graphics and description.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Методы Рунге-Кутты"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Пусть мы хотим решать задачу следующего вида:\n",
    "    \n",
    "У нас есть задача Коши $y' = f(x, y)$ и начальные значения $x_0$, $y_0 = y(x_0)$. При этом мы ищем функцию $y: \\mathbb{R} \\to \\mathbb{R}^n$, удовлетворяющую этому дифференциальному уравнению. У нас $f: \\mathbb{R} \\times \\mathbb{R}^n \\to \\mathbb{R}^n, x_0 \\in \\mathbb{R}, y_0 \\in \\mathbb{R}^n$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Чтобы найти эту фунцию, мы будем искать ее значение в точках с некоторым шагом $h \\in \\mathbb{R}_{>0}$, то есть в точках $x_i = x_0 + h \\cdot i$ для всех $i \\in \\mathbb{Z}_{\\geq 0}$ мы хотим найти $y_i = y(x_i)$.\n",
    "\n",
    "Первую точку $(x_0, y_0)$ мы знаем. Метод будет итеративный: научимся делать переход от $(x_i, y_i)$ к $(x_{i+1}, y_{i+1})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Какой самый простой метод мы можем придумать? Мы можем написать, что: $$y_{i+1} = y(x_{i+1}) = y(x_i + h) = y(x_i) + h y'(x_i) + O(h^2) = y_i + h f(x_i, y_i) + O(h^2)$$ Таким образом, вычислим $y_{i+1} = y_i + h f(x_i, y_i)$. Это дает нам **метод Эйлера**, который может давать довольно большую ошибку."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для того, чтобы получить более точный метод, надо переходить к $y_{i+1}$ используя значение производной не только в точке $(x_i, y_i)$.\n",
    "\n",
    "**Явный метод Рунге-Кутты** будет задаваться следующим образом. У метода будет порядок $p \\in \\mathbb{N}$. Также необходимо будет подобрать некоторые коэфициенты $c_2, c_3, \\ldots, c_p$, $a_{2,1}, a_{3,1}, a_{3,2}, \\ldots, a_{p,p-1}$, $b_1, b_2, \\ldots, b_n$. Коэфициенты $a$ можно записать в такую нижнедиагональную матрицу:\n",
    "\n",
    "$$\n",
    "\\begin{pmatrix}\n",
    "\\\\\n",
    "a_{2,1} \\\\\n",
    "a_{3,1} & a_{3,2} \\\\\n",
    "\\vdots & \\vdots \\\\\n",
    "a_{p,1} & a_{p,2} & \\ldots & a_{p,p-1} &  \\\\\n",
    "\\end{pmatrix}\n",
    "$$\n",
    "\n",
    "Коэфициенты $b$ должны удовлетворять условиям $b_1 + b_2 + \\ldots + b_n = 1$.\n",
    "\n",
    "Посчитаем итеративно следующие значения:\n",
    "\n",
    "$$k_1 = f(x_i, y_i)$$\n",
    "\n",
    "$$k_2 = f(x_i + c_2 h, y_i + k_1 a_{2,1} h)$$\n",
    "\n",
    "$$k_3 = f(x_i + c_3 h, y_i + k_1 a_{3,1} h + k_2 a_{3,2} h)$$\n",
    "\n",
    "$$\\vdots$$\n",
    "\n",
    "$$k_p = f(x_i + c_p h, y_i + k_1 a_{p,1} h + k_2 a_{p,2} h + \\ldots + k_{p-1} a_{p,p-1} h)$$\n",
    "\n",
    "То есть, $k_1$ это мы просто берем производную, как в методе Эйлера в точке $(x_i, y_i)$. Значение $k_2$ - мы считаем значение производной, сдвинувшись из $(x_i, y_i)$ на $(c_2, k_1 a_{2,1})h$. Значение $k_3$ - считаем значение производной, сдвинувшись из $(x_i, y_i)$ на $(c_3, k_1 a_{3,1} + k_2 a_{3,2})h$. И так далее. То есть мы считаем значение $p$ производных, сдвигаясь из точки $(x_i, y_i)$ на чуть чуть, каждый раз используя значения предыдущих производных для сдвига.\n",
    "\n",
    "Тогда, мы используя значения посчитанных производных $k_1, k_2, \\ldots, k_p$, вычисляем\n",
    "\n",
    "$$y_{i+1} = y_i + b_1 k_1 + b_2 k_2 + \\ldots + b_p k_p$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Пока что описанный метод звучит очень абстрактно, то есть мы как-то должны выбрать все эти коэфициенты, чтобы для любой функции $f$ метод давал маленькую ошибку.\n",
    "\n",
    "Для этого напишем, что мы хотим, чтобы $\\phi(h) = \\frac{y(x_i + h) - y(x_i)}{h} - \\sum\\limits_{i=1}^{k}{b_i k_i}$ было мало. Для этого, мы просто хотим, чтобы $$\\phi(0) = 0 \\\\ \\phi'(0) = 0 \\\\ \\phi^{(2)}(0) = 0 \\\\ \\vdots \\\\ \\phi^{(m-1)}(0) = 0$$\n",
    "\n",
    "Тогда из разложения $\\phi$ в ряд Тейлора, мы получим, что $\\phi(h) = O(h^m)$. Поэтому, умножив на $h$ определение функции $\\phi$, мы получим $$y(x_i + h) = y(x_i) + \\sum\\limits_{i=1}^{k}{b_i k_i} + O(h^{m+1})$$\n",
    "\n",
    "Число $m$ нужно постараться получить настолько большим, насколько получится. Если написать, что $\\phi^{(i)}(0) = 0$, то там получится сумма произведений каких-то алгебраических функций от коэфициентов на производные $f$. Таким образом, нужно, чтобы все эти функции от коэфициентов равнялись $0$. Нужно получить систему алгебраических уравнений и решить ее, взяв максимальное $m$, при котором решить систему получится.\n",
    "\n",
    "Проделывать эту техническую работу мы не будем, а лучше сразу перейдем к результатам."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Методы Рунге-Кутты разных порядков"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Метод Рунге-Кутты второго порядка**\n",
    "\n",
