{ "cells": [ { "cell_type": "markdown", "id": "ef674ab4-d343-474a-9b6e-a3888c353796", "metadata": {}, "source": [ "## MT09 - TP7 - Automne 2025\n", "### Schémas numériques pour les équations différentielles\n" ] }, { "cell_type": "markdown", "id": "3fe9daf9-8d95-4546-9983-987fbaaa6b56", "metadata": { "tags": [] }, "source": [ "### 1. Croissance cellulaire\n", "\n", "Dans les exercices de travaux dirigés, on a vu le modèle différentiel continu de croissance cellulaire\n", "$$\n", "\\frac{d\\rho(t)}{dt} = \\sigma \\frac{\\rho(t)}{\\rho_M}(\\rho_M-\\rho(t)),\\quad t\\in [0,T]\n", "$$\n", "\n", "où $\\rho$ représente la densité de cellules par unité de surface. À cette équation différentielle, on associe la condition initiale $\\rho(0) = \\rho_0$, $0<\\rho_0 \\ll \\rho_M$. On rappelle que la solution exacte s'écrit\n", "\n", "$$\n", "\\rho(t) = \\rho_M \\, \\frac{e^{\\sigma t}}{\\dfrac{\\rho_M}{\\rho_0}-1+e^{\\sigma t}}.\n", "$$\n", "\n", "\n", "Le module ```scipy.integrate``` donne accès à la méthode ```odeint()``` qui résout numériquement un problème différentiel pour la fonction\n", "$\\mathbf{f}(t,\\mathbf{y})$ implémentée dans la méthode `model(t,y)`:\n", "\n", "```\n", "y = odeint(model, y0, t, tfirst=True)\n", "```\n", "\n", "(voir l'aide de ```odeint()```, l'option `tfirst=True` précise que la première variable de $\\mathbf{f}$ est $t$). \n", "\n", "Ecrire une fonction\n", "```croissanceCell(y,t)``` qui implémente la fonction de l'équation différentielle de croissance cellulaire. Résoudre ensuite numériquement le problème différentiel et comparer à la solution exacte $\\rho(t)$.\n", "\n", "Pour l'application numérique, on utilisera les paramètres\n", "$T=20$, $\\rho_M=1000$, $\\rho_0=5$ et $\\sigma=0.7$ et ```t = np.linspace(0,T, 100)```." ] }, { "cell_type": "code", "execution_count": 1, "id": "526623a5-7281-4d52-a273-b2a21957284c", "metadata": { "tags": [] }, "outputs": [], "source": [ "import numpy as np\n", "def rho(t):\n", " sigma = 0.7\n", " rhoM = 1000\n", " rho0 = 5\n", " rho = rhoM * np.exp(sigma*t) / (rhoM/rho0 - 1 + np.exp(sigma*t))\n", " return rho" ] }, { "cell_type": "code", "execution_count": 2, "id": "b3abacb2-af35-4f4a-b671-9b6f3678bd8e", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "\n", "# function that returns ydot\n", "def croissanceCell(t,y):\n", " sigma = 0.7\n", " rhoM = 1000\n", " ydot = sigma*(y/rhoM)*(rhoM-y)\n", " return ydot\n", "\n", "# initial condition\n", "y0 = np.array([5.0])\n", "# final time\n", "T = 20.0\n", "# time points\n", "tref = np.linspace(0,T, 100)\n", "# solve ODE\n", "yref = odeint(croissanceCell, y0, tref, tfirst='true')\n", "\n", "# plot results\n", "plt.plot(tref, yref, '.-', label=\"odeint()\")\n", "plt.plot(tref, rho(tref), '-g', label=\"exact\")\n", "plt.legend(loc=\"upper left\")\n", "plt.xlabel('time t')\n", "plt.ylabel('rho(t)'); plt.grid();\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "039b31c2-1318-4f52-8a48-380ef43cd036", "metadata": {}, "source": [ "#### Schéma d'Euler explicite\n", "\n", "Ecrire une fonction python ```Euler(F, y0, t0, T, N)``` qui met en oeuvre le schéma d'Euler explicite \n", "\n", "$$\n", "z_{n+1} = z_n + h\\, F(t_n, z_n), \\quad t_n = t_0 + hn,\n", "$$\n", "\n", "pour une fonction $F$ (à valeurs scalaires ou vectorielles), une donnée initiale $y_0$, un temps initial $t_0$, un temps final $T$, sur une subdivision uniforme constituée de $N$ sous-intervalles, avec un pas\n", "$h=\\frac{T-t_0}{N}$. \n", "\n", "Les tableaux de sorties seront le tableau des temps discrets $t$ et le tableau (ou matrice) $z$ des états du système $y_n$ aux temps discrets $t_n$ : on devrait pouvoir écrire\n", "\n", "```\n", "t, z = Euler(, y0, t0, T, N)\n", "```" ] }, { "cell_type": "code", "execution_count": 3, "id": "9eaabc75-4fbd-473e-91f3-9102b2733031", "metadata": { "tags": [] }, "outputs": [], "source": [ "def Euler(F, y0, t0, T, N):\n", " d = y0.size\n", " h = (T-t0) / N;\n", " t = np.linspace(t0, T, N+1)\n", " z = np.zeros((N+1, d))\n", " z[0,:] = y0\n", " for n in range(0, N):\n", " z[n+1,:] = z[n,:] + h*F(t[n], z[n,:])\n", " return t, z" ] }, { "cell_type": "markdown", "id": "e5a14aa1-5d27-4dc3-be95-799d28da8de7", "metadata": {}, "source": [ "Appliquez la méthode d'Euler au problème de croissance cellulaire. On prendra toujours $y_0=5$, $T=20$, et $N=50$. Tracer la solution numérique $t\\mapsto z(t)$ et comparer à la solution de référence obtenue avec ```odeint()```. " ] }, { "cell_type": "code", "execution_count": 4, "id": "320268fa-31c1-4102-890c-b87006abf763", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "y0 = np.array([5.0])\n", "t0 = 0.0\n", "T = 20.0\n", "N = 50\n", "t, z = Euler(croissanceCell, y0, t0, T, N)\n", "plt.plot(t, z, '.