TrapezoidalRule.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "N \t Trapezoid Area \t Relative Error \n",
      "\n",
      "2 \t 6.8394E-01 \t 8.1977E-02\n",
      "3 \t 6.4524E-01 \t 2.0747E-02\n",
      "4 \t 6.3796E-01 \t 9.2422E-03\n",
      "5 \t 6.3541E-01 \t 5.2029E-03\n",
      "6 \t 6.3423E-01 \t 3.3311E-03\n",
      "7 \t 6.3358E-01 \t 2.3137E-03\n",
      "8 \t 6.3320E-01 \t 1.7001E-03\n",
      "9 \t 6.3294E-01 \t 1.3017E-03\n",
      "10 \t 6.3277E-01 \t 1.0286E-03\n",
      "11 \t 6.3265E-01 \t 8.3319E-04\n",
      "12 \t 6.3256E-01 \t 6.8861E-04\n",
      "13 \t 6.3249E-01 \t 5.7864E-04\n",
      "14 \t 6.3243E-01 \t 4.9305E-04\n",
      "15 \t 6.3239E-01 \t 4.2513E-04\n",
      "16 \t 6.3235E-01 \t 3.7034E-04\n",
      "17 \t 6.3233E-01 \t 3.2550E-04\n",
      "18 \t 6.3230E-01 \t 2.8833E-04\n",
      "19 \t 6.3228E-01 \t 2.5719E-04\n",
      "20 \t 6.3227E-01 \t 2.3083E-04\n",
      "21 \t 6.3225E-01 \t 2.0832E-04\n",
      "22 \t 6.3224E-01 \t 1.8896E-04\n",
      "23 \t 6.3223E-01 \t 1.7217E-04\n",
      "24 \t 6.3222E-01 \t 1.5752E-04\n",
      "25 \t 6.3221E-01 \t 1.4467E-04\n",
      "26 \t 6.3220E-01 \t 1.3333E-04\n",
      "27 \t 6.3220E-01 \t 1.2327E-04\n",
      "28 \t 6.3219E-01 \t 1.1431E-04\n",
      "29 \t 6.3219E-01 \t 1.0629E-04\n",
      "30 \t 6.3218E-01 \t 9.9086E-05\n",
      "31 \t 6.3218E-01 \t 9.2591E-05\n",
      "32 \t 6.3218E-01 \t 8.6714E-05\n",
      "33 \t 6.3217E-01 \t 8.1379E-05\n",
      "34 \t 6.3217E-01 \t 7.6522E-05\n",
      "35 \t 6.3217E-01 \t 7.2087E-05\n",
      "36 \t 6.3216E-01 \t 6.8026E-05\n",
      "37 \t 6.3216E-01 \t 6.4300E-05\n",
      "38 \t 6.3216E-01 \t 6.0871E-05\n",
      "39 \t 6.3216E-01 \t 5.7709E-05\n",
      "40 \t 6.3216E-01 \t 5.4788E-05\n",
      "41 \t 6.3215E-01 \t 5.2083E-05\n",
      "42 \t 6.3215E-01 \t 4.9573E-05\n",
      "43 \t 6.3215E-01 \t 4.7241E-05\n",
      "44 \t 6.3215E-01 \t 4.5069E-05\n",
      "45 \t 6.3215E-01 \t 4.3044E-05\n",
      "46 \t 6.3215E-01 \t 4.1152E-05\n",
      "47 \t 6.3215E-01 \t 3.9382E-05\n",
      "48 \t 6.3214E-01 \t 3.7724E-05\n",
      "49 \t 6.3214E-01 \t 3.6169E-05\n",
      "50 \t 6.3214E-01 \t 3.4708E-05\n",
      "51 \t 6.3214E-01 \t 3.3333E-05\n",
      "52 \t 6.3214E-01 \t 3.2039E-05\n",
      "53 \t 6.3214E-01 \t 3.0818E-05\n",
      "54 \t 6.3214E-01 \t 2.9666E-05\n",
      "55 \t 6.3214E-01 \t 2.8578E-05\n",
      "56 \t 6.3214E-01 \t 2.7548E-05\n",
      "57 \t 6.3214E-01 \t 2.6573E-05\n",