    "Если положить $p = 2$, то одно из решений будет: $c_2 = 1$, $a_{2,1} = 1$, $b_1 = b_2 = \\frac{1}{2}$.\n",
    "\n",
    "То есть:\n",
    "\n",
    "$$k_1 = f(x_i, y_i)$$\n",
    "\n",
    "$$k_2 = f(x_i + h, y_i + k_1 h)$$\n",
    "\n",
    "$$y_{i+1} = y_i + \\frac{k_1 + k_2}{2}$$\n",
    "\n",
    "Ошибка одного перехода будет $O(h^3)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Метод Рунге-Кутты третьего порядка**\n",
    "\n",
    "Если положить $p = 3$, то одно из решений будет: $c_2 = \\frac{1}{2}$, $c_3 = 1$, $a = \\begin{pmatrix} \\\\ \\frac{1}{2} \\\\ -1 & 2 & \\end{pmatrix}$, $b_1 = b_3 = \\frac{1}{6}$, $b_2 = \\frac{2}{3}$.\n",
    "\n",
    "То есть:\n",
    "\n",
    "$$k_1 = f(x_i, y_i)$$\n",
    "\n",
    "$$k_2 = f(x_i + \\frac{h}{2}, y_i + \\frac{k_1 h}{2})$$\n",
    "\n",
    "$$k_3 = f(x_i + h, y_i - k_1 h + 2 k_2 h)$$\n",
    "\n",
    "$$y_{i+1} = y_i + \\frac{k_1 + 4 k_2 + k_3}{6}$$\n",
    "\n",
    "Ошибка одного перехода будет $O(h^4)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Метод Рунге-Кутты четвертого порядка**\n",
    "\n",
    "Если положить $p = 4$, то одно из решений будет: $c_2 = c_3 = \\frac{1}{2}$, $a = \\begin{pmatrix} \\\\ \\frac{1}{2} \\\\ 0 & \\frac{1}{2} \\\\ 0 & 0 & 1 & \\end{pmatrix}$, $b_1 = b_4 = \\frac{1}{6}$, $b_2 = b_3 = \\frac{1}{3}$.\n",
    "\n",
    "То есть:\n",
    "\n",
    "$$k_1 = f(x_i, y_i)$$\n",
    "\n",
    "$$k_2 = f(x_i + \\frac{h}{2}, y_i + \\frac{k_1 h}{2})$$\n",
    "\n",
    "$$k_3 = f(x_i + \\frac{h}{2}, y_i + \\frac{k_2 h}{2})$$\n",
    "\n",
    "$$k_4 = f(x_i + h, y_i + k_3 h)$$\n",
    "\n",
    "$$y_{i+1} = y_i + \\frac{k_1 + 2 k_2 + 2 k_3 + k_4}{6}$$\n",
    "\n",
    "Ошибка одного перехода будет $O(h^5)$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "На практике чаще всего используется метод Рунге-Кутты четвертого порядка, потому что он имеет хорошую точность и при этом является эффективным.\n",
    "\n",
    "Далее рассмотрим разные примеры."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Примеры"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Пример 1**\n",
    "\n",
    "Подберем дифференциальное уравнение под конкреткую функцию $y = \\arctan{x}$. Построим некоторое дифференциальное уравнение для этой функции. Сделаем его дифференциальным уравнением $2$ порядка, чтобы показать, как сводить дифференциальные уравения более высокого порядка к дифференциальным уравнениям первого порядка, чтобы в итоге применить численные методы.\n",
    "\n",
    "Как известно, $y' = \\frac{1}{1+x^2}$, $y'' = \\frac{-2x}{(1+x^2)^2} = \\frac{1}{1+x^2}-\\frac{(1+x)^2}{(1+x^2)^2}$.\n",
    "\n",
    "Тогда напишем, что $y'' = \\frac{1}{1+x^2}-\\frac{(1+x)^2}{(1+x^2)^2} = y' - (1+x)(1+\\tan{y})(y')^2$.\n",
    "\n",
    "Получаем дифференциальное уравнение $y'' = y' - (1+x)(1+\\tan{y})(y')^2$. Чтобы получить уравнение Коши, единственное решение которого $y = \\arctan{x}$, зададим начальные значения $y(0) = 0$, $y'(0) = 1$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Решение примера 1**\n",
    "\n",
    "$y'' = y' - (1+x)(1+\\tan{y})(y')^2$, $y(0) = 0$, $y'(0) = 1$\n",
    "\n",
    "Для того, чтобы свести решение такого ДУ к методу Рунге-Кутты, сделаем такую замену $z = y'$. Тогда $z' = y''$.\n",
    "\n",
    "Получаем, что $y' = z$ и $z' = z - (1+x)(1+\\tan{y})z^2$. То есть:\n",
    "\n",
    "$\n",
    "\\begin{pmatrix}\n",
    "y \\\\\n",
    "z\n",
    "\\end{pmatrix}' = \n",
    "\\begin{pmatrix}\n",
    "z \\\\\n",
    "z - (1+x)(1+\\tan{y})z^2\n",
    "\\end{pmatrix}\n",
    "$ и\n",
    "$\n",
    "\\begin{pmatrix}\n",
    "y \\\\\n",
    "z\n",
    "\\end{pmatrix}(0) = \n",
    "\\begin{pmatrix}\n",
    "0 \\\\\n",
    "1\n",
    "\\end{pmatrix}\n",
    "$\n",
    "\n",
    "Тогда рассмотрим: $f(x, \\begin{pmatrix} y \\\\ z \\end{pmatrix}) = \\begin{pmatrix} z \\\\ z - (1+x)(1+\\tan{y})z^2 \\end{pmatrix}$ и можем применить метод Рунге-Кутты. Нам при этом будут интересны значения только первой компоненты ($y$)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 92,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "os.system('g++ -std=c++17 -O2 -o example1 example1.cpp')\n",
    "code = os.system('./example1')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
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       "      <th>x</th>\n",
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       "      <td>-0.000200</td>\n",
       "      <td>0.197391</td>\n",
       "      <td>-0.000005</td>\n",
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       "      <td>2</td>\n",
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       "      <td>0.400000</td>\n",
       "      <td>0.019494</td>\n",
       "      <td>0.383886</td>\n",
