Scratch3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "def AB_Predictor_Corrector(def_fn, a, b, ya, N):\n",
    "    \n",
    "    f = def_fn          #intakes function to method to approximate \n",
    "    h = (b-a)/N         #creates step size based on input values of a, b, N \n",
    "    t = np.arange(a, b+h, h) #array intialized to hold mesh points t\n",
    "    y = np.zeros((N+1,)) #array to hold Midpoint Method approximated y values\n",
    "    y[0] = ya           #intial condition \n",
    "    \n",
    "    #using fourth oreder Runge-Kutta to obtain the first 3 points\n",
    "    for i in range(0,N):\n",
    "        if i in range(0,3):\n",
    "            k1 = h * f(t[i],y[i])\n",
    "            k2 = h * f(t[i] + (h/2.0), y[i] +(k1/2.0))\n",
    "            k3 = h * f(t[i] + (h/2.0), y[i] + (k2/2.0))\n",
    "            k4 = h * f(t[i] + h, y[i] + k3)\n",
    "        \n",
    "            y[i + 1] = y[i] + (k1 + 2.0*k2 + 2.0*k3 + k4)/6.0            \n",
    "        else:           \n",
    "             y[i + 1] = y[i] + h*(55.0 * f(t[i],y[i]) - 59.0 * f(t[i-1],y[i-1]) + 37.0 * f(t[i-2],y[i-2]) - 9.0 * f(t[i-3],y[i-3]))/24.0                  \n",
    "             y[i + 1] = y[i] + h*(9.0 * f(t[i+1], y[i + 1]) + 19.0 * f(t[i],y[i]) - 5.0 * f(t[i-1],y[i-1]) + f(t[i-2],y[i-2]))/24.0  \n",
    "    print(\"v(t) =\", y)\n",
    "    print(\"t =\", t)\n",
    "    plt.plot(t,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v(t) = [20.         18.15289267 16.64060432 15.40244345 14.38859673 13.55855114\n",
      " 12.87898417 12.32261358 11.86710643 11.49417736 11.18885592 10.93888564\n",
      " 10.73423202 10.56667968 10.4295026  10.3171941  10.22524581 10.14996665\n",
      " 10.08833472 10.03787592  9.99656471  9.96274274  9.93505228  9.91238178\n",
      "  9.89382118  9.87862539  9.86618442  9.85599885  9.8476598   9.84083252\n",
      "  9.83524295  9.8306667   9.82692007  9.82385266  9.82134134  9.81928529\n",
      "  9.81760198  9.81622383  9.81509552  9.81417176  9.81341547  9.81279629\n",
      "  9.81228935  9.81187432  9.81153453  9.81125634  9.81102858  9.81084211\n",
      "  9.81068944  9.81056446  9.81046213]\n",
      "t = [ 0.   0.2  0.4  0.6  0.8  1.   1.2  1.4  1.6  1.8  2.   2.2  2.4  2.6\n",
      "  2.8  3.   3.2  3.4  3.6  3.8  4.   4.2  4.4  4.6  4.8  5.   5.2  5.4\n",
      "  5.6  5.8  6.   6.2  6.4  6.6  6.8  7.   7.2  7.4  7.6  7.8  8.   8.2\n",
      "  8.4  8.6  8.8  9.   9.2  9.4  9.6  9.8 10. ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "g = 9.81\n",
    "m = 1\n",
    "c = 1\n",
    "AB_Predictor_Corrector(lambda t,v: g-(c/m)*v, 0,10,20,50)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# def AB_Predictor_Corrector_for_y(def_fn, a, b, ya, N):\n",
    "    \n",
    "#     f = def_fn          #intakes function to method to approximate \n",
    "#     h = (b-a)/N         #creates step size based on input values of a, b, N \n",
    "#     t = np.arange(a, b+h, h) #array intialized to hold mesh points t\n",
    "#     y = np.zeros((N+1,)) #array to hold Midpoint Method approximated y values\n",
    "#     y[0] = ya           #intial condition \n",
    "    \n",
    "#     #using fourth oreder Runge-Kutta to obtain the first 3 points\n",
