09. Дифференциальные уравнения.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from scipy import integrate"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. Обыкновенные дифференциальные уравнения\n",
    "\n",
    "Дифференциальные уравнения – один из основных инструментов математического моделирования.\n",
    "С помощью диф.уравнений описывается огромное количество процессов и явлений в физике, технике, химиии, биологии, экономике, социологии и др. Исследуя дифференциальные уравнения, мы можем делать выводы по поводу описываемой ситуации.\n",
    "\n",
    "Рассмотрим следующую задачу.\n",
    "Скорость роста некоторой популяции организмов пропорциональна ее объему, причем на коэффициент пропорциональности влияет сезонная составляющая. Требуется определить объем популяции как функцию времени, если объем популяции в начальный момент известен.\n",
    "\n",
    "Обозначим объем популяции через $y$.\n",
    "Тот факт, что $y$ является функцией времени $t$ будем записывать так: $y=y(t)$.\n",
    "Тогда \n",
    "$$\n",
    "    y'\\equiv\\frac{dy}{dt}\n",
    "$$\n",
    "– скорость роста популяции.\n",
    "Получаем\n",
    "$$\n",
    "    y' = (\\alpha + \\beta \\sin t)y,   \\tag{1}\n",
    "$$\n",
    "где слагаемое $\\beta \\sin t$ соответствует сезонной составляющей.\n",
    "Коэффициенты $\\alpha$ и $\\beta$ предполагаются известными.\n",
    "Также известен объем популяции в начальный момент времени:\n",
    "$$\n",
    "    y(0) = y_0.                     \\tag{2}\n",
    "$$\n",
    "Мы свели задачу к задаче нахождения функции $y(t)$,\n",
    "удовлетворяющей *дифференциальному уравнению* (1) \n",
    "и *начальному условию* (2).\n",
    "\n",
    "Вообще, дифференциальными уравнениями называют уравнения, содержащие производные неизвестных функций. \n",
    "Простейшими из дифференциальных уравнений являются уравнения *первого порядка*\n",
    "$$\n",
    "    g(t, y, y') = 0,      \\tag{3}\n",
    "$$\n",
    "где $y = y(t)$ – неизвестная (искомая) функция, $t$ – независимая переменная,\n",
    "а $g$ – заданная функция трех аргументов.\n",
    "Уравнение (3) имеет первый порядок, так как\n",
    "в нем встречаются производные искомой функции только первого порядка.\n",
    "Простейшими из дифференциальных уравнений первого порядка\n",
    "являются уравнения, *разрешенные относительно производной*:\n",
    "$$\n",
    "    y' = f(t, y).  \\tag{4}\n",
    "$$\n",
    "Именно таким является уравнение (1).\n",
    "\n",
    "В огромном числе приложений дифференциальные уравнения\n",
    "описывают процессы, *протекающие во времени*, \n",
    "независимая переменная в таких примерах – это время, и хотя существуют примеры,\n",
    "в которых это не так, мы, следуя сложившейся традиции,\n",
    "в модельных задачах также будем называть независимую\n",
    "переменную временем.\n",
    "\n",
    "В отличие от алгебраических уравнений в дифференциальных уравнениях\n",
    "искомыми являются не скалярные значения, а целые функции.\n",
    "Любая дифференцируемая функция $y(t)$, \n",
    "удовлетворяющая уравнению (3) или, скажем, (4), \n",
    "называется его *частным решением*. Множество всех частных решений данного уравнений\n",
    "называется его *общим решением*.\n",
    "Нахождение решения (частного или общего) называют также\n",
    "*интегрированием* дифференциального уравнения.\n",
    "\n",
    "Неизвестные функции, которые у нас встречались и будут встречаться в дифференциальных уравнениях, зависят только от одной переменной. Такие дифференциальные уравнения называются *обыкновенными*. Кроме обыкновенных дифуров бывают еще *дифференциальные уравнения в частных производных* (дифур.ч.п.) - в них неизвестные функции зависят уже не от одной независимой переменной, а от двух или большего их количества, поэтому в уравнениях появляются частные производные.\n",
    "\n",
    "\n",
    "Иногда (но далеко не всегда)\n",