       "      <td>0.003379</td>\n",
       "      <td>0.380169</td>\n",
       "      <td>-0.000337</td>\n",
       "      <td>0.380503</td>\n",
       "      <td>-0.000003</td>\n",
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       "      <td>0.6</td>\n",
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       "      <td>0.582270</td>\n",
       "      <td>0.041850</td>\n",
       "      <td>0.543022</td>\n",
       "      <td>0.002602</td>\n",
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       "      <td>-0.000310</td>\n",
       "      <td>0.540414</td>\n",
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       "      <td>0.676045</td>\n",
       "      <td>0.001304</td>\n",
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       "      <td>0.785398</td>\n",
       "      <td>0.856127</td>\n",
       "      <td>0.070729</td>\n",
       "      <td>0.785601</td>\n",
       "      <td>0.000203</td>\n",
       "      <td>0.785374</td>\n",
       "      <td>-0.000025</td>\n",
       "      <td>0.785370</td>\n",
       "      <td>-0.000028</td>\n",
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       "      <td>6</td>\n",
       "      <td>1.2</td>\n",
       "      <td>0.876058</td>\n",
       "      <td>0.951273</td>\n",
       "      <td>0.075215</td>\n",
       "      <td>0.875575</td>\n",
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       "      <td>1.175574</td>\n",
       "      <td>-0.000431</td>\n",
       "      <td>1.176101</td>\n",
       "      <td>0.000096</td>\n",
       "      <td>1.175975</td>\n",
       "      <td>-0.000031</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>13</td>\n",
       "      <td>2.6</td>\n",
       "      <td>1.203622</td>\n",
       "      <td>1.265254</td>\n",
       "      <td>0.061632</td>\n",
       "      <td>1.203317</td>\n",
       "      <td>-0.000305</td>\n",
       "      <td>1.203703</td>\n",
       "      <td>0.000081</td>\n",
       "      <td>1.203594</td>\n",
       "      <td>-0.000028</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>14</td>\n",
       "      <td>2.8</td>\n",
       "      <td>1.227772</td>\n",
       "      <td>1.286944</td>\n",
       "      <td>0.059171</td>\n",
       "      <td>1.227575</td>\n",
       "      <td>-0.000197</td>\n",
       "      <td>1.227840</td>\n",
       "      <td>0.000068</td>\n",
       "      <td>1.227746</td>\n",
       "      <td>-0.000026</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>15</td>\n",
       "      <td>3.0</td>\n",
       "      <td>1.249046</td>\n",
       "      <td>1.305908</td>\n",
       "      <td>0.056862</td>\n",
       "      <td>1.248940</td>\n",
       "      <td>-0.000106</td>\n",
       "      <td>1.249102</td>\n",
       "      <td>0.000056</td>\n",
       "      <td>1.249021</td>\n",
       "      <td>-0.000024</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>16</td>\n",
       "      <td>3.2</td>\n",
       "      <td>1.267911</td>\n",
       "      <td>1.322614</td>\n",
       "      <td>0.054703</td>\n",
       "      <td>1.267880</td>\n",
       "      <td>-0.000031</td>\n",
       "      <td>1.267959</td>\n",
       "      <td>0.000047</td>\n",
       "      <td>1.267889</td>\n",
       "      <td>-0.000023</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>17</td>\n",
       "      <td>3.4</td>\n",
       "      <td>1.284745</td>\n",
       "      <td>1.337430</td>\n",
       "      <td>0.052685</td>\n",
       "      <td>1.284774</td>\n",
       "      <td>0.000029</td>\n",
       "      <td>1.284785</td>\n",
       "      <td>0.000040</td>\n",
       "      <td>1.284723</td>\n",
       "      <td>-0.000021</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>18</td>\n",
       "      <td>3.6</td>\n",
       "      <td>1.299849</td>\n",
       "      <td>1.350648</td>\n",
       "      <td>0.050799</td>\n",
       "      <td>1.299927</td>\n",
       "      <td>0.000078</td>\n",
       "      <td>1.299883</td>\n",
       "      <td>0.000033</td>\n",
       "      <td>1.299829</td>\n",
       "      <td>-0.000020</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>19</td>\n",
       "      <td>3.8</td>\n",
       "      <td>1.313473</td>\n",
       "      <td>1.362507</td>\n",
       "      <td>0.049035</td>\n",
       "      <td>1.313589</td>\n",
       "      <td>0.000116</td>\n",
       "      <td>1.313501</td>\n",
       "      <td>0.000028</td>\n",
       "      <td>1.313453</td>\n",
       "      <td>-0.000019</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>20</td>\n",
       "      <td>4.0</td>\n",
       "      <td>1.325818</td>\n",
       "      <td>1.373200</td>\n",
       "      <td>0.047383</td>\n",
       "      <td>1.325964</td>\n",