      "58 \t 6.3214E-01 \t 2.5649E-05\n",
      "59 \t 6.3214E-01 \t 2.4772E-05\n",
      "60 \t 6.3214E-01 \t 2.3939E-05\n",
      "61 \t 6.3214E-01 \t 2.3148E-05\n",
      "62 \t 6.3213E-01 \t 2.2395E-05\n",
      "63 \t 6.3213E-01 \t 2.1679E-05\n",
      "64 \t 6.3213E-01 \t 2.0996E-05\n",
      "65 \t 6.3213E-01 \t 2.0345E-05\n",
      "66 \t 6.3213E-01 \t 1.9724E-05\n",
      "67 \t 6.3213E-01 \t 1.9131E-05\n",
      "68 \t 6.3213E-01 \t 1.8564E-05\n",
      "69 \t 6.3213E-01 \t 1.8022E-05\n",
      "70 \t 6.3213E-01 \t 1.7503E-05\n",
      "71 \t 6.3213E-01 \t 1.7007E-05\n",
      "72 \t 6.3213E-01 \t 1.6531E-05\n",
      "73 \t 6.3213E-01 \t 1.6075E-05\n",
      "74 \t 6.3213E-01 \t 1.5638E-05\n",
      "75 \t 6.3213E-01 \t 1.5218E-05\n",
      "76 \t 6.3213E-01 \t 1.4815E-05\n",
      "77 \t 6.3213E-01 \t 1.4427E-05\n",
      "78 \t 6.3213E-01 \t 1.4055E-05\n",
      "79 \t 6.3213E-01 \t 1.3697E-05\n",
      "80 \t 6.3213E-01 \t 1.3353E-05\n",
      "81 \t 6.3213E-01 \t 1.3021E-05\n",
      "82 \t 6.3213E-01 \t 1.2701E-05\n",
      "83 \t 6.3213E-01 \t 1.2393E-05\n",
      "84 \t 6.3213E-01 \t 1.2097E-05\n",
      "85 \t 6.3213E-01 \t 1.1810E-05\n",
      "86 \t 6.3213E-01 \t 1.1534E-05\n",
      "87 \t 6.3213E-01 \t 1.1267E-05\n",
      "88 \t 6.3213E-01 \t 1.1010E-05\n",
      "89 \t 6.3213E-01 \t 1.0761E-05\n",
      "90 \t 6.3213E-01 \t 1.0521E-05\n",
      "91 \t 6.3213E-01 \t 1.0288E-05\n",
      "92 \t 6.3213E-01 \t 1.0063E-05\n",
      "93 \t 6.3213E-01 \t 9.8456E-06\n",
      "94 \t 6.3213E-01 \t 9.6350E-06\n",
      "95 \t 6.3213E-01 \t 9.4311E-06\n",
      "96 \t 6.3213E-01 \t 9.2336E-06\n",
      "97 \t 6.3213E-01 \t 9.0422E-06\n",
      "98 \t 6.3213E-01 \t 8.8568E-06\n",
      "99 \t 6.3213E-01 \t 8.6769E-06\n",
      "100 \t 6.3213E-01 \t 8.5025E-06\n",
      "101 \t 6.3213E-01 \t 8.3333E-06\n",
      "102 \t 6.3213E-01 \t 8.1691E-06\n",
      "103 \t 6.3213E-01 \t 8.0097E-06\n",
      "104 \t 6.3213E-01 \t 7.8550E-06\n",
      "105 \t 6.3213E-01 \t 7.7046E-06\n",
      "106 \t 6.3213E-01 \t 7.5586E-06\n",
      "107 \t 6.3213E-01 \t 7.4166E-06\n",
      "108 \t 6.3213E-01 \t 7.2786E-06\n",
      "109 \t 6.3213E-01 \t 7.1445E-06\n",
      "110 \t 6.3212E-01 \t 7.0140E-06\n",
      "111 \t 6.3212E-01 \t 6.8870E-06\n",
      "112 \t 6.3212E-01 \t 6.7635E-06\n",
      "113 \t 6.3212E-01 \t 6.6433E-06\n",
      "114 \t 6.3212E-01 \t 6.5262E-06\n",
      "115 \t 6.3212E-01 \t 6.4122E-06\n",