-', label=\"Schéma d'Euler\"); \n", "plt.plot(tref, yref, '-g', label=\"Reference odeint()\")\n", "plt.legend(loc=\"upper left\")\n", "plt.xlabel('time t')\n", "plt.ylabel('rho(t)')\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "b2edd6b6-9894-4c1e-94bf-6fbfc712e1c0", "metadata": {}, "source": [ "Testez plusieurs valeurs de $N$, par exemple $N=10,\\ 50,\\ 100, 200$ pour observer visuellement l'évolution de l'erreur en fonction de $N$ et vérifier la convergence de la méthode." ] }, { "cell_type": "code", "execution_count": 5, "id": "ba825e2e-e89f-456b-8e62-395dc4b9eeb9", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 10\n", "t, y = Euler(croissanceCell, y0, 0.0, T, N)\n", "plt.plot(t, y, '.-', label=\"Euler\"); \n", "plt.plot(tref, yref, '-g', label=\"Reference odeint()\")\n", "plt.legend(loc=\"upper left\")\n", "plt.xlabel('time t')\n", "plt.ylabel('rho(t)')\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "ff8d4442-5b3e-460e-8a05-753c593c2cc9", "metadata": {}, "source": [ "#### Mesure empirique de l'ordre du schéma d'Euler explicite\n", "\n", "Par l'expérimentation, il est possible de déterminer empiriquement l'ordre d'un schéma numérique. On considère ici $t_0=0$,\n", "$$\n", "T=10,\n", "$$\n", "\n", "$h=h(N)=\\frac{T-t_0}{N}$, $t_n = t_0 + hn$. On note\n", "\n", "$$\n", "e_N = |\\rho(t_N) - z_N| = |\\rho(T) - z_N|.\n", "$$\n", "\n", "Si le schéma est d'ordre $p$, alors on aura\n", "\n", "$$\n", "e_N \\approx C\\, h^p\n", "$$\n", "\n", "pour une certaine constante $C>0$. En passant à l'échelle logarithmique,\n", "on a\n", "\n", "$$\n", "\\log(e_N) \\approx K + p \\, \\log(h(N))\n", "$$\n", "\n", "où $K=\\log(C)$. Pour les valeurs successives $N=64,\\, 128,\\, 256,\\, 512, \\,1024,\\,2048$, affichez les valeurs $z_N$, $e_N$. Fabriquez deux tableaux\n", "$\\log(h(N)$ et $\\log(e_N)$ et tracez le graphe correspondant dans le plan\n", "$(\\log(h),\\,\\log(e))$. " ] }, { "cell_type": "code", "execution_count": 6, "id": "a7db41b5-b03c-48dd-8cc6-99b5d0615576", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "loghN = \n", " [-1.85629799 -2.54944517 -3.24259235 -3.93573953 -4.62888671 -5.32203389]\n", "logeN = \n", " [ 3.2338434 2.4956412 1.78009454 1.07579328 0.377082 -0.31884381]\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t0 = 0.0\n", "T = 10.0\n", "M = 6\n", "loghN = np.zeros(M)\n", "logeN = np.zeros(M)\n", "i = 0\n", "\n", "for N in np.array([64,128,256,512,1024,2048]):\n", " y0 = np.array([5.0])\n", " t, z = Euler(croissanceCell, y0, t0, T, N)\n", " hN = (T-t0)/N\n", " loghN[i] = np.log(hN)\n", " logeN[i] = np.log(np.abs(rho(T) - z[-1,0]))\n", " i += 1\n", "\n", "print('loghN = \\n', loghN)\n", "print('logeN = \\n', logeN)\n", "\n", "plt.plot(loghN, logeN, 'o-r'); plt.grid()" ] }, { "cell_type": "markdown", "id": "ee99ba3f-e629-419a-ab35-dd329338a5cd", "metadata": {}, "source": [ "En déduire une valeur empirique de $h$ par moindres carrés." ] }, { "cell_type": "code", "execution_count": 7, "id": "8364b511-7605-4306-92d6-33d5600f2edc", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "p estimé = 1.0232176436898712 \n", "\n", "\n" ] } ], "source": [ "A = np.zeros((M,2))\n", "A[:,0] = np.ones(M)\n", "A[:,1] = loghN\n", "\n", "# Résolution des équations normales :\n", "u = np.linalg.solve(A.T@A, A.T@logeN)\n", "\n", "# K = u[0], p = u[1]\n", "print(\"\\np estimé = \", u[1],'\\n\\n')" ] }, { "cell_type": "markdown", "id": "1ec97e7b-bd9d-42e3-b7b8-3f3585c2ceea", "metadata": {}, "source": [ "#### Schéma de Runge-Kutta RK2\n", "\n", "Le schéma de Runge-Kutta RK2 (ou schéma d'Euler-Cauchy) du cours s'écrit\n", "\n", "\\begin{align*}\n", "& k_1 = F(t_n, z_n), \\\\[1.3ex]\n", "& k_2 = F(t_n+h, z_n+h\\,k_1) \\\\\n", "& z_{n+1} = z_n + \\frac{h}{2}\\left( k_1+k_2\\right).