       "      <td>0.000146</td>\n",
       "      <td>1.325842</td>\n",
       "      <td>0.000024</td>\n",
       "      <td>1.325799</td>\n",
       "      <td>-0.000018</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>21</td>\n",
       "      <td>4.2</td>\n",
       "      <td>1.337053</td>\n",
       "      <td>1.382886</td>\n",
       "      <td>0.045833</td>\n",
       "      <td>1.337223</td>\n",
       "      <td>0.000169</td>\n",
       "      <td>1.337074</td>\n",
       "      <td>0.000021</td>\n",
       "      <td>1.337036</td>\n",
       "      <td>-0.000017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>22</td>\n",
       "      <td>4.4</td>\n",
       "      <td>1.347320</td>\n",
       "      <td>1.391697</td>\n",
       "      <td>0.044378</td>\n",
       "      <td>1.347507</td>\n",
       "      <td>0.000187</td>\n",
       "      <td>1.347338</td>\n",
       "      <td>0.000018</td>\n",
       "      <td>1.347303</td>\n",
       "      <td>-0.000017</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>23</td>\n",
       "      <td>4.6</td>\n",
       "      <td>1.356736</td>\n",
       "      <td>1.399744</td>\n",
       "      <td>0.043008</td>\n",
       "      <td>1.356937</td>\n",
       "      <td>0.000201</td>\n",
       "      <td>1.356751</td>\n",
       "      <td>0.000016</td>\n",
       "      <td>1.356720</td>\n",
       "      <td>-0.000016</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>24</td>\n",
       "      <td>4.8</td>\n",
       "      <td>1.365401</td>\n",
       "      <td>1.407119</td>\n",
       "      <td>0.041718</td>\n",
       "      <td>1.365612</td>\n",
       "      <td>0.000211</td>\n",
       "      <td>1.365415</td>\n",
       "      <td>0.000014</td>\n",
       "      <td>1.365386</td>\n",
       "      <td>-0.000015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>25</td>\n",
       "      <td>5.0</td>\n",
       "      <td>1.373401</td>\n",
       "      <td>1.413901</td>\n",
       "      <td>0.040500</td>\n",
       "      <td>1.373619</td>\n",
       "      <td>0.000218</td>\n",
       "      <td>1.373413</td>\n",
       "      <td>0.000012</td>\n",
       "      <td>1.373386</td>\n",
       "      <td>-0.000015</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      x         y  y (p = 1)  error (p = 1)  y (p = 2)  error (p = 2)  \\\n",
       "0   0.0  0.000000   0.000000       0.000000   0.000000       0.000000   \n",
       "1   0.2  0.197396   0.200000       0.002604   0.200000       0.002604   \n",
       "2   0.4  0.380506   0.400000       0.019494   0.383886       0.003379   \n",
       "3   0.6  0.540420   0.582270       0.041850   0.543022       0.002602   \n",
       "4   0.8  0.674741   0.734818       0.060077   0.676045       0.001304   \n",
       "5   1.0  0.785398   0.856127       0.070729   0.785601       0.000203   \n",
       "6   1.2  0.876058   0.951273       0.075215   0.875575      -0.000483   \n",
       "7   1.4  0.950547   1.026477       0.075930   0.949741      -0.000806   \n",
       "8   1.6  1.012197   1.086832       0.074635   1.011310      -0.000887   \n",
       "9   1.8  1.063698   1.136073       0.072376   1.062867      -0.000831   \n",
       "10  2.0  1.107149   1.176866       0.069717   1.106438      -0.000711   \n",
       "11  2.2  1.144169   1.211123       0.066954   1.143599      -0.000570   \n",
       "12  2.4  1.176005   1.240241       0.064236   1.175574      -0.000431   \n",
       "13  2.6  1.203622   1.265254       0.061632   1.203317      -0.000305   \n",
       "14  2.8  1.227772   1.286944       0.059171   1.227575      -0.000197   \n",
       "15  3.0  1.249046   1.305908       0.056862   1.248940      -0.000106   \n",
       "16  3.2  1.267911   1.322614       0.054703   1.267880      -0.000031   \n",
       "17  3.4  1.284745   1.337430       0.052685   1.284774       0.000029   \n",
       "18  3.6  1.299849   1.350648       0.050799   1.299927       0.000078   \n",
       "19  3.8  1.313473   1.362507       0.049035   1.313589       0.000116   \n",
       "20  4.0  1.325818   1.373200       0.047383   1.325964       0.000146   \n",
       "21  4.2  1.337053   1.382886       0.045833   1.337223       0.000169   \n",
       "22  4.4  1.347320   1.391697       0.044378   1.347507       0.000187   \n",
       "23  4.6  1.356736   1.399744       0.043008   1.356937       0.000201   \n",
       "24  4.8  1.365401   1.407119       0.041718   1.365612       0.000211   \n",
       "25  5.0  1.373401   1.413901       0.040500   1.373619       0.000218   \n",
       "\n",
       "    y (p = 3)  error (p = 3)  y (p = 4)  error (p = 4)  \n",
       "0    0.000000       0.000000   0.000000       0.000000  \n",
