mirror of
https://github.com/ArthurDanjou/ArtStudies.git
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480 lines
198 KiB
Plaintext
480 lines
198 KiB
Plaintext
{
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"cells": [
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{
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"metadata": {
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"ExecuteTime": {
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"end_time": "2025-03-03T14:27:00.244402Z",
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"start_time": "2025-03-03T14:27:00.241231Z"
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}
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},
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"cell_type": "code",
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"source": [
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"import numpy as np\n",
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"import matplotlib.pyplot as plt\n",
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"from scipy.integrate import odeint"
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],
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"id": "fe01d49f9c6740ce",
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"outputs": [],
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"execution_count": 100
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},
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{
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"metadata": {},
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"cell_type": "markdown",
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"source": "## Exercise 2.18 : Numerical precision",
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"id": "4a91fd48ddb1c4fc"
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},
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{
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"metadata": {
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"collapsed": true,
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"ExecuteTime": {
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"end_time": "2025-03-03T15:03:25.306403Z",
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"start_time": "2025-03-03T15:03:25.302289Z"
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}
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},
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"cell_type": "code",
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"source": [
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"def f(t, x):\n",
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" return 2 * np.power(np.abs(x), 1 / 2)\n",
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"\n",
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"\n",
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"def f_exact(x, lam):\n",
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" return np.power(x - lam, 2) * (x >= lam)"
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],
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"id": "initial_id",
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"outputs": [],
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"execution_count": 169
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},
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{
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"metadata": {
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"ExecuteTime": {
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"end_time": "2025-03-04T12:48:26.892060Z",
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"start_time": "2025-03-04T12:48:26.888087Z"
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}
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},
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"cell_type": "code",
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"source": [
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"def euler_explicit(N, T, y0, f, args=()):\n",
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" h = T / N\n",