\n", "\\end{align*}\n", "\n", "Mettre en oeuvre ce schéma dans une méthode ```RK2(F, y0, t0, T, N)```." ] }, { "cell_type": "code", "execution_count": 8, "id": "0af33a24-bb70-4677-8839-0dcf4444634d", "metadata": {}, "outputs": [], "source": [ "def RK2(F, y0, t0, T, N):\n", " d = y0.size\n", " h = (T-t0) / N;\n", " t = np.linspace(t0, T, N+1)\n", " z = np.zeros((N+1, d))\n", " z[0,:] = y0\n", " for n in range(0, N):\n", " k1 = F(t[n], z[n,:])\n", " k2 = F(t[n]+h, z[n,:]+h*k1)\n", " z[n+1,:] = z[n,:] + 0.5*h*(k1+k2)\n", " return t, z" ] }, { "cell_type": "markdown", "id": "9d85e898-52a7-4c66-ba0e-73ddd824964f", "metadata": {}, "source": [ "Appliquez le schéma RK2 au modèle de croissance cellulaire avec \n", "$T=20$ et $N=30$. Comparez au résultat obtenu par le schéma d'Euler explicite ainsi qu'à la solution de référence obtenue avec `odeint()`. Commentez." ] }, { "cell_type": "code", "execution_count": 9, "id": "6395c730-a5db-4057-acc6-cb5df990130e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T = 20\n", "N = 30\n", "t, yEuler = Euler(croissanceCell, y0, 0.0, T, N)\n", "plt.plot(t, yEuler, '.-', label=\"Euler\");\n", "t, yRK2 = RK2(croissanceCell, y0, 0.0, T, N)\n", "plt.plot(t, yRK2, '.-', label=\"RK2\"); \n", "plt.plot(tref, yref, '-g', label=\"Reference odeint()\")\n", "plt.legend(loc=\"upper left\")\n", "plt.xlabel('time t')\n", "plt.ylabel('rho(t)')\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "41e41980-a922-43ee-9cab-cfa827dd97e0", "metadata": {}, "source": [ "Estimez empiriquement l'ordre du schéma RK2 en répétant la méthodologie décrite plus haut." ] }, { "cell_type": "code", "execution_count": 10, "id": "fd4bd114-6573-406a-b73e-98587f6daa6e", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "loghN = \n", " [-1.85629799 -2.54944517 -3.24259235 -3.93573953 -4.62888671 -5.32203389]\n", "logeN = \n", " [ 0.09759958 -1.26427072 -2.63758704 -4.01718939 -5.40008552 -6.78466753]\n" ] }, { "data": { "image/png": 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AAConL09KSpKuv96EkIsvltLSpCFDCCGoNFZEAAAVl54u3X67WQ2RTPj4+9+lM890ti7UWAQRAEDFrF5tQsihQyZ4vPyy2QZOA6MZAED5cnOlRx6RbrjBhJA//lHatIkQgmrBiggAoGy7d0v9+5t7hEjmktxp08zJqUA1IIgAAEq3cqU0aJB0+LAUFSW98orUt6/TVSHIMJoBABSXkyM98IB0yy0mhLRpI/3nP4QQ2IIgAgA44ccfpY4dzUPrJOn++81YplUrR8tC8GI0AwAwUlLM5biZmdLZZ0vz50s9ezpdFYIcKyIAEOqOH5dGj5ZuvdWEkHbtpC1bCCHwC4IIAISy776TOnQwt2eXpPHjpY8/llq0cLYuhAxGMwAQqhYvlu66S/rtN8njkV5/XbrxRqerQohhRQQAQs2xYyaAJCaaENKxoxnFEELgAIIIAISSb76RrrrK3BPE5ZIee0xas0Zq1szpyhCiGM0AQKhYsEAaOVLKzpYaN5beeMM8QRdwECsiABDsfvvN3CF18GATQq67zoxiCCEIALYFkZ07d2ro0KFq2bKl6tSpo1atWmnSpEnKycmx6yMBACf7v/+TrrzSnIgaFiY98YS0apXUpInTlQGSbBzNbNu2Tfn5+Zo9e7bOO+88ffXVVxo+fLiOHj2qqVOn2vWxAABJsixzHsiYMeY+IU2bmqtkOnVyujKgGNuCSPfu3dW9e/fC7XPPPVfbt2/XrFmzCCIAYKesLOnuu6UlS8z2jTea80MaNXK2LqAUfj1ZNTMzUw0aNCjz916vV16vt3A7KytLkuTz+eTz+WyvLxAVfO9Q/f4SPZDogUQPpAr2YPNm1UpMlGvHDlm1ain/b39T/tixZiwTBL3jOKgZPahMbS7Lsiwbaym0Y8cOXXHFFZo2bZqGDRtW6j6TJ09WUlJSideTk5MVGRlpd4kAUHNZllq++64umT9f4bm5ym7USF888ICOXHih05UhBGVnZysxMVGZmZmKiooqd99KB5GywkJRaWlpio+PL9xOT09X586d1blzZ82dO7fM95W2IhIbG6uMjIxTfpFg5fP5lJqaqoSEBEVERDhdjiPoAT2Q6IFUTg+OHFH4XXcp7O23JUn5PXoob84cqZwV6JqK46Bm9CArK0sej6dCQaTSo5lRo0apX79+5e4TFxdX+Of09HR17dpV7du315w5c8p9n9vtltvtLvF6REREwDbbX+gBPZDogUQPpJN68PnnUr9+0s6dUkSENHWqwkaPVpjL5WiNduM4COweVKauSgcRj8cjj8dToX337t2rrl27qk2bNpo3b57CwrhtCQBUi/x8acYMacIEKTdXOvdcaelSqchqNFAT2Hayanp6urp06aLmzZtr6tSpOnToUOHvmnD9OgBU3c8/S8OGSe++a7b79pXmzJHq1XO2LqAKbAsiq1ev1vfff6/vv/9eMTExxX7np/NjASDoNPjvf1Vr1Chpzx7J7Zaef948wC7IRzEIXrbNSgYPHizLskr9AQBUUn6+wp5+WldPnCjXnj3S+eeb80PuvpsQghqNh94BQKA7cEAaOFDhqamSpPzERIXNni2ddZbDhQGnj7NHASCQrVkjtW4tpabKqlNHm0ePVt68eYQQBA2CCAAEorw8adIk84Tc/fulSy5R7qefatd11zGKQVAhiABAoElPNwFkyhTz8Lphw6SNG6WLL3a6MqDacY4IAASSVaukgQOlQ4fM+GX2bCkx0fwugJ8tAlQVKyIAEAh8Punhh6Xu3U0I+dOfpE2bToQQIEixIgIATtu1S+rfX9qwwWyPHClNmybVru1sXYAfEEQAwEkrVkiDB0tHjkhRUdKrr0q9eztdFeA3jGYAwAk5OdK4cVLPniaExMdLmzcTQhByCCIA4G8//CBdc415aJ0kjR0rffKJeXAdEGIYzQCAPy1bJg0dKmVlSfXrS/PnSz16OF0V4BhWRADAH44fl+69V+rTx4SQ9u2lLVsIIQh5BBEAsNu335rg8dJLZnvCBOmjj6TmzZ2tCwgAjGYAwE7JyeYJub/9Jnk80sKF5l4hACSxIgIA9sjONrdmHzDAhJDOnaUvvySEACchiABAdfvvf6WrrjL3BHG5pMcflz74QGra1OnKgIDDaAYAqotlmatg7r1XOnZMatJEWrRIuvZapysDAhZBBACqw2+/mVuzL1xothMSzJ8bN3a2LiDAMZoBgNP15ZfmzqgLF0phYdKTT0r/+hchBKgAVkQAoCLy8qT166V9+6ToaKljRxM65syRxoyRvF6pWTNp8WLzOwAVQhABgFNJSTFhY8+eE681bSrFxZ14Yu7NN5vzQzweJyoEaiyCCACUJyXFPIjOsoq/np5ufsLCpGefNc+LCWPaDVQW/60BgLLk5ZmVkJNDSFEej3T//YQQoIr4bw4AlGX9+uLjmNIcPGj2A1AlBBEAKMu+fdW7H4ASCCIAUJYmTSq2X3S0vXUAQYyTVQGgNIcPS9Onl7+PyyXFxHC5LnAaCCIAcLJPP5Vuu03avVuqVUvKzTWho+hJqy6X+efMmVJ4uCNlAsGA0QwAFMjPl557TurUyYSQP/xBSkuTli83NysrKiZGWrZM6tXLmVqBIMGKCABIUkaGNGiQ9N57Zrt/f2n2bKluXal1a6lnz5J3VmUlBDhtBBEA+Pe/pX79pL17JbdbeuEFadiwE+MXyYSOLl0cKxEIVoxmAISu/Hzp6adNwNi7Vzr/fGnjRmn48