       "1    0.197195      -0.000200   0.197391      -0.000005  \n",
       "2    0.380169      -0.000337   0.380503      -0.000003  \n",
       "3    0.540110      -0.000310   0.540414      -0.000006  \n",
       "4    0.674569      -0.000172   0.674725      -0.000016  \n",
       "5    0.785374      -0.000025   0.785370      -0.000028  \n",
       "6    0.876136       0.000078   0.876022      -0.000036  \n",
       "7    0.950677       0.000130   0.950508      -0.000039  \n",
       "8    1.012344       0.000147   1.012157      -0.000040  \n",
       "9    1.063841       0.000143   1.063660      -0.000038  \n",
       "10   1.107278       0.000130   1.107113      -0.000036  \n",
       "11   1.144282       0.000113   1.144136      -0.000033  \n",
       "12   1.176101       0.000096   1.175975      -0.000031  \n",
       "13   1.203703       0.000081   1.203594      -0.000028  \n",
       "14   1.227840       0.000068   1.227746      -0.000026  \n",
       "15   1.249102       0.000056   1.249021      -0.000024  \n",
       "16   1.267959       0.000047   1.267889      -0.000023  \n",
       "17   1.284785       0.000040   1.284723      -0.000021  \n",
       "18   1.299883       0.000033   1.299829      -0.000020  \n",
       "19   1.313501       0.000028   1.313453      -0.000019  \n",
       "20   1.325842       0.000024   1.325799      -0.000018  \n",
       "21   1.337074       0.000021   1.337036      -0.000017  \n",
       "22   1.347338       0.000018   1.347303      -0.000017  \n",
       "23   1.356751       0.000016   1.356720      -0.000016  \n",
       "24   1.365415       0.000014   1.365386      -0.000015  \n",
       "25   1.373413       0.000012   1.373386      -0.000015  "
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = pd.read_csv(\"report1.csv\", sep=\",\")\n",
    "table"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Для того, чтобы продемонстрировать работу метода специально возьмем немаленький шаг $h = 0.2$ и рассмотрим $y(x)$ на отрезке $[0, 5]$.\n",
    "\n",
    "Можно увидеть, насколько хорошо работают методы даже с таким немаленьким шагом и что ошибка уменьшается при увеличении $p$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Пример 2**\n",
    "\n",
    "Сделаем дифференциальное уравнение для функции $y(x) = 5 e^{-\\frac{x}{10}}\\cos{7x} + 3\\sin{5x}$ (для того, чтобы получить интересный график). Собственные числа характеристического многочлена: $\\lambda_1 = -\\frac{1}{10} + 7i$, $\\lambda_2 = 5i$ и их сопряженные. Характеристический многочлен должен быть $(\\lambda-\\lambda_1)(\\lambda-\\overline{\\lambda_1})(\\lambda-\\lambda_2)(\\lambda-\\overline{\\lambda_2})=\\lambda^4+\\frac{1}{5}\\lambda^3+\\frac{7401}{100}\\lambda^2+5\\lambda+\\frac{4901}{4}$.\n",
    "\n",
    "Получаем дифференциальное уравнение: $y^{(4)}+\\frac{1}{5}y^{(3)}+\\frac{7401}{100}y^{(2)}+5y'+\\frac{4901}{4}y = 0$. Начальные условия: $y(0) = 5$, $y'(0) = \\frac{29}{2}$, $y^{(2)}(0) = -\\frac{4899}{20}$, $y^{(3)}(0) = -\\frac{60301}{200}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Решение примера 2**\n",
    "\n",
    "Аналогичным способом (как в примере 1) можно свести решение уравнения к уравнению для численного метода размерности $4$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.system('g++ -std=c++17 -O2 -o example2 example2.cpp')\n",
    "code = os.system('./example2')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<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>y (p = 1)</th>\n",
       "      <th>error (p = 1)</th>\n",
       "      <th>y (p = 2)</th>\n",
       "      <th>error (p = 2)</th>\n",
       "      <th>y (p = 3)</th>\n",
       "      <th>error (p = 3)</th>\n",
       "      <th>y (p = 4)</th>\n",
       "      <th>error (p = 4)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>0.00</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>5.000000</td>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>0.05</td>\n",
       "      <td>5.415650</td>\n",
       "      <td>5.725000</td>\n",
       "      <td>0.309350</td>\n",
       "      <td>5.418812</td>\n",
       "      <td>0.003163</td>\n",
       "      <td>5.412531</td>\n",
       "      <td>-0.003119</td>\n",
       "      <td>5.415654</td>\n",
       "      <td>0.000004</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>0.10</td>\n",
       "      <td>5.224436</td>\n",
       "      <td>5.837625</td>\n",
       "      <td>0.613189</td>\n",
       "      <td>5.206297</td>\n",
       "      <td>-0.018139</td>\n",
       "      <td>5.218635</td>\n",
       "      <td>-0.005801</td>\n",
       "      <td>5.224590</td>\n",
       "      <td>0.000154</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>0.15</td>\n",
