{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "43dad5d3-e15e-4537-8241-85b08c66f40c",
   "metadata": {},
   "source": [
    "## Численное решение задачи Коши: библиотека SciPy\n",
    "\n",
    "Материалы этой части основаны на книге (JBoook):\n",
    "\n",
    "Qingkai Kong, Timmy Siauw, Alexandre M. Bayen. «Python Programming And Numerical Methods: A Guide For Engineers And Scientists»: https://pythonnumericalmethods.berkeley.edu/notebooks/Index.html\n",
    "\n",
    "__Задача Коши:__ \n",
    "Рассмотрим решение начальной задачи (_Intial value problem_) для сисетемы обыкновенных дифференциальных уравнений первого порядка, разрешенных ошносительно производной:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "\\begin{cases}\n",
    "     \\frac{dy(t)}{dt} = f(t,y(t)),\\\\\n",
    "     y|_{t=t_0} = y_0,\n",
    "\\end{cases}\n",
    "\\label{eq1}\n",
    "\\tag{1}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "где $ y=(y_1,...,y_n)^T $ - вектор-функция.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7c96eb14-d9a3-4cd4-bf16-d4ff7c73ac70",
   "metadata": {},
   "source": [
    "#### Пример 1: Численно решить задачу Коши:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "\\begin{cases}\n",
    "    \\frac{dy}{dt} = y\\cos(t), \\\\\n",
    "    y(0)=y_0.\n",
    "\\label{eq2}\n",
    "\\tag{2}\n",
    "\\end{cases}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "__Для сравнения приведем аналитическое решение задачи (2):__\n",
    "\n",
    "$$\n",
    "y_{exact} = y_0 e^{sin(t)}.\n",
    "$$\n",
    "\n",
    "Воспользуемся библиотекой SciPy, содержащей [функцию для решения начальной задачи](https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.solve_ivp.html):\n",
    "```python\n",
    "scipy.integrate.solve_ivp(fun, t_span, y0, method='RK45', t_eval=None, dense_output=False, events=None, vectorized=False, args=None, **options)[source]\n",
    "Solve an initial value problem for a system of ODEs.\n",
    "```\n",
    "Для этого необходимо задать правые части уравнений (2)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "bd1c9b25-65f1-4586-b929-ae21df67b99d",
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline \n",
    "\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.integrate import solve_ivp\n",
    "from functools import partial\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "sns.set(style=\"whitegrid\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cff0ce70-08c2-418b-9598-eb98278927aa",
   "metadata": {},
   "outputs": [],
   "source": [
    "def F_right(t, y):\n",
    "    ''' Определяет правую часть ДУ,\n",
    "        примера 1'''\n",
    "    return y*np.cos(t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "2996e64d-034d-4443-8d48-125b1995959d",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Параметры численного счета\n",
    "t0 = 0\n",
    "tf = 10\n",
    "nt = 1000\n",
    "# Массив точек (сетка) в которых будет находится решение\n",
    "t_e = np.linspace(t0, tf, nt)\n",
    "# Начальное условие\n",
    "y0 = np.array([3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "6920b13e-aa40-4102-a88f-37ee5510b6e9",
   "metadata": {},
   "outputs": [],
   "source": [
    "def y_exact(y0, t):\n",
    "    ''' Определяет точное решение ДУ,\n",
    "        примера 1'''\n",
    "    return y0*np.exp(np.sin(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "981d5f85-cec3-45cd-8404-5aa0b126dbb6",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Численное решение\n",
    "sol_1 = solve_ivp(F_right, [t0, tf], y0, t_eval=t_e,\n",
    "                  method='RK45', rtol=1e-8, atol=1e-8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "7b32522f-be62-422f-a134-ea1caa6f4632",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(sol_1.t, sol_1.y[0], label='Численное решение задачи (2) $y(t)$',\n",
    "         linewidth=3.0)\n",
    "plt.plot(t_e, y_exact(y0, t_e), label='Аналитическое решение $y_{exact}(t)$',\n",
