Create the_Simpson’s_method.ipynb

Create a simple solution for the Simpson's numerical method

Author: CheshirLvova

numerical_methods/the_Simpson’s_method.ipynb

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+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Simpson's Rule is a numerical method that approximates the value of a definite integral by using quadratic functions. This method is named after the English mathematician Thomas Simpson (1710−1761)."
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Let's check this method for the next function: $$f(x) = ({e^x / 2})*(cos(x)-sin(x))$$ with $\\varepsilon = 0.001$"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 1,
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "import math \n",
+    "import numpy as np\n",
+    "\n",
+    "def simpsone(a, b, n, func):\n",
+    "    h = float((b-a)/n)\n",
+    "    s = (func(a) + func(b)) * 0.5\n",
+    "    for i in np.arange(0, n-1):\n",
+    "        xk = a + h*i\n",
+    "        xk1 = a + h*(i-1)\n",
+    "        s = s + func(xk) + 2*func((xk1+xk)/2)\n",
+    "    x = a + h*n\n",
+    "    x1 = a + h*(n-1)\n",
+    "    s += 2 *func((x1 + x)/2)\n",
+    "    return s*h/3.0"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## Some input data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 2,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "Result:  -8.404153016168566\n"
+     ]
+    }
+   ],
+   "source": [
+    "f = lambda x: (math.e**x / 2)*(math.cos(x)-math.sin(x))\n",
+    "\n",
+    "n = 10000  \n",
+    "a = 2.0\n",
+    "b = 3.0\n",
+    "\n",
+    "print(\"Result: \", simpsone(a, b, n, f))"
+   ]
+  }
+ ],
+ "metadata": {
+  "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": "3.7.6"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 4
+}