       "      <td>4.495732</td>\n",
       "      <td>5.300187</td>\n",
       "      <td>0.804455</td>\n",
       "      <td>4.436819</td>\n",
       "      <td>-0.058913</td>\n",
       "      <td>4.488699</td>\n",
       "      <td>-0.007033</td>\n",
       "      <td>4.496148</td>\n",
       "      <td>0.000416</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>0.20</td>\n",
       "      <td>3.357421</td>\n",
       "      <td>4.149937</td>\n",
       "      <td>0.792516</td>\n",
       "      <td>3.248190</td>\n",
       "      <td>-0.109231</td>\n",
       "      <td>3.351312</td>\n",
       "      <td>-0.006109</td>\n",
       "      <td>3.358148</td>\n",
       "      <td>0.000727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>0.25</td>\n",
       "      <td>1.977728</td>\n",
       "      <td>2.500120</td>\n",
       "      <td>0.522392</td>\n",
       "      <td>1.821536</td>\n",
       "      <td>-0.156193</td>\n",
       "      <td>1.974949</td>\n",
       "      <td>-0.002779</td>\n",
       "      <td>1.978737</td>\n",
       "      <td>0.001008</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>6</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.542857</td>\n",
       "      <td>0.531868</td>\n",
       "      <td>-0.010989</td>\n",
       "      <td>0.356404</td>\n",
       "      <td>-0.186453</td>\n",
       "      <td>0.545538</td>\n",
       "      <td>0.002682</td>\n",
       "      <td>0.544035</td>\n",
       "      <td>0.001178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>7</td>\n",
       "      <td>0.35</td>\n",
       "      <td>-0.766740</td>\n",
       "      <td>-1.522937</td>\n",
       "      <td>-0.756198</td>\n",
       "      <td>-0.955635</td>\n",
       "      <td>-0.188896</td>\n",
       "      <td>-0.757240</td>\n",
       "      <td>0.009500</td>\n",
       "      <td>-0.765571</td>\n",
       "      <td>0.001169</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>8</td>\n",
       "      <td>0.40</td>\n",
       "      <td>-1.798494</td>\n",
       "      <td>-3.406561</td>\n",
       "      <td>-1.608067</td>\n",
       "      <td>-1.955475</td>\n",
       "      <td>-0.156980</td>\n",
       "      <td>-1.781972</td>\n",
       "      <td>0.016522</td>\n",
       "      <td>-1.797552</td>\n",
       "      <td>0.000942</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>9</td>\n",
       "      <td>0.45</td>\n",
       "      <td>-2.445599</td>\n",
       "      <td>-4.865747</td>\n",
       "      <td>-2.420148</td>\n",
       "      <td>-2.535955</td>\n",
       "      <td>-0.090356</td>\n",
       "      <td>-2.423199</td>\n",
       "      <td>0.022400</td>\n",
       "      <td>-2.445102</td>\n",
       "      <td>0.000497</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      x         y  y (p = 1)  error (p = 1)  y (p = 2)  error (p = 2)  \\\n",
       "0  0.00  5.000000   5.000000       0.000000   5.000000       0.000000   \n",
       "1  0.05  5.415650   5.725000       0.309350   5.418812       0.003163   \n",
       "2  0.10  5.224436   5.837625       0.613189   5.206297      -0.018139   \n",
       "3  0.15  4.495732   5.300187       0.804455   4.436819      -0.058913   \n",
       "4  0.20  3.357421   4.149937       0.792516   3.248190      -0.109231   \n",
       "5  0.25  1.977728   2.500120       0.522392   1.821536      -0.156193   \n",
       "6  0.30  0.542857   0.531868      -0.010989   0.356404      -0.186453   \n",
       "7  0.35 -0.766740  -1.522937      -0.756198  -0.955635      -0.188896   \n",
       "8  0.40 -1.798494  -3.406561      -1.608067  -1.955475      -0.156980   \n",
       "9  0.45 -2.445599  -4.865747      -2.420148  -2.535955      -0.090356   \n",
       "\n",
       "   y (p = 3)  error (p = 3)  y (p = 4)  error (p = 4)  \n",
       "0   5.000000       0.000000   5.000000       0.000000  \n",
       "1   5.412531      -0.003119   5.415654       0.000004  \n",
       "2   5.218635      -0.005801   5.224590       0.000154  \n",
       "3   4.488699      -0.007033   4.496148       0.000416  \n",
       "4   3.351312      -0.006109   3.358148       0.000727  \n",
       "5   1.974949      -0.002779   1.978737       0.001008  \n",
       "6   0.545538       0.002682   0.544035       0.001178  \n",
       "7  -0.757240       0.009500  -0.765571       0.001169  \n",
       "8  -1.781972       0.016522  -1.797552       0.000942  \n",
       "9  -2.423199       0.022400  -2.445102       0.000497  "
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = pd.read_csv(\"report2.csv\", sep=\",\")\n",
    "table.head(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
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       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>x</th>\n",