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" t = np.linspace(0, T, N + 1)\n",
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" y = np.zeros(N + 1, dtype=complex)\n",
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" y[0] = y0\n",
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" for n in range(N):\n",
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" y[n + 1] = y[n] + h * f(t[n], y[n], *args)\n",
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" return t, y"
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],
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"id": "f447a3bdff49e850",
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"outputs": [],
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"execution_count": 244
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},
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{
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"metadata": {
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"ExecuteTime": {
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"end_time": "2025-03-03T15:26:18.887962Z",
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"start_time": "2025-03-03T15:26:18.799687Z"
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}
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},
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"cell_type": "code",
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"source": [
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"T = 10\n",
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"N = 1000\n",
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"u0 = 0\n",
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"\n",
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"t, sol_appr = euler_explicit(N, T, u0, f)\n",
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"x = np.linspace(u0, T, 100)\n",
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"\n",
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"plt.scatter(t, sol_appr, label=\"Approximation\")\n",
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"plt.plot(x, f_exact(x, T), label=\"Exact solution\", color=\"red\")\n",
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"plt.legend()\n",
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"plt.show()"
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],
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"id": "957b7a23b6076f77",
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"outputs": [
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{
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"data": {
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"text/plain": [
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"<Figure size 640x480 with 1 Axes>"
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],
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"image/png": 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"
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"execution_count": 218
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2025-03-03T15:25:45.054499Z",
|
|
"start_time": "2025-03-03T15:25:45.049904Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"def euler_implicit(N, T, y0):\n",
|
|
" h = T / N\n",
|
|
" t = np.linspace(0, T, N + 1)\n",
|
|
" y = np.zeros(N + 1)\n",
|
|
" y[0] = y0\n",
|
|
" for n in range(N):\n",
|
|
" y[n + 1] = np.power(h + np.sqrt(h ** 2 + y[n]), 2)\n",
|
|
" return t, y"
|
|
],
|
|
"id": "57527c2e5eb6d17d",
|
|
"outputs": [],
|
|
"execution_count": 214
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2025-03-03T15:25:51.105580Z",
|
|
"start_time": "2025-03-03T15:25:51.038176Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"T = 10\n",
|
|
"N = 1000\n",
|
|
"u0 = 0\n",
|
|
"\n",
|
|
"t, sol_appr = euler_implicit(N, T, u0)\n",
|
|
"x = np.linspace(0, T, 100)\n",
|
|
"\n",
|
|
"plt.scatter(t, sol_appr, label=\"Approximation\")\n",
|
|
"plt.plot(x, f_exact(x, T), label=\"Exact solution\", color=\"red\")\n",
|
|
"plt.plot(x, x ** 2, label=\"Square function\", color=\"green\")\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