      "116 \t 6.3212E-01 \t 6.3012E-06\n",
      "117 \t 6.3212E-01 \t 6.1930E-06\n",
      "118 \t 6.3212E-01 \t 6.0876E-06\n",
      "119 \t 6.3212E-01 \t 5.9849E-06\n",
      "120 \t 6.3212E-01 \t 5.8847E-06\n",
      "121 \t 6.3212E-01 \t 5.7870E-06\n",
      "122 \t 6.3212E-01 \t 5.6918E-06\n",
      "123 \t 6.3212E-01 \t 5.5988E-06\n",
      "124 \t 6.3212E-01 \t 5.5082E-06\n",
      "125 \t 6.3212E-01 \t 5.4197E-06\n",
      "126 \t 6.3212E-01 \t 5.3333E-06\n",
      "127 \t 6.3212E-01 \t 5.2490E-06\n",
      "128 \t 6.3212E-01 \t 5.1667E-06\n",
      "129 \t 6.3212E-01 \t 5.0863E-06\n",
      "130 \t 6.3212E-01 \t 5.0077E-06\n",
      "131 \t 6.3212E-01 \t 4.9310E-06\n",
      "132 \t 6.3212E-01 \t 4.8560E-06\n",
      "133 \t 6.3212E-01 \t 4.7827E-06\n",
      "134 \t 6.3212E-01 \t 4.7110E-06\n",
      "135 \t 6.3212E-01 \t 4.6410E-06\n",
      "136 \t 6.3212E-01 \t 4.5725E-06\n",
      "137 \t 6.3212E-01 \t 4.5055E-06\n",
      "138 \t 6.3212E-01 \t 4.4399E-06\n",
      "139 \t 6.3212E-01 \t 4.3758E-06\n",
      "140 \t 6.3212E-01 \t 4.3131E-06\n",
      "141 \t 6.3212E-01 \t 4.2517E-06\n",
      "142 \t 6.3212E-01 \t 4.1916E-06\n",
      "143 \t 6.3212E-01 \t 4.1328E-06\n",
      "144 \t 6.3212E-01 \t 4.0752E-06\n",
      "145 \t 6.3212E-01 \t 4.0188E-06\n",
      "146 \t 6.3212E-01 \t 3.9635E-06\n",
      "147 \t 6.3212E-01 \t 3.9094E-06\n",
      "148 \t 6.3212E-01 \t 3.8564E-06\n",
      "149 \t 6.3212E-01 \t 3.8045E-06\n",
      "150 \t 6.3212E-01 \t 3.7536E-06\n",
      "151 \t 6.3212E-01 \t 3.7037E-06\n",
      "152 \t 6.3212E-01 \t 3.6548E-06\n",
      "153 \t 6.3212E-01 \t 3.6069E-06\n",
      "154 \t 6.3212E-01 \t 3.5599E-06\n",
      "155 \t 6.3212E-01 \t 3.5138E-06\n",
      "156 \t 6.3212E-01 \t 3.4686E-06\n",
      "157 \t 6.3212E-01 \t 3.4243E-06\n",
      "158 \t 6.3212E-01 \t 3.3808E-06\n",
      "159 \t 6.3212E-01 \t 3.3381E-06\n",
      "160 \t 6.3212E-01 \t 3.2963E-06\n",
      "161 \t 6.3212E-01 \t 3.2552E-06\n",
      "162 \t 6.3212E-01 \t 3.2149E-06\n",
      "163 \t 6.3212E-01 \t 3.1753E-06\n",
      "164 \t 6.3212E-01 \t 3.1365E-06\n",
      "165 \t 6.3212E-01 \t 3.0984E-06\n",
      "166 \t 6.3212E-01 \t 3.0609E-06\n",
      "167 \t 6.3212E-01 \t 3.0241E-06\n",
      "168 \t 6.3212E-01 \t 2.9880E-06\n",
      "169 \t 6.3212E-01 \t 2.9526E-06\n",
      "170 \t 6.3212E-01 \t 2.9177E-06\n",
      "171 \t 6.3212E-01 \t 2.8835E-06\n",
      "172 \t 6.3212E-01 \t 2.8499E-06\n",