       "      <th>y</th>\n",
       "      <th>y (p = 1)</th>\n",
       "      <th>error (p = 1)</th>\n",
       "      <th>y (p = 2)</th>\n",
       "      <th>error (p = 2)</th>\n",
       "      <th>y (p = 3)</th>\n",
       "      <th>error (p = 3)</th>\n",
       "      <th>y (p = 4)</th>\n",
       "      <th>error (p = 4)</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>391</td>\n",
       "      <td>19.55</td>\n",
       "      <td>-0.924406</td>\n",
       "      <td>5.395204e+09</td>\n",
       "      <td>5.395204e+09</td>\n",
       "      <td>-3.258431</td>\n",
       "      <td>-2.334024</td>\n",
       "      <td>-0.892725</td>\n",
       "      <td>0.031681</td>\n",
       "      <td>-0.927101</td>\n",
       "      <td>-0.002695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>392</td>\n",
       "      <td>19.60</td>\n",
       "      <td>-1.357609</td>\n",
       "      <td>4.773239e+09</td>\n",
       "      <td>4.773239e+09</td>\n",
       "      <td>-3.803760</td>\n",
       "      <td>-2.446151</td>\n",
       "      <td>-1.334429</td>\n",
       "      <td>0.023181</td>\n",
       "      <td>-1.360324</td>\n",
       "      <td>-0.002714</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>393</td>\n",
       "      <td>19.65</td>\n",
       "      <td>-1.729883</td>\n",
       "      <td>3.496472e+09</td>\n",
       "      <td>3.496472e+09</td>\n",
       "      <td>-4.093706</td>\n",
       "      <td>-2.363823</td>\n",
       "      <td>-1.713097</td>\n",
       "      <td>0.016786</td>\n",
       "      <td>-1.731779</td>\n",
       "      <td>-0.001896</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>394</td>\n",
       "      <td>19.70</td>\n",
       "      <td>-2.028290</td>\n",
       "      <td>1.647656e+09</td>\n",
       "      <td>1.647656e+09</td>\n",
       "      <td>-4.082403</td>\n",
       "      <td>-2.054113</td>\n",
       "      <td>-2.012738</td>\n",
       "      <td>0.015552</td>\n",
       "      <td>-2.028707</td>\n",
       "      <td>-0.000417</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>395</td>\n",
       "      <td>19.75</td>\n",
       "      <td>-2.240318</td>\n",
       "      <td>-6.110535e+08</td>\n",
       "      <td>-6.110535e+08</td>\n",
       "      <td>-3.748487</td>\n",
       "      <td>-1.508168</td>\n",
       "      <td>-2.218861</td>\n",
       "      <td>0.021458</td>\n",
       "      <td>-2.238880</td>\n",
       "      <td>0.001439</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>396</td>\n",
       "      <td>19.80</td>\n",
       "      <td>-2.353973</td>\n",
       "      <td>-3.049034e+09</td>\n",
       "      <td>-3.049034e+09</td>\n",
       "      <td>-3.099174</td>\n",
       "      <td>-0.745201</td>\n",
       "      <td>-2.318919</td>\n",
       "      <td>0.035054</td>\n",
       "      <td>-2.350652</td>\n",
       "      <td>0.003321</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>397</td>\n",
       "      <td>19.85</td>\n",
       "      <td>-2.358424</td>\n",
       "      <td>-5.387750e+09</td>\n",
       "      <td>-5.387750e+09</td>\n",
       "      <td>-2.171494</td>\n",
       "      <td>0.186929</td>\n",
       "      <td>-2.303104</td>\n",
       "      <td>0.055320</td>\n",
       "      <td>-2.353559</td>\n",
       "      <td>0.004865</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>398</td>\n",
       "      <td>19.90</td>\n",
       "      <td>-2.245186</td>\n",
       "      <td>-7.329486e+09</td>\n",
       "      <td>-7.329486e+09</td>\n",
       "      <td>-1.030390</td>\n",
       "      <td>1.214796</td>\n",
       "      <td>-2.165431</td>\n",
       "      <td>0.079755</td>\n",
       "      <td>-2.239443</td>\n",
       "      <td>0.005744</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>399</td>\n",
       "      <td>19.95</td>\n",
       "      <td>-2.009680</td>\n",
       "      <td>-8.591668e+09</td>\n",
       "      <td>-8.591668e+09</td>\n",
       "      <td>0.236246</td>\n",
       "      <td>2.245926</td>\n",
       "      <td>-1.905000</td>\n",
       "      <td>0.104680</td>\n",
       "      <td>-2.003965</td>\n",
       "      <td>0.005715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>400</td>\n",
       "      <td>20.00</td>\n",
       "      <td>-1.652953</td>\n",
       "      <td>-8.943188e+09</td>\n",
       "      <td>-8.943188e+09</td>\n",
       "      <td>1.525154</td>\n",
       "      <td>3.178107</td>\n",
       "      <td>-1.527218</td>\n",
       "      <td>0.125735</td>\n",
       "      <td>-1.648292</td>\n",