    "         linestyle='--', linewidth=3.0)\n",
    "plt.xlabel('t', size=16)\n",
    "plt.ylabel('$y(t)$', size=12)\n",
    "plt.legend(loc='upper center', fontsize=11)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "60874b0e-37bd-408e-ae32-5cb76cc9adba",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(t_e, np.abs(y_exact(y0, t_e)-sol_1.y[0]),\n",
    "         label='Ошибка $|y_{exact}(t) - y(t)|$', linestyle='--', linewidth=3.0)\n",
    "plt.xlabel('t', size=16)\n",
    "plt.ylabel('$error(t)$', size=12)\n",
    "plt.legend(fontsize=12)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac57628d-aa70-4c3a-b1c8-f1fb0d1372e9",
   "metadata": {},
   "source": [
    "#### Пример 2: Численно решить задачу Коши:\n",
    "\n",
    "$$\n",
    "\\begin{eqnarray}\n",
    "\\begin{cases}\n",
    "    \\frac{dy}{dt} = y\\cos(\\omega t), \\\\\n",
    "    y(0)=y_0.\n",
    "\\end{cases}\n",
    "\\label{eq3}\n",
    "\\tag{3}\n",
    "\\end{eqnarray}\n",
    "$$\n",
    "\n",
    "__Для сравнения приведем аналитическое решение задачи (3):__\n",
    "\n",
    "$$\n",
    "y_{exact} = y_0 e^{\\frac{1}{\\omega}sin(\\omega t)}.\n",
    "$$\n",
    "\n",
    "__Отметим, что в модель входит параметр $\\omega$. Для корректной передачи параметра в функцию SciPy воспользуемся методом:__\n",
    "```python\n",
    "from functools import partial\n",
    "```\n",
    "[Модуль _functools_](https://docs.python.org/3/library/functools.html) предназначен для функций высшего порядка: функций, которые воздействуют на другие функции или возвращают их.\n",
    "Для решения задачи:\n",
    "* Зададим  правые части уравнений (3);\n",
    "* \"Обернем\" вызов решателя с помощью функции _partial_,  для частичного применения функции, которое «замораживает» некоторую часть аргументов функции и/или ключевых слов."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "ba3518fd-c8b9-43f1-90e1-eb76299bd883",
   "metadata": {},
   "outputs": [],
   "source": [
    "def F_right2(t, y, omega):\n",
    "    ''' Определяет правую часть ДУ примера 2\n",
    "    omega - параметр'''\n",
    "    return y*np.cos(omega*t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "031ec140-5f90-47b0-84e4-af110aa4a8fd",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Параметр модели\n",
    "omega = np.pi/2\n",
    "# Параметры численного счета\n",
    "t0 = 0\n",
    "tf = 10\n",
    "nt = 1000\n",
    "# Массив точек (сетка) в которых будет находится решение\n",
    "t_e = np.linspace(t0, tf, nt)\n",
    "# Начальное условие\n",
    "y0 = np.array([3])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "9e0512c5-aaa1-4555-8b3d-8939f50ae094",
   "metadata": {},
   "outputs": [],
   "source": [
    "f = partial(F_right2, omega=omega)\n",
    "t_e = np.linspace(t0, tf, nt)\n",
    "sol_2 = solve_ivp(f, [t0, tf], y0, t_eval=t_e, method='RK45',\n",
    "                  rtol=1e-8, atol=1e-8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "316149ef-0ff5-438d-8a6e-a0d3816a2275",
   "metadata": {},
   "outputs": [],
   "source": [
    "def y_exact2(y0, t, omega):\n",
    "    ''' Определяет точное решение ДУ,\n",
    "        примера 2'''\n",
    "    return y0*np.exp(np.sin(omega*t)/omega)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "1891035e-adcb-4688-b187-824cbb4ab56f",
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(8, 6))\n",
    "plt.plot(sol_2.t, sol_2.y[0], label='Численное решение задачи (3) $y(t)$',\n",
    "         linewidth=3.0)\n",
    "plt.plot(t_e, y_exact2(y0, t_e, omega),\n",
    "         label='Аналитическое решение $y_{exact}(t) $',\n",
    "         linestyle='--', linewidth=3.0)\n",
    "plt.xlabel('t', size=16)\n",
    "plt.ylabel('$y(t)$', size=12)\n",
    "plt.legend(loc='upper center', fontsize=11)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "4db6bbaa-09fa-4c70-9125-829ce05e6b00",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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