    "дифференциальное уравнение удается решить аналитически,\n",
    "т.е. указать его общее решение.\n",
    "Например, общее решение уравнения (1) описывается\n",
    "формулой\n",
    "$$\n",
    "      y(t) = c e^{\\alpha t - \\beta \\cos t},\n",
    "$$\n",
    "где $c$ – произвольная константа\n",
    "(cделайте проверку, подставив решение в исходное уравнение!)\n",
    "\n",
    "*Задача Коши* заключается в определении частного решения $y(t)$,\n",
    "определенного на заданном отрезке $[t_0, T]$, удовлетворяющего \n",
    "кроме самого уравнения (1) также\n",
    "*начальному условию*\n",
    "$$\n",
    "    y(t_0) = y_0. \\tag{5}\n",
    "$$\n",
    "В частности,\n",
    "$$\n",
    "    y(t) = e^{t-\\cos t + 1}\n",
    "$$\n",
    "является решением задачи Коши, удовлетворяющим уравнению \n",
    "$y'=(1+\\cos t) y$ и начальному условию $y(0) = 1$.\n",
    "\n",
    "\n",
    "Можно предложить следующую \n",
    "\"геометрическую\" формулировку задачи Коши.\n",
    "Требуется определить функцию, график которой проходит через точку $(t_0, y_0)$,\n",
    "и в каждой своей точке $(t, y)$ имеет наклон (а точнее: тангенс угла наклона\n",
    "касательной) $f(t, y)$.\n",
    "Такое определение позволяет дать следующее геометрическое \"решение\"\n",
    "задачи Коши. В каждой точке $(t, y)$ плоскости строится единичный вектор\n",
    "с наклоном $f(t, y)$. Множество таких векторов называется *полем направлений*.\n",
    "График искомой функции теперь рисуется так, чтобы, в каждой точке\n",
    "касательная к нему была соноправлена с соответствующим вектором поля направлений.\n",
    "\n",
    "Поле направлений изобразим с помощью следующей функции:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "def dirfield(f, t0, t1, y0, y1, m=16):\n",
    "\n",
    "    T, Y = np.meshgrid(np.linspace(t0, t1, m), np.linspace(y0, y1, m))\n",
    "    F = f(T, Y)\n",
    "    DT = 1/np.sqrt(1 + F**2)\n",
    "    DY = F/np.sqrt(1 + F**2)\n",
    "    plt.quiver(T, Y, DT, DY, color='grey')\n",
    "    plt.xlabel('t')\n",
    "    plt.ylabel('y')\n",
    "    plt.axis([t0, t1, y0, y1])\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Чтобы воспользоваться функцией `dirfield`, сперва необходимо подготовить функцию, вычисляющую правую часть\n",
    "дифференциального уравнения.\n",
    "\n",
    "**Пример 1.** \n",
    "Например, рассмотрим частный случай уравнения ($1$):\n",
    "$$\n",
    "    y' = (1 + 0.1 \\sin t) y. \n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fun(t, y):\n",
    "    return (1 + .1*np.sin(t))*y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Построим поле направлений для этого уравнения при $0\\le t \\le 1$, $0\\le y \\le 1$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "dirfield(fun, 0, 1, 0, 1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Поверх построенного поля направлений\n",
    "нарисуем графики некоторых частных решений:\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "dirfield(fun, 0, 1, 0, 1)\n",
    "t = np.linspace(0, 1)\n",
    "y = np.exp(t - .1*np.cos(t))\n",
    "c = np.arange(.1, .9, .1)*np.exp(.1);\n",
    "plt.plot(t, np.outer(y, c))\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Пример 2.** В качестве другого примера рассмотрим уравнение:\n",
    "$$\n",
    "y' = -10ty.\n",
    "$$\n",
    "Ее общее решение имеет вид $y=c e^{-5t^2}$, где $c$ - произвольная константа (проверьте подстановкой в уравнение!).\n",
    "\n",
    "Изобразим поле направлений и некоторые частные решения для $-1\\le t\\le 1$, $0\\le y\\le 2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def fun2(t, y):\n",
    "    return -10*t*y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "dirfield(fun2, -1, 1, 0, 2)\n",
    "t = np.linspace(-1, 1)\n",
    "y = np.exp(-5*t**2)\n",
    "c = np.arange(.1, 1.9, .25)*np.exp(.1);\n",
    "plt.plot(t, np.outer(y, c))\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2. Метод Эйлера\n",