OIhBIBtWBEBEJoOHZLuuMM8JVeSbr9dmjVLOussZ+sCQgxBBEDo+fhjcw5IerpUp4704ovSnXeyCgI4gNEMgNCRny89+aTUtasJIRdeaEYxQ4YQQgCHsCICIDQcOCANHCilpprtQYOk//f/pDPPdLYuIMQRRAAEv7VrpcREaf9+KTLSBJDBg52uCoAYzQAIZnl5UlKSdP31JoRccom5QRkhBAgYtgaRHj16qHnz5qpdu7aio6M1cOBApaen2/mRAGDs3y916yZNnmzODRkyxJwPcvHFTlcGoAhbg0jXrl315ptvavv27Vq+fLl27Nih3r172/mRACB9+KG5G+qaNeYckNdfl1591YxlAAQUW88RGTt2bOGfW7RooQkTJugvf/mLfD6fIiIi7PxoAKGoYBTzxBPmAXWXXSa9+aa5OgZAQPLbyaqHDx/WokWL1KFDhzJDiNfrldfrLdzOysqSJPl8Pvl8Pr/UGWgKvneofn+JHkj0QKpAD9LTFX7HHQr7+GNJUv7QocqbPt3cJyRI+sZxQA+kmtGDytTmsqyiz7Wufg899JBefPFFZWdnq127dlq5cqUaNmxY6r6TJ09WUlJSideTk5MVyZIqgDI02rxZbWbOlDszU7m1a2vLyJHa26mT02UBISs7O1uJiYnKzMxUVFRUuftWOoiUFRaKSktLU3x8vCQpIyNDhw8f1k8//aSkpCTVq1dPK1eulKuUmweVtiISGxurjIyMU36RYOXz+ZSamqqEhISQHWfRA3ogldGD3FyFJSUp/JlnJEnWH/+o3ORk88yYIMRxQA+kmtGDrKwseTyeCgWRSo9mRo0apX79+pW7T1xcXOGfPR6PPB6Pzj//fF100UWKjY3VZ599pvbt25d4n9vtltvtLvF6REREwDbbX+gBPZDogVSkB3v2mHuDrF9vfjFihFwzZiiidm1nC/QDjgN6IAV2DypTV6WDSEGwqIqCxZeiqx4AUGnvv2/ukvrzz1LdutLcuVLfvk5XBaAKbDtZdePGjdq4caOuueYa1a9fXz/88IMef/xxtWrVqtTVEAA4FVdursIefliaNs28cMUV0tKl0nnnOVsYgCqzLYjUqVNHKSkpmjRpko4eParo6Gh1795dS5YsKXX8AgDl2r1bV0+cqPBt28z2qFHS1KkS/3sC1Gi2BZHLLrtMa9assetfDyCUrFypWoMGqeHhw7KiouR69VWJmyMCQYFnzQAIXD6f9OCD0i23yHX4sI6cd55yN24khABBhKfvAghMP/0k3Xab9PnnkqS80aP1706d1P3ccx0uDEB1YkUEQOB5+23zrJjPP5fOPlv65z+VP22a8gP0UkUAVUcQARA4cnKksWOlv/xF+uUX6aqrpM2bzTaAoEQQARAYfvxRuuYaaeZMsz1unLlZWZEbJAIIPpwjAsB5KSnSkCFSZqZUv760YIF0yy1OVwXAD1gRAeAcr1e67z7p1ltNCGnfXtqyhRAChBCCCABn7NghXX219MILZnv8eOmjj6TmzZ2tC4BfMZoB4H//+Ic0bJiUlSU1bGhGMTff7HRVABzAiggA/zl+XLr3XvOAuqwssyKyZQshBAhhBBEA/vHdd+YckJdeMtsPPyytWyfFxDhaFgBnMZoBYL8lS6Thw6XffpM8HmnhQql7d6erAhAAWBEBYJ9jx6QRI6T+/U0I6dTJjGIIIQB+RxABYI/t26V27aTZsyWXS5o4UfrwQ6lZM6crAxBAGM0AqH6LFkl33y0dPSqdc470xhtSQoLTVQEIQKyIAKg+2dnmstzbbzchpEsXM4ohhAAoA0EEQPX45hupbVvp1VfNKGbSJOmDD6ToaKcrAxDAGM0AOH2vvy7dc49ZEWncWEpOlq691umqANQArIgAqLqjR6U775QGDTIh5LrrzCiGEAKggggiAKrm66+lq66S5s+XwsKkKVOkVaukJk2crgxADcJoBkDlWJYJH/fea+4TEh0tLV4sde7sdGUAaiBWRABU3G+/mTHMkCEmhHTrZkYxhBAAVUQQAVAxW7dKV15pbs8eFiY9+aT0/vvmPiEAUEWMZgCUz7LMJbmjR5un5zZrZkYxHTs6XRmAIEAQAVC2X381z4pJTjbbN95oLtX1eJytC0DQYDQDoHRffinFx5sQEh4uPf20tHIlIQRAtWJFBEBxlmUeVHf//ZLXK8XESEuWSFdf7XRlAIIQQQTACVlZ0l13SUuXmu0//9lcqtuwoaNlAQhejGYAGJs3S23amBBSq5Y0daq0YgUhBICtWBEBQp1lSS+9JI0bJ+XkSM2bmzDSrp3TlQEIAQQRIJRlZkrDhknLlpntHj2kefOkBg2crQtAyGA0A4SqL76QLr/chJCICGnGDOmttwghAPyKFREg1FiW9MIL0oMPSj6fFBcnvfmmuWsqAPgZQQQIJUeOSEOHSv/8p9nu1cvcNfXssx0tC0DoYjQDhIqNG6UrrjAh5IwzpL//3YxlCCEAHEQQAYKdZUnTp5sbku3cKZ17rrRhg3l2jMvldHUAQhyjGSCYHT4s3XmnuR+IJPXpI73yilSvnrN1AcDv/LIi4vV61bp1a7lcLm3ZssUfHwmEjrw8ad0680TcdevMtiR9+qm5KmbFCjOKeeklc38QQgiAAOKXFZHx48eradOm+vLLL/3xcUDoSEmRxoyR9uw58VpMjNS1qwkmubnSeeeZq2Iuv9y5OgGgDLaviLz//vtavXq1pk6davdHAaElJUXq3bt4CJHM9sKFJoT06ydt2kQIARCwbF0ROXDggIYPH6633npLkZGRdn4UEFry8sxKiGWVvU/9+iaQ1OJUMACBy7b/hbIsS4MHD9aIESMUHx+vnTt3nvI9Xq9XXq+3cDsrK0uS5PP55PP57Co1oBV871D9/hI9kEr2wPXRR6p18krIyY4cUe66dbI6d7a7PL/gOKAHEj2QakYPKlOby7LK+79UJU2ePFlJSUnl7pOWlqYNGzZo6dKl+vjjjxUeHq6dO3eqZcuW2rx5s1q3bl2pf3dycjIrKkARzT7+WPHTp59yvy/GjdPeTp38UBEAnJCdna3ExERlZmYqKiqq3H0rHUQyMjKUkZFR7j5xcXHq16+f3nnnHbmK3KcgLy9P4eHhGjBggBYsWFDifaWtiMTGxiojI+OUXyRY+Xw+paamKiEhQREREU6X4wh6ULIHro8+Uq2EhFO+Lzc1NahWRDgO6AE9qBk9yMrKksfjqVAQqfRoxuPxyOPxnHK/v//973riiScKt9PT03XDDTdo6dKlatu2banvcbvdcrvdJV6PiIgI2Gb7Cz2gB9LvPQgPlz7/vPwdXS4pJka1unaVwsP9U5yfcBzQA4keSIHdg8rUZds5Is2bNy+2fdZZZ0mSWrVqpZiYGLs+Fghuhw5JQ4ZIq1adeM3lKn7SasEq5MyZQRdCAAQfbvEO1BANv/5ata680oSQOnXMw+qWLZOaNSu+Y0yMeb1XL2cKBYBK8Nt1fXFxcark6SgAJCk/X2FPP62rJ0+WKz9fuvBC6R//kC691Pz+L3+R1q+X9u2ToqOljh1ZCQFQY3CDASCQHTwoDRyo8NWrJUn5t9+usFmzpN9HnZJM6OjSxZn6AOA0MZoBAtVHH0mtW0urV8uqU0f/GT1aea+9VjyEAEANRxABAk1+vvTkk9K115pxy0UXKXfDBu2+7jqnKwOAakcQAQLJwYNS9+7SxIkmkAweLKWlSZdc4nRlAGALgggQKNatM6OY1FQpMlKaP1+aN08680yHCwMA+xBEAKfl5Ul/+5t03XVmFHPxxWYVZNAgpysDANtx1QzgpAMHpNtvlz74wGzfeaf0wgusggAIGQQRwClr10qJidL+/WYUM2uWdMcdTlcFAH7FaAbwt7w8acoU6frrTQi55BLpiy8IIQBCEisigD/t3y8NGCCtWWO2hwwxo5jISGfrAgCHEEQAf1mzxoxiDhwwwePll6WBA52uCgAcxWgGsFtenjR5shnFHDhgnhHzxReEEAAQKyKAvfbvN6sga9ea7WHDpOefZxQDAL8jiAB2+eADcz7IwYPmctyXXzaX6gIACjGaAapbXp40aZLUrZsJIZddZkYxhBAAKIEVEaA67dtnRjHr1pnt4cPNKKZOHUfLAoBARRABqktqqln1OHhQOussafZsE0oAAGViNAOcrtxc6bHHpBtuMCHkj380oxhCCACcEisiwOlITzeB46OPzPbdd0szZjCKAYAKIogAVbV6tRnFHDpkRjFz5kj9+ztdFQDUKIxmgMrKzZUmTpS6dzch5E9/kjZtIoQAQBWwIgJURnq6CRwff2y2R4wwo5jatZ2tCwBqKIIIUFGrVpnbsh86JNWtK73yinTbbU5XBQA1GqMZ4FRyc6VHHz0ximnd2oxiCCEAcNpYEQHKs3evGcWsX2+277