      "173 \t 6.3212E-01 \t 2.8168E-06\n",
      "174 \t 6.3212E-01 \t 2.7844E-06\n",
      "175 \t 6.3212E-01 \t 2.7525E-06\n",
      "176 \t 6.3212E-01 \t 2.7211E-06\n",
      "177 \t 6.3212E-01 \t 2.6903E-06\n",
      "178 \t 6.3212E-01 \t 2.6599E-06\n",
      "179 \t 6.3212E-01 \t 2.6301E-06\n",
      "180 \t 6.3212E-01 \t 2.6008E-06\n",
      "181 \t 6.3212E-01 \t 2.5720E-06\n",
      "182 \t 6.3212E-01 \t 2.5437E-06\n",
      "183 \t 6.3212E-01 \t 2.5158E-06\n",
      "184 \t 6.3212E-01 \t 2.4884E-06\n",
      "185 \t 6.3212E-01 \t 2.4614E-06\n",
      "186 \t 6.3212E-01 \t 2.4349E-06\n",
      "187 \t 6.3212E-01 \t 2.4088E-06\n",
      "188 \t 6.3212E-01 \t 2.3831E-06\n",
      "189 \t 6.3212E-01 \t 2.3578E-06\n",
      "190 \t 6.3212E-01 \t 2.3329E-06\n",
      "191 \t 6.3212E-01 \t 2.3084E-06\n",
      "192 \t 6.3212E-01 \t 2.2843E-06\n",
      "193 \t 6.3212E-01 \t 2.2606E-06\n",
      "194 \t 6.3212E-01 \t 2.2372E-06\n",
      "195 \t 6.3212E-01 \t 2.2142E-06\n",
      "196 \t 6.3212E-01 \t 2.1915E-06\n",
      "197 \t 6.3212E-01 \t 2.1692E-06\n",
      "198 \t 6.3212E-01 \t 2.1473E-06\n",
      "199 \t 6.3212E-01 \t 2.1256E-06\n",
      "\n",
      " Print Exact Area is = 6.3212E-01\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": [
    "import matplotlib.pyplot as plt\n",
    "from numpy import*\n",
    "\n",
    "def fn(t):\n",
    "    return(exp(-t))\n",
    "def exact(t):\n",
    "    return(-exp(-t))\n",
    "def Trapezoid(A,B,n):\n",
    "    h = (B-A)/(n-1)\n",
    "    sum_trap = (fn(A)+fn(B))/2\n",
    "    for i in range(1,n-1):\n",
    "        sum_trap += fn(A+(i*h))\n",
    "    sum_trap *=h\n",
    "    return (sum_trap)\n",
    "A = 0\n",
    "B = 1\n",
    "N = 200\n",
    "exact_sum = exact(B)-exact(A)\n",
    "Et =[]\n",
    "It=[]\n",
    "print(\"N\", \"\\t\", \"Trapezoid Area\", '\\t', \"Relative Error\", \"\\n\")\n",
    "for j in range(2,N):\n",
    "    err_t = abs((Trapezoid(A,B,j)-exact_sum)/exact_sum)\n",
    "    Et.append(err_t)\n",
    "    It.append(j)\n",
    "    print(j, \"\\t\", \"%.4E\"%Trapezoid(A,B,j), \"\\t\",\"%.4E\"%err_t)\n",
    "print(\"\\n Print Exact Area is =\", \"%.4E\"%exact_sum)\n",
    "    \n",
    "#plt.plot(It, Et)\n",
    "plt.loglog(It,Et)\n",
    "plt.title(\"A plot of relative errors versus N\")\n",
    "plt.xlabel(\"N\")\n",
    "plt.ylabel(\"Relative Error\")\n",
    "plt.grid()\n",
    "plt.show()\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
}