    "\n",
    "К сожалению, не все дифференциальные уравнения можно решить аналитически. Однако их можно решать численно.\n",
    "*Метод Эйлера* - один из самых простых численных методов решения задачи Коши.\n",
    "\n",
    "Итак, пусть дано дифференциальное уравнение\n",
    "$$\n",
    "    y' = f(t, y).  \\tag{4}\n",
    "$$\n",
    "и начальное условие\n",
    "$$\n",
    "y(t_0) = y_0. \\tag{5}\n",
    "$$\n",
    "\n",
    "Если $h$ - достачно мало, то\n",
    "$$\n",
    "    y' \\approx \\frac{y(t_0 + h) - y(t_0)}{h},\n",
    "$$\n",
    "поэтому, учитывая ($****$) получаем:\n",
    "$$\n",
    "y(t_0+h) \\approx y(t_0) + h y'(t_0) = y_0 + h f(t_0, y_0).\n",
    "$$\n",
    "Значение \n",
    "$$\n",
    "y_1 = y_0 + h f(t_0, y_0)\n",
    "$$\n",
    "является приближением к $y(t_1)$, где $t_1 = t_0+h$.\n",
    "Аналогично получаем\n",
    "$$\n",
    "y(t_1+h) \\approx y(t_1) + h y'(t_1) \\approx y_1 + h f(t_1, y_1).\n",
    "$$\n",
    "Значение \n",
    "$$\n",
    "y_2 = y_1 + h f(t_1, y_1)\n",
    "$$\n",
    "является приближением к $y(t_2)$, где $t_2 = t_1+h$.\n",
    "\n",
    "Такого сорта итерации можно продолжать.\n",
    "Получаем следующие расчетные формулы метода Эйлера:\n",
    "$$\n",
    "t_{k+1} = t_k + h,\n",
    "\\qquad\n",
    "y_{k+1} = y_k + h f(t_k, y_k), \n",
    "\\qquad\n",
    "(k=0,1,2,\\dots).\n",
    "$$\n",
    "$h$ называется *шагом интегрирования*.\n",
    "\n",
    "Напишем код, реализующий метод Эйлера.\n",
    "Функция `euler`, приведенная ниже, находит численное решение, представленное в векторах `t` и `y` для задачи Коши, решаемой на отрезке `t0`, `T`. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def euler(fun, t0, T, y0, h):\n",
    "\n",
    "    n = int((T - t0)/h) + 1\n",
    "    t = np.zeros(n)\n",
    "    y = np.zeros(n)\n",
    "\n",
    "    t[0] = t0\n",
    "    y[0] = y0\n",
    "\n",
    "    for k in range(n - 1):\n",
    "        t[k + 1] = t[k] + h\n",
    "        y[k + 1] = y[k] + h*fun(t[k], y[k])\n",
    "\n",
    "    return t, y"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Пример 1.** *(продолжение)*\n",
    "Применим метод Эйлера к задаче."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "t0 = 0\n",
    "T  = 1\n",
    "y0 = 1\n",
    "h  = .1\n",
    "t, y = euler(fun, t0, T, y0, h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Точное ее решение"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "tt = np.linspace(t0, T, 500)\n",
    "yy = y0*np.exp(tt - np.cos(tt) + 1)\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Изобразим численное и точное решение:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(tt, yy, label='Exact solution')\n",
    "plt.plot(t,  y,  label='Numerical solution')\n",
    "plt.legend()\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы видим, что наблюдается большое расхождение с точным решением.\n",
    "\n",
    "Решение можно попробовать улучшить, если уменьшить шаг интегрирования"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "h  = .00001\n",
    "t, y = euler(fun, t0, T, y0, h)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(tt, yy, label='Exact solution')\n",
    "plt.plot(t,  y,  label='Numerical solution')\n",
    "plt.legend()\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Несмотря на то, что шаг взят очень маленьким, численное решение сильно отклоняется от точного. Проблемы возникают вследствие того, что уравнение неустойчиво.\n",
    "\n",
    "В таком варианте метод Эйлера не может обеспечить приемлемую точность для данной задачи."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Пример 2.** *(продолжение)* Опробуем функцию `euler` на задаче "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "t0 = -1\n",
    "T  = 1\n",
    "y0 = .1\n",
    "h  = .001\n",