lHmj6dUQwAVBOCCFCWf/3LjGIyMswoZu5cqW9fp6sCgKDCaAY4WW6u9PDD0o03mhBy+eXSf/5DCAEAG7AiAhS1Z48Zxfz732Z75Ehp2jRGMQBgE4IIUOD9980o5uefzSjm1VelPn2crgoAghqjGcDnkyZMkG66yYSQK64woxhCCADYjhURhLbdu6V+/aQNG8z2qFHS1KmS2+1sXQAQIggiCF3vvivdcYd0+LAUFWVGMb17O10VAIQURjMIPT6fNH689Oc/mxDSpo0ZxRBCAMDvWBFBaNm1y4xiPv3UbI8eLT33HKMYAHAIQQShY+VKadAgswpSr5702mtSr15OVwUAIY3RDIKfzyf99a/SLbeYEBIfb0YxhBAAcBwrIghuP/1kRjGffWa2x4yRnnmGUQwABAiCCILXO++YUcyRI2YUM2+e9D//43RVAIAibB3NxMXFyeVyFfuZMGGCnR8JSDk50gMPSD16mBBy5ZXS5s2EEAAIQLaviEyZMkXDhw8v3D7rrLPs/kiEsp9+km67Tfr8c7N9//1mFHPGGY6WBQAone1BpG7dumrSpIndHwNIK1aYUcwvv0hnn21GMX/5i8NFAQDKY3sQeeaZZ/S3v/1NsbGx6tOnj/7617/qjDL+36nX65XX6y3czsrKkiT5fD75fD67Sw1IBd87VL+/VIEe5OQobOJEhc+cKUnKv/JK5S1aJMXFmStmggDHAT2Q6IFED6Sa0YPK1OayLMuyq5AZM2boiiuuUP369bVx40Y9/PDD6tmzp+bOnVvq/pMnT1ZSUlKJ15OTkxUZGWlXmajB6hw4oCunTlX9776TJH3fo4f+O3CgrIgIhysDgNCVnZ2txMREZWZmKioqqtx9Kx1EygoLRaWlpSk+Pr7E68uXL1fv3r2VkZGhhg0blvh9aSsisbGxysjIOOUXCVY+n0+pqalKSEhQRIj+5VpWD1wrVih82DC5fvlF1tlnK2/uXFk9ejhYqX04DuiBRA8keiDVjB5kZWXJ4/FUKIhUejQzatQo9evXr9x94uLiSn29Xbt2kqTvv/++1CDidrvlLuX+DhEREQHbbH+hB0V6kJMjPfSQ9PsoRm3byrVkiWqVcdwFE44DeiDRA4keSIHdg8rUVekg4vF45PF4Kvs2SdLmzZslSdHR0VV6P6AffzRXxaSlme0HHpCeeoqrYgCghrLtZNVPP/1Un332mbp27ap69eopLS1NY8eOVY8ePdS8eXO7PhZBzPXWW9Lw4VJmplS/vjR/vrlXCACgxrItiLjdbi1dulRJSUnyer1q0aKFhg8frvHjx9v1kQhWOTm6dO5c1Vq50my3ayctWSK1aOFsXQCA02ZbELniiiv0WcHzPYCq+uEHhfftq1abNpntBx80o5gAnYsCACqHZ80gcKWkSEOGKCwzUzl16yrs9ddVixuUAUBQsfVZM0CVeL3SffdJt94qZWYqv107rZs+XdbNNztdGQCgmhFEEFh++EG6+mrphRfM9vjxyvvwQx1r1MjZugAAtmA0g8CxbJk0dKiUlSU1aCC9/rp0881Bc5t2AEBJrIjAeV6vNHq01KePCSEdOkhbtpgQAgAIagQROGvHDhM8XnzRbD/0kLRunRQb62hZAAD/YDQD5/zjH9KwYWYVpGFDM4q56SanqwIA+BErIvC/48ele++V+vY1IeTqq6XNmwkhABCCWBGBffLypPXrpX37pOhoqWNH86yYvn1N8JCkCROkKVO4QRkAhCiCCOyRkiKNGSPt2XPitQYNpOxssyLSsKG0cKF0443O1QgAcBxBBNUvJUXq3VuyrOKvHz5s/nnhhVJqqhQT4//aAAABhXNEUL3y8sxKyMkhpKjffjOjGgBAyCOIoHqtX198HFOaPXvMfgCAkEcQQfXat6969wMABDWCCKpXXl7F9mM0AwAQJ6uiOi1ZIo0YUf4+Lpc5SbVjR//UBAAIaKyI4PQdPy7dc4/Uv7909Kh08cUmcLhcxfcr2J45UwoP93uZAIDAQxDB6fn2W6ldO+nll03QePRR6csvzZN0mzUrvm9MjHm9Vy9nagUABBxGM6i6JUuk4cPN5biNGklvvCF162Z+16uX1LNnyTurshICACiCIILKO3ZMGjtWmj3bbHfqJC1eLDVtWny/8HCpSxe/lwcAqDkYzaByvv1Wat/ehBCXS5o4Ufrww5IhBACACmBFBBW3eLF0112lj2IAAKgCVkRwaseOmctyExNNCOncWdqyhRACADhtBBGUr7RRzAcfMIoBAFQLRjMoG6MYAIDNWBFBSceOSXffzSgGAGA7ggiKK7hB2Zw5jGIAALZjNIMTTh7FLFokJSQ4XRUAIIixIoKyRzGEEACAzQgioW779uKjmMceYxQDAPAbRjOhLDnZrIQwigEAOIQVkVB07Jg5F2TAAEYxAABHEURCTcEo5pVXGMUAABzHaCaUJCeblZCjRxnFAAACAisioaDoKOboUalLF0YxAICAQBAJdtu3S23bnhjFPP44oxgAQMBgNBPMFi0yV8UcPSqdc47Zvv56p6sCAKAQKyLBqGAUc/vtxUcxhBAAQICxPYi8++67atu2rerUqSOPx6NevXrZ/ZGhbdu20kcx0dFOVwYAQAm2jmaWL1+u4cOH66mnntK1114ry7K0detWOz8ytDGKAQDUMLYFkdzcXI0ZM0bPPfechg4dWvj6BRdcYNdHhq5jx6T77pPmzjXbXbuaEMIqCAAgwNkWRP7zn/9o7969CgsL0+WXX679+/erdevWmjp1qi655JJS3+P1euX1egu3s7KyJEk+n08+n8+uUgNawfcu8/tv26ZaiYlyffWVLJdL+Y8+qvxHH5XCw6Ug6dkpexAC6AE9kOiBRA+kmtGDytTmsizLsqOIJUuWqH///mrevLmmT5+uuLg4TZs2TatXr9a3336rBg0alHjP5MmTlZSUVOL15ORkRUZG2lFmjRbz0Uf606xZqnX8uI7Xq6dN48Yp409/crosAECIy87OVmJiojIzMxUVFVXuvpUOImWFhaLS0tL07bffasCAAZo9e7buuusuSWbFIyYmRk888YTuvvvuEu8rbUUkNjZWGRkZp/wiwcrn8yk1NVUJCQmKiIgwLx47pvCxYxX22muSpPwuXZS3YEHQjmJK7UGIoQf0QKIHEj2QakYPsrKy5PF4KhREKj2aGTVqlPr161fuPnFxcfr1118lSRdffHHh6263W+eee6527dpV6vvcbrfcbneJ1yMiIgK22f5S2INt26S+faWtWwuvigl77DGFhYc7XaLtOA7ogUQPJHog0QMpsHtQmboqHUQ8Ho88Hs8p92vTpo3cbre2b9+ua665RpJJcTt37lSLFi0q+7GQil8V07ix2b7uOqerAgCgymw7WTUqKkojRozQpEmTFBsbqxYtWui5556TJPXp08eujw1K4V6vwu++W5o3z7zQtat5gF2TJs4WBgDAabL1PiLPPfecatWqpYEDB+rYsWNq27at1qxZo/r169v5scFl2zZ1+utfFbZr14kblD32mLkqBgCAGs7WIBIREaGpU6dq6tSpdn5M8HrjDdUaMUJRR4/KatxYLkYxAIAgw0PvAlF2trlB2auvyiXp0GWX6ex331VEbKzTlQEAUK0IIoFm2zapTx/pq68kl0t5EydqQ+vWuonzQQAAQYin7waShQul+HgTQho3llJTlc/5IACAIEYQCQTZ2dLQodIdd5hLc6+9VtqyhfNBAABBjyDitG++kdq2lV57zVwVk5QkrV7NpbkAgJDAOSJOWrhQGjHCrIg0bmzuDXLttU5XBQCA37Ai4oSio5jsbDOC2bKFEAIACDkEEX/75hvpqquKj2JWrWIUAwAISYxm/On116V77mEUAwDA71gR8YeCUcygQYxiAAAogiBit//+l1EMAABlYDRjp6KjmCZNzCima1enqwIAIGCwImKH7GxpyJCSoxhCCAAAxRBEqlvBKGbePCksTJoyxYxiGjd2ujIAAAIOo5nqxCgGAIBKYUWkOhw9Kt1554lRzPXXM4oBAKACCCKnq2AUM3/+iVHMv/7FKAYAgApgNHM6FiyQRo5kFAMAQBWxIlIVBaOYwYMZxQAAcBoIIpXFKAYAgGrDaKYyTh7FLF4sdenidFUAANRYrIhURFmjGEIIAACnhSByKiePYv72N0YxAABUE0Yz5Zk/X7r3XkYxAADYhBWR0hw9asYwd95pQkhCAqMYAABsQBA52ddfm1HMggVmFPPEE4xiAACwSWiOZvLypPXrpX37pOhoqWNHKTzcjGJGjpSOHTOvL14sde7sdLUAAASt0AsiKSnSmDHSnj0nXmvWTPrDH6R168x2QoL0xhvSOec4UiIAAKEitIJISorUu7dkWcVf37vX/Lhc5qqYhx82YxkAAGCr0PnbNi/PrIScHEKKatRImjCBEAIAgJ+Ezt+469cXH8eU5uBBsx8AAPCL0Aki+/ZV734AAOC0hU4QiY6u3v0AAMBpC50g0rGjFBNjTkgtjcslxcaa/QAAgF+EThAJD5eef978+eQwUrA9c6bZDwAA+EXoBBFJ6tVLWrbM3DekqJgY83qvXs7UBQBAiAqt+4hIJmz07Fn6nVUBAIBfhV4QkUzo4AF2AAA4zrbRzLp16+RyuUr9SUtLs+tjAQBADWLbikiHDh2076R7cjz22GP64IMPFB8fb9fHAgCAGsS2IHLGGWeoSZMmhds+n08rVqzQqFGj5CrrEloAABBS/HaOyIoVK5SRkaHBgweXuY/X65XX6y3czsrKkmRCjM/ns7vEgFTwvUP1+0v0QKIHEj2Q6IFED6Sa0YPK1OayrPKeAld9brrpJknSe++9V+Y+kydPVlJSUonXk5OTFRkZaVttAACg+mRnZysxMVGZmZmKiooqd99KB5GywkJRaWlpxc4D2bNnj1q0aKE333xTt956a5nvK21FJDY2VhkZGaf8IsHK5/MpNTVVCQkJioiIcLocR9ADeiDRA4keSPRAqhk9yMrKksfjqVAQqfRoZtSoUerXr1+5+8TFxRXbnjdvnho2bKgePXqU+z632y23213i9YiIiIBttr/QA3og0QOJHkj0QKIHUmD3oDJ1VTqIeDweeTyeCu9vWZbmzZunO+64I2AbBgAAnGH7Ld7XrFmjH3/8UUOHDrX7owAAQA1j+1Uzr776qjp06KCLLrqo0u8tOH2l4OqZUOTz+ZSdna2srKyQXVGiB/RAogcSPZDogVQzelDw93ZFTkP121UzVbFnzx7FxsY6XQYAAKiC3bt3KyYmptx9AjqI5OfnKz09XXXr1g3Zm6AVXDm0e/fukL1yiB7QA4keSPRAogdSzeiBZVn69ddf1bRpU4WFlX8WSEA/9C4sLOyUSSpUREVFBewB5y/0gB5I9ECiBxI9kAK/B/Xq1avQfrafrAoAAFAWgggAAHAMQSTAud1uTZo0qdQbvYUKekAPJHog0QOJHkjB14OAPlkVAAAEN1ZEAACAYwgiAADAMQQRAADgGIIIAABwDEEkwMTFxcnlchX7mTBhQrnvsSxLkydPVtOmTVWnTh116dJFX3/9tZ8qto/X61Xr1q3lcrm0ZcuWcvcdPHhwib61a9fOP4XaqDI9CLbjoEePHmrevLlq166t6OhoDRw4UOnp6eW+JxiPg6r0IZiOhZ07d2ro0KFq2bKl6tSpo1atWmnSpEnKyckp933BdCxUtQc15TggiASgKVOmaN++fYU/EydOLHf/Z599VtOnT9eLL76otLQ0NWnSRAkJCfr111/9VLE9xo8fr6ZNm1Z4/+7duxfr23vvvWdjdf5RmR4E23HQtWtXvfnmm9q+fbuWL1+uHTt2qHfv3qd8X7AdB1XpQzAdC9u2bVN+fr5mz56tr7/+WjNmzNDLL7+sRx555JTvDZZjoao9qDHHgYWA0qJFC2vGjBkV3j8/P99q0qSJ9fTTTxe+dvz4catevXrWyy+/bEOF/vHee+9ZF154ofX1119bkqzNmzeXu/+gQYOsnj17+qU2f6lMD4L1OCjq7bfftlwul5WTk1PmPsF4HJzsVH0IhWPh2WeftVq2bFnuPsF+LJyqBzXpOGBFJAA988wzatiwoVq3bq0nn3yy3OW3H3/8Ufv371e3bt0KX3O73ercubM2bNjgj3Kr3YEDBzR8+HAtXLhQkZGRFX7funXrdM455+j888/X8OHDdfDgQRurtFdlexCMx0FRhw8f1qJFi9ShQ4dTPvY8mI6Dk1WkD8F+LEhSZmamGjRocMr9gvlYOFUPatJxQBAJMGPGjNGSJUu0du1ajRo1SjNnztTIkSPL3H///v2SpMaNGxd7vXHjxoW/q0ksy9LgwYM1YsQIxcfHV/h9N954oxYtWqQ1a9Zo2rRpSktL07XXXiuv12tjtfaoSg+C7Tgo8NBDD+nMM89Uw4YNtWvXLr399tvl7h9Mx0FRlelDsB4LBXbs2KEXXnhBI0aMKHe/YD0WpIr1oEYdB04vyYSCSZMmWZLK/UlLSyv1vcuWLbMkWRkZGaX+/pNPPrEkWenp6cVeHzZsmHXDDTdU+3epqor24Pnnn7c6dOhg5ebmWpZlWT/++GOFRjMnS09PtyIiIqzly5fb8G2qxs4eBNtxUODQoUPW9u3brdWrV1tXX321ddNNN1n5+fkV/rxAPA4sy94+BOuxYFmWtXfvXuu8886zhg4dWunPC8Rjwc4e1JTjwLIsq1Y1ZBmcwqhRo9SvX79y94mLiyv19YKzvL///ns1bNiwxO+bNGkiyaTf6OjowtcPHjxYIgk7qaI9eOKJJ/TZZ5+VeIZCfHy8BgwYoAULFlTo86Kjo9WiRQt99913Va65utnZg2A7Dgp4PB55PB6df/75uuiiixQbG6vPPvtM7du3r9DnBeJxINnbh2A9FtLT09W1a1e1b99ec+bMqfTnBeKxYGcPaspxIIkVkUD3zjvvWJKsn376qdTfF5yQ9MwzzxS+5vV6A/KEpIr46aefrK1btxb+rFq1ypJkLVu2zNq9e3eF/z0ZGRmW2+22FixYYGO19qhKD4LtOCjNrl27LEnW2rVrK/yemnwclOVUfQjGY2HPnj3WH/7wB6tfv36FK4WVVdOPhcr2oCYdBwSRALJhwwZr+vTp1ubNm60ffvjBWrp0qdW0aVOrR48exfa74IILrJSUlMLtp59+2qpXr56VkpJibd261erfv78VHR1tZWVl+fsrVLuyxhJFe/Drr79aDzzwgLVhwwbrxx9/tNauXWu1b9/eatasWcj0wLKC6zj4/PPPrRdeeMHavHmztXPnTmvNmjXWNddcY7Vq1co6fvx44X7BfhxUpQ+WFVzHQsEo4tprr7X27Nlj7du3r/CnqGA+FqrSA8uqOccBQSSAbNq0yWrbtq1Vr149q3bt2tYFF1xgTZo0yTp69Gix/SRZ8+bNK9zOz8+3Jk2aZDVp0sRyu91Wp06drK1bt/q5enuU9Zdw0R5kZ2db3bp1sxo1amRFRERYzZs3twYNGmTt2rXL/wXboCI9sKzgOg7+7//+z+ratavVoEEDy+12W3FxcdaIESOsPXv2FNsv2I+DqvTBsoLrWJg3b16Z508UFczHQlV6YFk15zhwWZZl+WcIBAAAUByX7wIAAMcQRAAAgGMIIgAAwDEEEQAA4BiCCAAAcAxBBAAAOIYgAgAAHEMQAQAAjiGIAAAAxxBEAACAYwgiAADAMQQRAADgmP8PHdwQBw4QWF0AAAAASUVORK5CYII=", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t0 = 0.0\n", "T = 10.0\n", "M = 6\n", "loghN = np.zeros(M)\n", "logeN = np.zeros(M)\n", "i = 0\n", "\n", "for N in np.array([64,128,256,512,1024,2048]):\n", " y0 = np.array([5.0])\n", " t, z = RK2(croissanceCell, y0, t0, T, N)\n", " hN = (T-t0)/N\n", " loghN[i] = np.log(hN)\n", " logeN[i] = np.log(np.abs(rho(T) - z[-1,0]))\n", " i += 1\n", "\n", "print('loghN = \\n', loghN)\n", "print('logeN = \\n', logeN)\n", "\n", "plt.plot(loghN, logeN, 'o-r'); plt.grid()" ] }, { "cell_type": "code", "execution_count": 11, "id": "3d7241d6-c799-469d-acda-5f0d2f608832", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "p estimé = 1.9867304905996814 \n", "\n", "\n" ] } ], "source": [ "A = np.zeros((M,2))\n", "A[:,0] = np.ones(M)\n", "A[:,1] = loghN\n", "\n", "# Résolution des équations normales :\n", "u = np.linalg.solve(A.T@A, A.T@logeN)\n", "\n", "# K = u[0], p = u[1]\n", "print(\"\\np estimé = \", u[1],'\\n\\n')" ] }, { "cell_type": "markdown", "id": "0ba9aa89-764c-44f0-b7a7-2d6084fc76bc", "metadata": {}, "source": [ "### 2. Oscillateur non linéaire de Duffing\n", "\n", "Le système non linéaire de Duffing modélise un système masse-ressort isolé avec une loi d'élasticité non linéaire cubique. Les équations de la cinématique et de la dynamique autour de l'équilibre donnent\n", "\n", "\\begin{align*}\n", "& \\dot x(t) = v(t), \\\\\n", "& \\dot v(t) = - \\alpha\\, x(t) -\\beta\\, x^3(t).