johnymontana/gist:4694576

## gistfile1.txt
{
 "metadata": {
  "name": "Simple_ODEs_Conservation"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pylab import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def y_prime(yn, vn, dt):\n",
      "    return yn+vn*dt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 106
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def v_prime(vn, dt, an=-9.8):\n",
      "    return vn+an*dt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 108
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def euler(x, dt, f=None):\n",
      "    # takes state x(y, velocity), returns new y, velocity\n",
      "    return array([y_prime(yn=x[0], vn=x[1], dt=dt), v_prime(vn=x[1], dt=dt)])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 109
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "state=[array([10, 0])]\n",
      "while True:\n",
      "    state.append(euler(dt=0.1, x=state[-1]))\n",
      "    if state[-1][0]<0:\n",
      "        break"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 134
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "array_state=array(state)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 135
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "euler_method_falling_list = array_state[:,0]\n",
      "print euler_method_falling_list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "[ 10.     10.      9.902   9.706   9.412   9.02    8.53    7.942   7.256\n",
        "   6.472   5.59    4.61    3.532   2.356   1.082  -0.29 ]\n"
       ]
      }
     ],
     "prompt_number": 136
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def analytic_sol(y0, t, g=9.8):\n",
      "    return -0.5*g*(t*t)+y0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 137
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "drop_list=[]\n",
      "for i in xrange(0,145):\n",
      "    drop_list.append(i*0.1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 138
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#drop_list"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 139
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def falling(x):\n",
      "    # input: x[position, velocity]\n",
      "    # returns [velocity, acceleration] or [dy/dt, dv/dt]\n",
      "    return array([x[1], -9.8])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 140
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#state = "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 141
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "analytic_data=[]\n",
      "for time_period in drop_list:\n",
      "    analytic_data.append(analytic_sol(y0=10, t=time_period))\n",
      "    if analytic_data[-1]<0:\n",
      "        break"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 142
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "zero_list=[0.0]*len(analytic_data)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 143
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plot(analytic_data,label='analytic solution')\n",
      "plot(euler_method_falling_list, label='euler method')\n",
      "plot(zero_list)\n",
      "legend(loc='upper right')\n",
      "xlabel(r'Number of timesteps, dt=0.1s')\n",
      "ylabel(r'Height of object (m)')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 146,
       "text": [
        "<matplotlib.text.Text at 0x10c13ba10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ChqUbMr7+eDJnyGy+oOKtYvLO4r59+/Lll19y/fp1IiMjiYyM5PHjx28UUoj0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\nQggrERam7Wy2Zw+UKWO+15VTQ0IIYSW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      }
     ],
     "prompt_number": 146
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}