    "t, y = euler(fun2, t0, T, y0, h)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Точное решение:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "tt = np.linspace(t0, T, 500)\n",
    "yy = y0*np.exp(5*(1 - tt**2))\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(tt, yy, label='Exact solution')\n",
    "plt.plot(t,  y,  label='Numerical solution')\n",
    "plt.legend()\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Мы видим, что численное решение хорошо аппроксимирует аналитическое решение, однако такая точность достигается за счет слишком маленького шага и, следовательно, больших вычислительных затрат. Экспериментально исследуйте, как меняется точность при разных шагах.\n",
    "\n",
    "Более сложные, чем метод Эйлера, методы позволяют получить хорошую точность при умеренном количестве итераций."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3. Решатели задачи Коши из библиотеки `scipy`\n",
    "\n",
    "Продвинутые численные методы решения задачи Коши реализованы в функции `solve_ivp` модуля `integrate` библиотеки `scipy`. Функцию можно вызвать следующим образом: \n",
    "```\n",
    "sol = integrate.solve_ivp(fun, tspan, y0)\n",
    "```\n",
    "Здесь `fun` - функция, вычисляющая правую часть дифференциального уравнения, `tspan` - отрезок интегрирования, `y0` - начальное значение для $y$ (`ivp` *означает initial-value problem* - начальная задача - это другое название для задачи Коши).\n",
    "\n",
    "`sol` - структура, хранящая вычисленное решение и другую информацию о процессе решения. \n",
    "В частности, `sol.y` - вычисленные значения функции y в точках, указанных в дополнительном параметре `t_eval`"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Пример 1.** *(продолжение)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "t0 = 0\n",
    "T  = 1\n",
    "y0 = 1\n",
    "tt  = np.linspace(t0, T, 500) \n",
    "sol = integrate.solve_ivp(fun, [t0, T], [y0], t_eval=tt)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "yy = y0*np.exp(tt - np.cos(tt) + 1)\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(tt, yy, label='Exact solution')\n",
    "plt.plot(sol.t,  sol.y[0],  label='Numerical solution')\n",
    "plt.legend()\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Если в решателе установить дополнительный параметр `dense_output=True`, то в `sol.sol` возвращается функция, вычисляющая $y$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "sol = integrate.solve_ivp(fun, [t0, T], [y0], dense_output=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(tt, yy, label='Exact solution')\n",
    "plt.plot(tt,  sol.sol(tt)[0],  label='Numerical solution')\n",
    "plt.legend()\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Пример 2.** *(продолжение)*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "t0 = -1\n",
    "T  = 1\n",
    "y0 = .1\n",
    "tt  = np.linspace(t0, T, 500) \n",
    "sol = integrate.solve_ivp(fun2, [t0, T], [y0], t_eval=tt)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Точное решение:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "yy = y0*np.exp(5*(1 - tt**2))\n",
    "pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "plt.plot(tt, yy, label='Exact solution')\n",
    "plt.plot(tt, sol.y[0], label='Numerical solution')\n",
    "plt.legend()\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Визуально численное и аналитическое решения совпадают.\n",
    "Найдем максимальное отклонение:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0047411227386895405"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy import linalg\n",
    "linalg.norm(yy-sol.y[0], np.Inf)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4. Системы дифференциальных уравнений\n",
    "\n",
    "Рассмотрим простую экосистему, состоящую из особей двух видов:\n",
    "хищников и жертв. Классическая *модель Вольтерра-Лотке* описывает ее \n",
    "системой двуx дифференциальных уравнений\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{l}\n",