\n", "\\end{align*}\n", "\n", "Le terme $\\alpha x$ est le terme d'élasticité linéaire classique avec $\\alpha>0$ le coefficient de raideur du ressort. Le terme non linéaire\n", "$\\beta x^3$, $\\beta>0$, agit pour les plus forts déplacements et exprime une plus grande force de rappel.\n", "\n", "On peut vérifier que l'énergie totale du système (somme d el'énergie élastique et de l'énergie cinétique)\n", "\n", "$$\n", "E=E(x,v) = \\alpha \\frac{x^2}{2} + \\beta \\frac{x^4}{4}\n", "+ \\frac{v^2}{2}\n", "$$\n", "\n", "est conservée au cours du temps (système hamiltonien).\n", "\n", "Ecrire d'abord le système sous la forme vectorielle générique\n", "\n", "$$\n", "\\frac{d\\mathbf{y}}{dt} = \\mathbf{F}(t, \\mathbf{y}(t))\n", "$$\n", "\n", "où l'on précisera $\\mathbf{y}$ et $\\mathbf{F}(t,\\mathbf{y})$. Ecrire une fonction python ```Duffing(y,t)``` qui implémente $F$.\n", "Pour les paramètres, on prendra $\\alpha=1$ et $\\beta=12$." ] }, { "cell_type": "code", "execution_count": 12, "id": "5f77a176-60cb-4158-bbc7-85ac797be179", "metadata": { "tags": [] }, "outputs": [], "source": [ "# function that returns ydot\n", "def Duffing(t,y):\n", " x = y[0]\n", " v = y[1]\n", " alpha = 1.0\n", " beta = 12.0\n", " ydot = np.zeros(2)\n", " ydot[0] = v\n", " ydot[1] = -alpha*x - beta*x**3\n", " return ydot" ] }, { "cell_type": "markdown", "id": "eb5c0628-5ff4-4d94-9517-7d480384ee14", "metadata": { "tags": [] }, "source": [ "Intégrer numériquement le problème différentiel en utilisant ```odeint()```. On prendra $t_0=0$, $T=4$, \n", "$y_0=(x_0,v_0)^T=(2,0)^T$ et ```t = np.linspace(0,T, 200)```.\n", "Tracer les solutions numériques $t\\mapsto x(t)$ et $t\\mapsto v(t)$ obtenues. Tracer de même l'évolution de l'énergie totale $t\\mapsto E(t)$ et faites attention à l'échelle de l'axe des ordonnées." ] }, { "cell_type": "code", "execution_count": 13, "id": "d82c7fb8-e7ca-4947-b419-71240bcf2a32", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from scipy.integrate import odeint\n", "import matplotlib.pyplot as plt\n", "\n", "# initial condition\n", "y0 = np.array([2, 0])\n", "# final time\n", "T = 4\n", "# time points\n", "t = np.linspace(0,T, 200)\n", "# solve ODE\n", "y = odeint(Duffing, y0, t, tfirst='true')\n", "\n", "# plot results\n", "fig, ax = plt.subplots(2)\n", "ax[0].plot(t, y[:,0], '.-'); plt.grid();\n", "ax[0].set(xlabel='time t', ylabel='x(t)');ax[0].grid()\n", "ax[1].plot(t, y[:,1], '.-'); plt.grid();\n", "ax[1].set(xlabel='time t', ylabel='v(t)');ax[1].grid()\n", "\n", "x = y[:,0]\n", "v = y[:,1]\n", "alpha = 1.0; beta = 12.0\n", "E = alpha*x**2/2 + beta*x**4/4 + v**2/2;\n", "plt.figure()\n", "plt.plot(t, E, '.-'); plt.grid();\n", "plt.xlabel('time t');\n", "plt.ylabel('E(t)');\n", "plt.ylim((49,51));" ] }, { "cell_type": "markdown", "id": "7d3b9136-7065-4677-b97b-9143f4600960", "metadata": {}, "source": [ "Tracer de même la solution $(x(t),v(t))_{t\\in[0,T]}$ dans le plan de phase $(x,v)$. La courbe fermée ainsi obtenue est dite une orbite." ] }, { "cell_type": "code", "execution_count": 14, "id": "3e3081a6-0eb7-4b1b-8fc5-95cee3abb261", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.plot(y[:,0], y[:,1], '.-');\n", "plt.grid();\n", "plt.xlabel('x(t)');\n", "plt.ylabel('v(t)');" ] }, { "cell_type": "markdown", "id": "7a4e2a84-b2fd-4886-9d98-08ece9f06110", "metadata": {}, "source": [ "Appliquer le schéma d'Euler à l'oscillateur de Duffing avec $N=500$. Tracer les solutions numériques obtenues ainsi que l'évolution de l'énergie totale. Est-ce satisfaisant ? " ] }, { "cell_type": "code", "execution_count": 15, "id": "c49bf475-54a7-42ee-85a8-ccd109961c8e", "metadata": { "scrolled": true, "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "t, y = Euler(Duffing, y0, 0.0, T, 500)\n", "# plot results\n", "fig, ax = plt.subplots(2)\n", "ax[0].plot(t, y[:,0], '.-'); plt.grid();\n", "ax[0].set(xlabel='time t', ylabel='x(t)');ax[0].grid()\n", "ax[1].plot(t, y[:,1], '.