],
|
|
"id": "2ff29a8872a51c89",
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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"
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"execution_count": 216
|
|
},
|
|
{
|
|
"metadata": {},
|
|
"cell_type": "markdown",
|
|
"source": "## Exercise 2.19 : SIR model, schema order",
|
|
"id": "ecea2cd935dea93a"
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2025-03-03T15:25:14.888616Z",
|
|
"start_time": "2025-03-03T15:25:14.884827Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"def F(y, t, a, r):\n",
|
|
" S, I, R = y\n",
|
|
" dS = -r * S * I\n",
|
|
" dI = r * S * I - a * I\n",
|
|
" dR = a * I\n",
|
|
" return np.array([dS, dI, dR])"
|
|
],
|
|
"id": "61588e94b56ea779",
|
|
"outputs": [],
|
|
"execution_count": 208
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2025-03-03T15:25:15.302160Z",
|
|
"start_time": "2025-03-03T15:25:15.298178Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"def euler_explicit_sir(N, T, u0, f, args):\n",
|
|
" t = np.linspace(0, T, N + 1)\n",
|
|
" y = np.zeros((N + 1, len(y0)))\n",
|
|
" y[0] = y0\n",
|
|
" h = T / N\n",
|
|
" for i in range(N):\n",
|
|
" y[i + 1] = y[i] + h * F(y[i], t[i], *args)\n",
|
|
" return t, y"
|
|
],
|
|
"id": "a32f0facb958a1a0",
|
|
"outputs": [],
|
|
"execution_count": 209
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2025-03-03T15:25:15.672410Z",
|
|
"start_time": "2025-03-03T15:25:15.667465Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"def heun_sir(N, T, u0, f, args):\n",
|
|
" t = np.linspace(0, T, N + 1)\n",
|
|
" y = np.zeros((N + 1, len(y0)))\n",
|
|
" y[0] = y0\n",
|
|
" h = T / N\n",
|
|
" for i in range(N):\n",
|
|
" k1 = h * F(y[i], t[i], *args)\n",
|
|
" k2 = h * F(y[i] + k1, t[i + 1], *args)\n",
|
|
" y[i + 1] = y[i] + 0.5 * (k1 + k2)\n",
|
|
" return t, y"
|
|
],
|
|
"id": "ca061c36b09f7200",
|
|
"outputs": [],
|
|
"execution_count": 210
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2025-03-03T15:25:16.031135Z",
|
|
"start_time": "2025-03-03T15:25:16.028109Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"def runge_kutta_order_4_sir(N, T, u0, f, args):\n",
|
|
" t = np.linspace(0, T, N + 1)\n",
|
|
" y = np.zeros((N + 1, len(y0)))\n",
|
|
" y[0] = y0\n",
|
|
" h = T / N\n",
|
|
" for i in range(N):\n",
|
|
" k1 = h * F(y[i], t[i], *args)\n",
|
|
" k2 = h * F(y[i] + 0.5 * k1, t[i] + 0.5 * h, *args)\n",
|
|
" k3 = h * F(y[i] + 0.5 * k2, t[i] + 0.5 * h, *args)\n",
|
|
" k4 = h * F(y[i] + k3, t[i + 1], *args)\n",
|
|
" y[i + 1] = y[i] + (k1 + 2 * k2 + 2 * k3 + k4) / 6\n",
|
|
" return t, y"
|
|
],
|
|
"id": "afc8571b14a6b464",
|
|
"outputs": [],
|
|
"execution_count": 211
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2025-03-03T18:10:51.913835Z",
|
|
"start_time": "2025-03-03T18:10:51.827148Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"t0, T = 52, 60\n",
|
|
"N = 150\n",
|
|
"\n",
|
|
"y0 = np.array([10e6, 10, 0], dtype=np.float64) # Initial conditions: S, I, R\n",
|
|
"y0 = y0 / np.sum(y0) # Normalize initial conditions\n",
|
|
"a = 0.33 # Recovery rate\n",
|
|
"r = 0.5 # Infection rate\n",
|
|
"t = np.linspace(t0, T, N)\n",
|
|
"\n",
|
|
"sol = odeint(F, y0, t, args=(a, r))\n",
|
|
"\n",
|
|
"plt.plot(t, sol[:, 0], label='S(t)')\n",
|
|
"plt.plot(t, sol[:, 1], label='I(t)')\n",
|
|
"plt.plot(t, sol[:, 2], label='R(t)')\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
],
|
|
"id": "3ff4bbd4286d2b69",
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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"
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"execution_count": 235
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2025-03-03T18:10:54.382031Z",
|
|
"start_time": "2025-03-03T18:10:54.014044Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"errors_EE = []\n",
|
|
"errors_H = []\n",
|
|
"errors_RK4 = []\n",
|
|
"\n",
|
|
"h_list = [0.05, 0.01, 0.1, 0.5, 1, 2, 4]\n",
|
|
"\n",
|
|
"\n",
|
|
"def calculate_errors(sol_exact, sol_appr):\n",
|
|
" return np.max(\n",
|
|
" np.power(np.abs(sol_appr - sol_exact), 2)[np.isfinite(np.power(np.abs(sol_appr - sol_exact), 2))]\n",
|
|
" )\n",
|
|
"\n",
|
|
"\n",