    "#     for i in range(0,N):\n",
    "#         for j in range(0,2*N+2):\n",
    "#             k1 = h/2 * f(t[i],y[i])\n",
    "#             k2 = h/2 * f(t[i] + (h/2.0), y[i] +(k1/2.0))\n",
    "#             k3 = h/2 * f(t[i] + (h/2.0), y[i] + (k2/2.0))\n",
    "#             k4 = h/2 * f(t[i] + h, y[i] + k3)\n",
    "\n",
    "#             y[i + 1] = y[i] + (k1 + 2.0*k2 + 2.0*k3 + k4)/6.0            \n",
    "       \n",
    "#     print(\"v(t) =\", y)\n",
    "#     print(\"t =\", t)\n",
    "#     plt.plot(t,y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "v(t) = [20, 17.96, 16.328, 15.0224, 13.97792, 13.142336, 12.4738688, 11.93909504, 11.511276032, 11.1690208256, 10.895216660480001, 10.676173328384001, 10.5009386627072, 10.36075093016576, 10.24860074413261, 10.158880595306087, 10.08710447624487, 10.029683580995895, 9.983746864796716, 9.946997491837372, 9.917597993469897, 9.894078394775917, 9.875262715820734, 9.860210172656586, 9.848168138125269, 9.838534510500216, 9.830827608400172, 9.824662086720139, 9.81972966937611, 9.815783735500888, 9.81262698840071, 9.810101590720569, 9.808081272576455, 9.806465018061164, 9.805172014448932, 9.804137611559145, 9.803310089247317, 9.802648071397854, 9.802118457118283, 9.801694765694627, 9.801355812555702, 9.801084650044562, 9.800867720035649, 9.80069417602852, 9.800555340822816, 9.800444272658254, 9.800355418126603, 9.800284334501283, 9.800227467601026, 9.800181974080822, 9.800145579264658, 9.800116463411726]\n",
      "y(t) = [0, 3.7960000000000003, 7.2248, 10.35984, 13.259872, 15.9718976, 18.53351808, 20.974814464, 23.3198515712, 25.58788125696, 27.794305005568, 29.951444004454398, 32.06915520356352, 34.15532416285082, 36.21625933028066, 38.25700746422453, 40.281605971379626, 42.2932847771037, 44.29462782168296, 46.28770225734637, 48.27416180587709, 50.25532944470167, 52.232263555761335, 54.20581084460907, 56.176648675687254, 58.1453189405498, 60.112255152439836, 62.077804121951864, 64.04224329756148, 66.00579463804918, 67.96863571043934, 69.93090856835147, 71.89272685468117, 73.85418148374494, 75.81534518699594, 77.77627614959675, 79.7370209196774, 81.69761673574192, 83.65809338859353, 85.61847471087482, 87.57877976869986, 89.53902381495989, 91.49921905196791, 93.45937524157434, 95.41950019325947, 97.37960015460757, 99.33968012368607, 101.29974409894885, 103.25979527915908, 105.21983622332726, 107.17986897866182, 109.13989518292945]\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f2fcb702090>]"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "h1 = 0.2\n",
    "h2 = 0.5\n",
    "h3 = 0.1\n",
    "a = 0\n",
    "b = 10\n",
    "N = int((b-a)/h1)\n",
    "def g1(v):\n",
    "    g = 9.8\n",
    "    return g-v\n",
    "v0 = [20]\n",
    "t0 = [0]\n",
    "y0 = [0]\n",
    "\n",
    "for i in range(N+1):\n",
    "    v1 = v0[i] + h1*g1(v0[i])\n",
    "    v0.append(v1)\n",
    "    t0.append(t0[i]+h1)\n",
    "print(\"v(t) =\", v0)\n",
    "plt.plot(t0,v0)\n",
    "\n",
    "for j in range(N+1):\n",
    "    y1 = y0[j] + (h1/2)*(v0[j] + v0[j+1])\n",
    "    y0.append(y1)\n",
    "print(\"y(t) =\", y0)\n",
    "plt.plot(t0,y0)\n",
    "   \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "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
}