-'); plt.grid();\n", "ax[1].set(xlabel='time t', ylabel='v(t)');ax[1].grid()" ] }, { "cell_type": "code", "execution_count": 16, "id": "8d64568e-bf66-4400-9277-2213b3903796", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "x = y[:,0]\n", "v = y[:,1]\n", "alpha = 1.0; beta = 12.0\n", "E = alpha*x**2/2 + beta*x**4/4 + v**2/2;\n", "plt.figure()\n", "plt.plot(t, E, '.-'); plt.grid();\n", "plt.xlabel('time t');\n", "plt.ylabel('E(t)');" ] }, { "cell_type": "markdown", "id": "1d4cf1ee-a498-473c-a504-0d774ab6dcbe", "metadata": {}, "source": [ "Appliquez le schéma RK2 au système de Duffing où l'on comparerea les solutions avec celles obtenues avec ```odeint()``` ainsi que l'évolution de l'énergie totale $E$. Commentez. " ] }, { "cell_type": "code", "execution_count": 17, "id": "622dbff9-c7a7-42b0-a2d2-9276bd3b91fa", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "T = 4.0\n", "N = 80\n", "t, y = RK2(Duffing, y0, 0.0, T, N)\n", "# plot results\n", "fig, ax = plt.subplots(2)\n", "ax[0].plot(t, y[:,0], '.-'); plt.grid();\n", "ax[0].set(xlabel='time t', ylabel='x(t)');ax[0].grid()\n", "ax[1].plot(t, y[:,1], '.-'); plt.grid();\n", "ax[1].set(xlabel='time t', ylabel='v(t)');ax[1].grid()\n", "\n", "x = y[:,0]\n", "v = y[:,1]\n", "E = alpha*x**2/2 + beta*x**4/4 + v**2/2;\n", "plt.figure(figsize=(3,3))\n", "plt.plot(t, E, '-'); plt.grid()" ] }, { "cell_type": "markdown", "id": "0323a455-b410-4d74-8483-3e1573f43648", "metadata": {}, "source": [ "#### Schéma à variables décalées de Verlet\n", "\n", "\\begin{align*}\n", "\t& x_{n+1} = x_n + h v_{n+1/2}, \\\\\n", "\t& v_{n+3/2} = v_{n+1/2} - h\\alpha\\, x_{n+1} - h \\beta\\, x_{n+1}^3. \n", "\\end{align*}\n", "\n", "Les données initiales sont toujours $x_0=2$ et $v_0=0$. Pour \"l'initialisation\" de $v_{1/2}$ on utilisera ici simplement le schéma d'Euler explicite sur $v$ (sachant que l'on peut faire mieux) :\n", "\n", "$$\n", "v_{1/2} = v_0 - \\frac{h}{2}\\alpha\\, x_0 - \\frac{h}{2}\\beta\\, x_0^3.\n", "$$\n", "\n", "Mettre en oeuvre le schéma de Verlet pour l'oscillateur de Duffing. On utilisera une subdivision uniforme comme pour le schéma d'Euler avec $h=\\frac{T-t_0}{N}$. Tracer les solutions numériques $t\\mapsto x(t)$ et $t\\mapsto v(t)$ ainsi obtenues. On utilisera \n", "$N=100$." ] }, { "cell_type": "code", "execution_count": 24, "id": "4409d7d5-e980-40db-8004-962b7c2bbaf0", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "N = 200\n", "t0 = 0; T = 8\n", "h = (T-t0) / N\n", "t = np.linspace(t0, T, N+1)\n", "x = np.zeros(N+1)\n", "vdec = np.zeros(N+1)\n", "x[0] = 2\n", "v0 = 0\n", "# Calcul de v_{1/2}\n", "vdec[0] = v0 - (h/2)*alpha*x[0] - (h/2)*beta*x[0]**3\n", "\n", "for n in range(0,N):\n", " x[n+1] = x[n] + h*vdec[n]\n", " vdec[n+1] = vdec[n] - h*alpha*x[n+1] - h*beta*x[n+1]**3 \n", "\n", "# plot results\n", "#plt.figure(figsize=(20, 6));\n", "fig, ax = plt.subplots(2)\n", "ax[0].plot(t, x, '.-'); plt.grid();\n", "ax[0].set(xlabel='time t', ylabel='x(t)');ax[0].grid();\n", "ax[1].plot(t, vdec, '.-'); plt.grid();\n", "ax[1].set(xlabel='time t', ylabel='v(t)');ax[1].grid();" ] }, { "cell_type": "markdown", "id": "3d4f9f88-7a43-4812-97d7-f2a6eb876be1", "metadata": {}, "source": [ "Les variables discrètes de positions $x_n$ et de vitesse $v_{n+1/2}$ ne sont pas définies aux mêmes instants discrets, si bien que l'on ne peut pas définir strictement une énergie totale. On peut toutefois définir une estimation en calculant une valeur moyenne $\\hat v_n$ de vitesse aux temps $t_n$ par\n", "\n", "$$\n", "\\hat v_n = \\frac{v_{n-1/2}+v_{n+1/2}}{2}\n", "$$\n", "\n", "et définir une énergie totale approchée $\\hat E_n$ par\n", "\n", "$$\n", "\\hat E_n = \\alpha\\frac{x_n^2}{2}+\\beta \\frac{x_n^4}{4} + \\frac{\\hat v_n^2}{2}.\n", "$$\n", "\n", "Tracer dans ce cas l'évolution de $\\hat E_n$ ainsi définie au cours du temps. Est-ce satisfaisant ? \n", "\n", "Refaire le calcul et les graphiques avec $N=200$." ] }, { "cell_type": "code", "execution_count": 19, "id": "c54e2a69-acd3-41d7-8086-3940d2f25a8d", "metadata": { "tags": [] }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "vhat = np.zeros(N+1)\n", "vhat[0] = v0\n", "vhat[1:N+1] = 0.5*(vdec[0:N]+vdec[1:N+1])\n", "Ehat = alpha*x**2/2 + beta*x**4/4 + vhat**2/2\n", "plt.plot(t, Ehat, '.-')\n", "plt.grid()" ] }, { "cell_type": "markdown", "id": "c0f2275a-17f0-4840-afb6-00a64e1dd5e3", "metadata": {}, "source": [ "C'est fini pour les TPs !" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.13.5" } }, "nbformat": 4, "nbformat_minor": 5 }