|
|
"for h in h_list:\n",
|
|
" N = int(T / h)\n",
|
|
" t = np.linspace(0, T, N + 1)\n",
|
|
"\n",
|
|
" _, sol_appr_EE = euler_explicit_sir(N, T, y0, F, args=(a, r))\n",
|
|
" _, sol_appr_H = heun_sir(N, T, y0, F, args=(a, r))\n",
|
|
" _, sol_appr_RK4 = runge_kutta_order_4_sir(N, T, y0, F, args=(a, r))\n",
|
|
" sol_exact = odeint(F, y0, t, args=(a, r))\n",
|
|
"\n",
|
|
" errors_EE.append(calculate_errors(sol_exact, sol_appr_EE))\n",
|
|
" errors_H.append(calculate_errors(sol_exact, sol_appr_H))\n",
|
|
" errors_RK4.append(calculate_errors(sol_exact, sol_appr_RK4))\n",
|
|
"\n",
|
|
"plt.plot(errors_EE, label=\"Euler Explicit\")\n",
|
|
"plt.plot(errors_H, label=\"Heun\")\n",
|
|
"plt.plot(errors_RK4, label=\"Runge Kutta order 4\")\n",
|
|
"plt.yscale('log')\n",
|
|
"plt.xscale('log')\n",
|
|
"plt.legend()\n",
|
|
"plt.show()"
|
|
],
|
|
"id": "c147c62e0a55bf28",
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 640x480 with 1 Axes>"
|
|
],
|
|
"image/png": 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"
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"execution_count": 236
|
|
},
|
|
{
|
|
"metadata": {},
|
|
"cell_type": "markdown",
|
|
"source": "## Exercise 2.20 : Stability of Euler Explicit",
|
|
"id": "ee44f24a438fb7b6"
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2025-03-04T12:48:41.100446Z",
|
|
"start_time": "2025-03-04T12:48:41.096706Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"def euler_implicit(N, T, u0, lam):\n",
|
|
" h = T / N\n",
|
|
" t = np.linspace(0, T, N + 1)\n",
|
|
" u = np.zeros(N + 1, dtype=complex)\n",
|
|
" u[0] = u0\n",
|
|
" for n in range(N):\n",
|
|
" u[n + 1] = u[n] / (1 - lam * h)\n",
|
|
" return t, u"
|
|
],
|
|
"id": "4484c71f50b8e691",
|
|
"outputs": [],
|
|
"execution_count": 246
|
|
},
|
|
{
|
|
"metadata": {
|
|
"ExecuteTime": {
|
|
"end_time": "2025-03-04T12:48:58.948153Z",
|
|
"start_time": "2025-03-04T12:48:58.791130Z"
|
|
}
|
|
},
|
|
"cell_type": "code",
|
|
"source": [
|
|
"def f(t, x, lam):\n",
|
|
" return x * lam\n",
|
|
"\n",
|
|
"\n",
|
|
"T = 10 * 2 * np.pi\n",
|
|
"lam = 1j\n",
|
|
"N = 400\n",
|
|
"x0 = 1\n",
|
|
"\n",
|
|
"t, x_appr_EE = euler_explicit(N, T, x0, f, args=(lam,))\n",
|
|
"_, x_appr_EI = euler_implicit(N, T, x0, lam)\n",
|
|
"x_exact = x0 * np.exp(lam * t)\n",
|
|
"\n",
|
|
"# Plot the real parts\n",
|
|
"plt.figure(figsize=(12, 6))\n",
|
|
"plt.subplot(1, 2, 1)\n",
|
|
"plt.plot(t, np.real(x_appr_EI), label='Numerical Solution by EI')\n",
|
|
"plt.plot(t, np.real(x_appr_EE), label='Numerical Solution by EE')\n",
|
|
"plt.plot(t, np.real(x_exact), label='Exact Solution', linestyle='--')\n",
|
|
"plt.xlabel('Time')\n",
|
|
"plt.ylabel('Real Part')\n",
|
|
"plt.legend()\n",
|
|
"plt.title('Real Part of the Solution')\n",
|
|
"\n",
|
|
"# Plot the imaginary parts\n",
|
|
"plt.subplot(1, 2, 2)\n",
|
|
"plt.plot(t, np.imag(x_appr_EI), label='Numerical Solution by EI')\n",
|
|
"plt.plot(t, np.imag(x_appr_EE), label='Numerical Solution by EE')\n",
|
|
"plt.plot(t, np.imag(x_exact), label='Exact Solution', linestyle='--')\n",
|
|
"plt.xlabel('Time')\n",
|
|
"plt.ylabel('Imaginary Part')\n",
|
|
"plt.legend()\n",
|
|
"plt.title('Imaginary Part of the Solution')\n",
|
|
"\n",
|
|
"plt.show()"
|
|
],
|
|
"id": "1b8a3146e7060c52",
|
|
"outputs": [
|
|
{
|
|
"data": {
|
|
"text/plain": [
|
|
"<Figure size 1200x600 with 2 Axes>"
|
|
],
|
|
"image/png": 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"
|
|
},
|
|
"metadata": {},
|
|
"output_type": "display_data"
|
|
}
|
|
],
|
|
"execution_count": 250
|
|
},
|
|
{
|
|
"metadata": {},
|
|
"cell_type": "code",
|
|
"outputs": [],
|
|
"execution_count": null,
|
|
"source": "",
|
|
"id": "aeb67c5158f41a0b"
|
|
}
|
|
],
|
|
"metadata": {
|
|
"kernelspec": {
|
|
"display_name": "Python 3",
|
|
"language": "python",
|
|
"name": "python3"
|
|
},
|
|
"language_info": {
|
|
"codemirror_mode": {
|
|
"name": "ipython",
|
|
"version": 2
|
|
},
|
|
"file_extension": ".py",
|
|
"mimetype": "text/x-python",
|
|
"name": "python",
|
|
"nbconvert_exporter": "python",
|
|
"pygments_lexer": "ipython2",
|
|
"version": "2.7.6"
|
|
}
|
|
},
|
|
"nbformat": 4,
|
|
"nbformat_minor": 5
|
|
}
|