8.10.3.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "import math\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Прежде было показано, что исходная задача:\n",
    "$$y\"=ysinx$$\n",
    "\n",
    "$$0\\leq x \\leq 1$$\n",
    "$$y(0)=0, y'(0)=1$$\n",
    "\n",
    "Сводится заменой к следущей системе:\n",
    "\n",
    "$$v_{n+1}=v_n+hy_nsinx_n$$\n",
    "$$y_{n+1}=y_n+hv_n$$\n",
    "\n",
    "$$0\\leq x \\leq 1$$\n",
    "$$x_0=y_0=0, v_0=1$$\n",
    "\n",
    "Используя начальные данные построим приближенное решение задачи коши при заданном шаге h."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0,0.5,'dy/dx')"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1440x576 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "h = 0.0001\n",
    "\n",
    "x = []\n",
    "v = []\n",
    "y = []\n",
    "\n",
    "x.append(0)\n",
    "y.append(0)\n",
    "v.append(1)\n",
    "\n",
    "for i in np.arange(0.0,1.0+h,h):\n",
    "    x.append(i)\n",
    "    y.append(y[-1]+h*v[-1])\n",
    "    v.append(v[-1]+h*y[-1]*np.sin(x[-1]))\n",
    "\n",
    "a, axes = plt.subplots(1,2, figsize=(20,8))\n",
    "axes[0].plot(x,y, c='orange')\n",
    "axes[0].set_xlabel('x')\n",
    "axes[0].set_ylabel('y')\n",
    "axes[1].plot(y,v, c='green')\n",
    "axes[1].set_xlabel('y')\n",
    "axes[1].set_ylabel('dy/dx')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>dy/dx</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.000100</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.0001</td>\n",
       "      <td>0.000200</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.0002</td>\n",
       "      <td>0.000300</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.0003</td>\n",
       "      <td>0.000400</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.0004</td>\n",
       "      <td>0.000500</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.0005</td>\n",
       "      <td>0.000600</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.0006</td>\n",
       "      <td>0.000700</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.0007</td>\n",
       "      <td>0.000800</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.0008</td>\n",
       "      <td>0.000900</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.0009</td>\n",
       "      <td>0.001000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.0010</td>\n",
       "      <td>0.001100</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.0011</td>\n",
       "      <td>0.001200</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.0012</td>\n",
       "      <td>0.001300</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.0013</td>\n",
       "      <td>0.001400</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.0014</td>\n",
       "      <td>0.001500</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.0015</td>\n",
       "      <td>0.001600</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.0016</td>\n",
       "      <td>0.001700</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.0017</td>\n",
       "      <td>0.001800</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.0018</td>\n",
       "      <td>0.001900</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.0019</td>\n",
       "      <td>0.002000</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.0020</td>\n",
       "      <td>0.002100</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.0021</td>\n",
       "      <td>0.002200</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.0022</td>\n",
       "      <td>0.002300</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.0023</td>\n",
       "      <td>0.002400</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.0024</td>\n",
       "      <td>0.002500</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.0025</td>\n",
       "      <td>0.002600</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.0026</td>\n",
       "      <td>0.002700</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.0027</td>\n",
       "      <td>0.002800</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.0028</td>\n",
       "      <td>0.002900</td>\n",
       "      <td>1.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9972</th>\n",
       "      <td>0.9971</td>\n",
       "      <td>1.075984</td>\n",
       "      <td>1.310436</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9973</th>\n",
       "      <td>0.9972</td>\n",
       "      <td>1.076115</td>\n",
       "      <td>1.310526</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9974</th>\n",
       "      <td>0.9973</td>\n",
       "      <td>1.076247</td>\n",
       "      <td>1.310616</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9975</th>\n",
       "      <td>0.9974</td>\n",
       "      <td>1.076378</td>\n",
       "      <td>1.310707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9976</th>\n",
       "      <td>0.9975</td>\n",
       "      <td>1.076509</td>\n",
       "      <td>1.310797</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9977</th>\n",
       "      <td>0.9976</td>\n",
       "      <td>1.076640</td>\n",
       "      <td>1.310888</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9978</th>\n",
       "      <td>0.9977</td>\n",
       "      <td>1.076771</td>\n",
       "      <td>1.310978</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9979</th>\n",
       "      <td>0.9978</td>\n",
       "      <td>1.076902</td>\n",
       "      <td>1.311069</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9980</th>\n",
       "      <td>0.9979</td>\n",
       "      <td>1.077033</td>\n",
       "      <td>1.311159</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9981</th>\n",
       "      <td>0.9980</td>\n",
       "      <td>1.077164</td>\n",
       "      <td>1.311250</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9982</th>\n",
       "      <td>0.9981</td>\n",
       "      <td>1.077295</td>\n",
       "      <td>1.311340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9983</th>\n",
       "      <td>0.9982</td>\n",
       "      <td>1.077426</td>\n",
       "      <td>1.311431</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9984</th>\n",