       "      <td>0.004661</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         x         y     y (p = 1)  error (p = 1)  y (p = 2)  error (p = 2)  \\\n",
       "391  19.55 -0.924406  5.395204e+09   5.395204e+09  -3.258431      -2.334024   \n",
       "392  19.60 -1.357609  4.773239e+09   4.773239e+09  -3.803760      -2.446151   \n",
       "393  19.65 -1.729883  3.496472e+09   3.496472e+09  -4.093706      -2.363823   \n",
       "394  19.70 -2.028290  1.647656e+09   1.647656e+09  -4.082403      -2.054113   \n",
       "395  19.75 -2.240318 -6.110535e+08  -6.110535e+08  -3.748487      -1.508168   \n",
       "396  19.80 -2.353973 -3.049034e+09  -3.049034e+09  -3.099174      -0.745201   \n",
       "397  19.85 -2.358424 -5.387750e+09  -5.387750e+09  -2.171494       0.186929   \n",
       "398  19.90 -2.245186 -7.329486e+09  -7.329486e+09  -1.030390       1.214796   \n",
       "399  19.95 -2.009680 -8.591668e+09  -8.591668e+09   0.236246       2.245926   \n",
       "400  20.00 -1.652953 -8.943188e+09  -8.943188e+09   1.525154       3.178107   \n",
       "\n",
       "     y (p = 3)  error (p = 3)  y (p = 4)  error (p = 4)  \n",
       "391  -0.892725       0.031681  -0.927101      -0.002695  \n",
       "392  -1.334429       0.023181  -1.360324      -0.002714  \n",
       "393  -1.713097       0.016786  -1.731779      -0.001896  \n",
       "394  -2.012738       0.015552  -2.028707      -0.000417  \n",
       "395  -2.218861       0.021458  -2.238880       0.001439  \n",
       "396  -2.318919       0.035054  -2.350652       0.003321  \n",
       "397  -2.303104       0.055320  -2.353559       0.004865  \n",
       "398  -2.165431       0.079755  -2.239443       0.005744  \n",
       "399  -1.905000       0.104680  -2.003965       0.005715  \n",
       "400  -1.527218       0.125735  -1.648292       0.004661  "
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table.tail(10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы взяли шаг $h = 0.05$ и рассматриваем $y(x)$ на отрезке $[0, 20]$.\n",
    "\n",
    "Посмотрим на значения, которые получаются в начале и в конце работы алгоритма. Можно видеть, насколько метод четвертого порядка работает лучше методов меньших порядков:\n",
    "\n",
    "- метод Эйлера сразу улетает в бесконечность\n",
    "- метод второго порядка получает ошибку, сопоставимую с самой функцией, что плохо\n",
    "- метод третьего порядка имеет ошибку примерно $0.1$, что не так плохо\n",
    "- метод четвертого порядка имеет крайне маленькую ошибку"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Нарисуем график функции и график, который построит метод с $p=2$, чтобы посмотреть в каких местах метод ошибается:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x1152 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x_coords = np.array(table['x'])\n",
    "y_coords = np.array(table['y'])\n",
    "y_2 = np.array(table['y (p = 2)'])\n",
    "plt.figure(figsize=(16, 16))\n",
    "plt.plot(x_coords, y_coords, color='red', label='function')\n",
    "plt.plot(x_coords, y_2, color='blue', label='p=2')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Пример 3**\n",
    "\n",
    "Раз мы изучаем численные методы, давайте придумаем какое-нибудь сложное дифференциальное уравнение, которое мы бы точно не смогли решить руками и решим его методом Рунге-Кутты, а потом посмотрим на график.\n",
    "\n",
    "Итак, сделаем какое-нибудь страшное уравнение:\n",
    "\n",
    "$$y' = 5\\sin{(x^2 + y)}\\cos(y^3 + x^2) + \\frac{\\log{(2x^2+3)}(x + y)^2}{2} - 2 \\frac{e^{-\\frac{x}{2}} \\sqrt{x^2+y^4}}{1+x^2}$$\n",
    "\n",
    "Начальное условие сделаем $y(0) = 0$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Решение примера 3**\n",
    "\n",
    "Посмотрим, какие значения получаются методом Рунге-Кутты $4$ порядка и нарисуем график. Мы берем шаг $h = 0.01$, смотрим на функцию на отрезке $[0, 1.5]$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [],
   "source": [
    "os.system('g++ -std=c++17 -O2 -o example3 example3.cpp')\n",
    "code = os.system('./example3')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1152x1152 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "table = pd.read_csv(\"report3.csv\", sep=\",\")\n",
    "\n",
    "x_coords = np.array(table['x'])\n",
    "y_coords = np.array(table['y'])\n",
    "plt.figure(figsize=(16, 16))\n",
    "plt.plot(x_coords, y_coords, color='red', label='y')\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Таким образом, мы видим, что мы получили очень мощный, точный и эффективный метод.\n",
    "\n",
    "Весь проект (вместе с кодом) можно найти тут: https://github.com/isaf27/runge_kutta."
   ]
  }
 ],
 "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": "3.7.1"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}