAACAHWaDCQAAAIAhCiYAAAAAhiiYAAAAABiiYAIAAABgiIIJAAAAgCEKJgAAAACGKJgAAAAAGPI3m2/p/kFDGQoAAAAASUVORK5CYII=\n",
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]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
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},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
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\n",
"text/plain": [
""
]
},
"metadata": {
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},
"output_type": "display_data"
},
{
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
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\n",
"text/plain": [
""
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"t0, y0, tfinal = 0, 2, 3\n",
"sol_exacte = lambda t : 1/(t**2+1/y0)\n",
"phi = lambda t,y : -2*t*y**2\n",
"\n",
"i=0\n",
"for alpha in ALPHA:\n",
" H = []\n",
" err = []\n",
" for k in range(8):\n",
" N = 2**(k+3) \n",
" tt = linspace(t0,tfinal,N+1)\n",
" h = tt[1]-tt[0]\n",
" H.append(h)\n",
" yy = [sol_exacte(t) for t in tt]\n",
" uu = RKalpha(phi,tt)\n",
" err.append(max([abs(uu[i]-yy[i]) for i in range(len(uu))]))\n",
" i+=1\n",
" figure(i,figsize=(20,5))\n",
" loglog(H,err, 'r-o')\n",
" title('Alpha={}, Ordre = {:1.4f}'.format(alpha,polyfit(log(H),log(err), 1)[0]))\n",
" xlabel('$h$')\n",
" ylabel('$e$')\n",
" #legend() \n",
" grid(True)"
]
}
],
"metadata": {
"hide_input": false,
"kernelspec": {
"display_name": "Python 3",
"language": "python",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.8.5"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": true,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
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