       "      <td>0.9983</td>\n",
       "      <td>1.077558</td>\n",
       "      <td>1.311521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9985</th>\n",
       "      <td>0.9984</td>\n",
       "      <td>1.077689</td>\n",
       "      <td>1.311612</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9986</th>\n",
       "      <td>0.9985</td>\n",
       "      <td>1.077820</td>\n",
       "      <td>1.311703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9987</th>\n",
       "      <td>0.9986</td>\n",
       "      <td>1.077951</td>\n",
       "      <td>1.311793</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9988</th>\n",
       "      <td>0.9987</td>\n",
       "      <td>1.078082</td>\n",
       "      <td>1.311884</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9989</th>\n",
       "      <td>0.9988</td>\n",
       "      <td>1.078213</td>\n",
       "      <td>1.311975</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9990</th>\n",
       "      <td>0.9989</td>\n",
       "      <td>1.078345</td>\n",
       "      <td>1.312065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9991</th>\n",
       "      <td>0.9990</td>\n",
       "      <td>1.078476</td>\n",
       "      <td>1.312156</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9992</th>\n",
       "      <td>0.9991</td>\n",
       "      <td>1.078607</td>\n",
       "      <td>1.312247</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9993</th>\n",
       "      <td>0.9992</td>\n",
       "      <td>1.078738</td>\n",
       "      <td>1.312337</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9994</th>\n",
       "      <td>0.9993</td>\n",
       "      <td>1.078869</td>\n",
       "      <td>1.312428</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9995</th>\n",
       "      <td>0.9994</td>\n",
       "      <td>1.079001</td>\n",
       "      <td>1.312519</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9996</th>\n",
       "      <td>0.9995</td>\n",
       "      <td>1.079132</td>\n",
       "      <td>1.312610</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9997</th>\n",
       "      <td>0.9996</td>\n",
       "      <td>1.079263</td>\n",
       "      <td>1.312700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9998</th>\n",
       "      <td>0.9997</td>\n",
       "      <td>1.079394</td>\n",
       "      <td>1.312791</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9999</th>\n",
       "      <td>0.9998</td>\n",
       "      <td>1.079526</td>\n",
       "      <td>1.312882</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10000</th>\n",
       "      <td>0.9999</td>\n",
       "      <td>1.079657</td>\n",
       "      <td>1.312973</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10001</th>\n",
       "      <td>1.0000</td>\n",
       "      <td>1.079788</td>\n",
       "      <td>1.313064</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>10002 rows × 3 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            x         y     dy/dx\n",
       "0      0.0000  0.000000  1.000000\n",
       "1      0.0000  0.000100  1.000000\n",
       "2      0.0001  0.000200  1.000000\n",
       "3      0.0002  0.000300  1.000000\n",
       "4      0.0003  0.000400  1.000000\n",
       "5      0.0004  0.000500  1.000000\n",
       "6      0.0005  0.000600  1.000000\n",
       "7      0.0006  0.000700  1.000000\n",
       "8      0.0007  0.000800  1.000000\n",
       "9      0.0008  0.000900  1.000000\n",
       "10     0.0009  0.001000  1.000000\n",
       "11     0.0010  0.001100  1.000000\n",
       "12     0.0011  0.001200  1.000000\n",
       "13     0.0012  0.001300  1.000000\n",
       "14     0.0013  0.001400  1.000000\n",
       "15     0.0014  0.001500  1.000000\n",
       "16     0.0015  0.001600  1.000000\n",
       "17     0.0016  0.001700  1.000000\n",
       "18     0.0017  0.001800  1.000000\n",
       "19     0.0018  0.001900  1.000000\n",
       "20     0.0019  0.002000  1.000000\n",
       "21     0.0020  0.002100  1.000000\n",
       "22     0.0021  0.002200  1.000000\n",
       "23     0.0022  0.002300  1.000000\n",
       "24     0.0023  0.002400  1.000000\n",
       "25     0.0024  0.002500  1.000000\n",
       "26     0.0025  0.002600  1.000000\n",
       "27     0.0026  0.002700  1.000000\n",
       "28     0.0027  0.002800  1.000000\n",
       "29     0.0028  0.002900  1.000000\n",
       "...       ...       ...       ...\n",
       "9972   0.9971  1.075984  1.310436\n",
       "9973   0.9972  1.076115  1.310526\n",
       "9974   0.9973  1.076247  1.310616\n",
       "9975   0.9974  1.076378  1.310707\n",
       "9976   0.9975  1.076509  1.310797\n",
       "9977   0.9976  1.076640  1.310888\n",
       "9978   0.9977  1.076771  1.310978\n",
       "9979   0.9978  1.076902  1.311069\n",
       "9980   0.9979  1.077033  1.311159\n",
       "9981   0.9980  1.077164  1.311250\n",
       "9982   0.9981  1.077295  1.311340\n",
       "9983   0.9982  1.077426  1.311431\n",
       "9984   0.9983  1.077558  1.311521\n",
       "9985   0.9984  1.077689  1.311612\n",
       "9986   0.9985  1.077820  1.311703\n",
       "9987   0.9986  1.077951  1.311793\n",
       "9988   0.9987  1.078082  1.311884\n",
       "9989   0.9988  1.078213  1.311975\n",
       "9990   0.9989  1.078345  1.312065\n",
       "9991   0.9990  1.078476  1.312156\n",
       "9992   0.9991  1.078607  1.312247\n",
       "9993   0.9992  1.078738  1.312337\n",
       "9994   0.9993  1.078869  1.312428\n",
       "9995   0.9994  1.079001  1.312519\n",
       "9996   0.9995  1.079132  1.312610\n",
       "9997   0.9996  1.079263  1.312700\n",
       "9998   0.9997  1.079394  1.312791\n",
       "9999   0.9998  1.079526  1.312882\n",
       "10000  0.9999  1.079657  1.312973\n",
       "10001  1.0000  1.079788  1.313064\n",
       "\n",
       "[10002 rows x 3 columns]"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df = pd.DataFrame()\n",
    "df['x'] = x\n",
    "df['y'] = y\n",
    "df['dy/dx'] = v\n",
    "df"
   ]
  }
 ],
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