Ajouts des questions

QUESTION15.ipynb

@@ -0,0 +1,124 @@
+{
+ "cells": [
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "id": "fcdc8220-ff32-44a6-a1aa-008c9d2ab047",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "import numpy as np\n",
+    "import matplotlib.pyplot as plt"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 3,
+   "id": "f6807c1d-c008-4661-a888-5244338ff765",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "def f(x):\n",
+    "    return x**-2"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 4,
+   "id": "b1095809-d35b-475a-887e-728695022470",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "def integrNC(fct, a, b, N, m, n, r, coeff, tol=1e10):\n",
+    "    h = (b-a)/m/N\n",
+    "    I = 0\n",
+    "    for k in range(N):\n",
+    "        # Ajout d'un shéma élementaire\n",
+    "        Ie = 0\n",
+    "        \n",
+    "        Xk = a + h*k*m\n",
+    "        for i in range(n+1):\n",
+    "            Ie += coeff[i] * fct(Xk + (i+r)*h)\n",
+    "   \n",
+    "        I += Ie * h\n",
+    "    \n",
+    "    return I"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 7,
+   "id": "36508cd9-143a-4174-bc98-6c01634f1fcd",
+   "metadata": {
+    "tags": []
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "0.998686802598624\n"
+     ]
+    }
+   ],
+   "source": [
+    "I = 0\n",
+    "a, b = 1, 5\n",
+    "N=100\n",
+    "m=1\n",
+    "n=1\n",
+    "r=0\n",
+    "coeff = [.5, .5]\n",
+    " \n",
+    "while True:\n",
+    "    Ie = integrNC(f, a, b, N, m, n, r, coeff)\n",
+    "    \n",
+    "    \n",
+    "    d= b-a\n",
+    "    b += d\n",
+    "    a += d\n",
+    "    # print(I, abs(Ie), abs(Ie)<1e-10)\n",
+    "    if abs(I+Ie) - abs(I) < 1e-5:\n",
+    "        break\n",
+    "    I += Ie\n",
+    " \n",
+    "print(I)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d52567ea-6629-4433-9df9-e3f93de1c36c",
+   "metadata": {},
+   "outputs": [],
+   "source": []
+  }
+ ],
+ "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": "3.11.5"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}