{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from __future__ import division\n",
      "\n",
      "import numpy\n",
      "from math import sin, cos"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "f = sin\n",
      "df = cos"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "x = 2.3\n",
      "\n",
      "for k in range(3, 10):\n",
      "    h = 2**(-k)\n",
      "\n",
      "    fd1 = (f(x+2*h) - f(x))/(2*h)\n",
      "    fd2 = (f(x+h) - f(x))/h\n",
      "    \n",
      "    richardson = (-1)*fd1 + 2*fd2\n",
      "    \n",
      "    true = df(x)\n",
      "    \n",
      "    print \"Err FD1: %g\\tErr FD2: %g\\tErr Rich: %g\" % (\n",
      "            abs(true-fd1),\n",
      "            abs(true-fd2),    \n",
      "            abs(true-richardson))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Err FD1: 0.08581\tErr FD2: 0.0448122\tErr Rich: 0.00381441\n",
        "Err FD1: 0.0448122\tErr FD2: 0.022862\tErr Rich: 0.000911846\n",
        "Err FD1: 0.022862\tErr FD2: 0.0115423\tErr Rich: 0.000222501\n",
        "Err FD1: 0.0115423\tErr FD2: 0.00579859\tErr Rich: 5.49282e-05\n",
        "Err FD1: 0.00579859\tErr FD2: 0.00290612\tErr Rich: 1.3644e-05\n",
        "Err FD1: 0.00290612\tErr FD2: 0.00145476\tErr Rich: 3.39995e-06\n",
        "Err FD1: 0.00145476\tErr FD2: 0.000727804\tErr Rich: 8.48602e-07\n"
       ]
      }
     ],
     "prompt_number": 19
    }
   ],
   "metadata": {}
  }
 ]
}