    "   \\frac{\\displaystyle dx}{\\displaystyle dt} = \\alpha x - \\gamma x y,\\\\\n",
    "   \\frac{\\displaystyle dy}{\\displaystyle dt} = -\\beta y + \\gamma x y \\\\\n",
    "\\end{array}\n",
    "\\right.\n",
    "$$\n",
    "и начальными условиями\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{l}\n",
    "   x(0) = x_0,\\\\\n",
    "   y(0) = y_0.\\\\\n",
    "\\end{array}\n",
    "\\right.\n",
    "$$\n",
    "Здесь $x$ - численность жертв, $y$ - численность хищников,\n",
    "$\\alpha$, $\\beta$, $\\gamma$ - некоторые константы.\n",
    "Если $\\gamma = 0$, то популяции не взаимодействуют\n",
    "и жертвы размножаются со скоростью, пропорциональной их численности,\n",
    "а хищники вымирают. Если $\\gamma > 1$, то хищники встречают жертв\n",
    "с вероятностью пропорциональной произведению числа тех и других.\n",
    "В результате таких встреч число жертв увеличивается,\n",
    "а число хищников возрастает. \n",
    "\n",
    "Рассматриваемая нами система является системой дифференциальных уравнений\n",
    "первого порядка, разрешенных относительно производных.\n",
    "Общий вид такой системы следующий:\n",
    "$$\n",
    "\\left\\{\n",
    "\\begin{array}{l}\n",
    "y'_1 = f_1(t, y_1,y_2,\\dots,y_n),\\\\\n",
    "y'_2 = f_2(t, y_1,y_2,\\dots,y_n),\\\\\n",
    "\\dots \\\\\n",
    "y'_n = f_n(t, y_1,y_2,\\dots,y_n)\\\\\n",
    "\\end{array}\n",
    "\\right.                   \\tag{6}\n",
    "$$\n",
    "Здесь $y_1(t),\\dots,y_n(t)$ - искомые функции.\n",
    "Вводя вектор-функции $y(t)$ и $f(t,y)$:\n",
    "$$\n",
    "  y(t) = \n",
    "         \\left[\n",
    "             \\begin{array}{c} \n",
    "                 y_1(t) \\\\ y_2(t) \\\\ \\vdots \\\\ y_n(t)\n",
    "             \\end{array}\n",
    "         \\right],\n",
    "  \\qquad\n",
    "  f(t,y) = \n",
    "         \\left[\n",
    "             \\begin{array}{c} \n",
    "                 f_1(t,y_1,y_2,\\dots,y_n) \\\\ f_2(t,y_1,y_2,\\dots,y_n) \\\\ \\vdots \\\\ f_n(t,y_1,y_2,\\dots,y_n)\n",
    "             \\end{array}\n",
    "         \\right]\n",
    "$$\n",
    "и определяя \n",
    "$$\n",
    "   y' = \\frac{dy}{dt} = \n",
    "           \\left[\n",
    "               \\begin{array}{c} \n",
    "                   y_1' \\\\ y_2' \\\\ \\vdots \\\\ y_n'\n",
    "               \\end{array}\n",
    "           \\right],\n",
    "$$\n",
    "мы можем записать (6)\n",
    "в более простом виде\n",
    "$$\n",
    "    y'=f(t, y).\n",
    "$$\n",
    "\n",
    "*Частным решением* называется вектор-функция $y(t)$, такая, что все ее компоненты\n",
    "удовлтворяют всем уравнениям системы.\n",
    "Множество всех частных решений образует *общее решение*.\n",
    "*Задача Коши* для системы уравнений заключается в поиске такого частного решения $y(t)$,\n",
    "которе удовлетворяет также начальным условиям:\n",
    "$$\n",
    "    \\left\\{\n",
    "    \\begin{array}{l}\n",
    "    y_1(t_0) = y_{10},\\\\\n",
    "    y_2(t_0) = y_{20},\\\\\n",
    "    \\dots \\\\\n",
    "    y_n(t_0) = y_{n0},\\\\\n",
    "    \\end{array}\n",
    "    \\right.\n",
    "                 \\quad\\mbox{т.е.} \\quad\n",
    "    y(t_0)= y_0.\n",
    "$$\n",
    "\n",
    "Каждое частное решение мы можем изобразить в виде кривой $y=y(t)$ в пространстве\n",
    "$y_1, y_2, \\dots, y_n$, называемом *фазовым пространством*.\n",
    "Сами кривые, изображающие решения, называются в этом пространстве *траекториями*.\n",
    "\n",
    "Теория и алгоритмы для одного уравнения в основном переносятся и на случай системы дифференциальных\n",
    "уравнений. В частности, разобранный выше метод Эйлера работает и для систем."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Пример 3.** Модель распространения эпидемии SIR - см. отдельный файл"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5. Дифференциальные уравнения высших порядков\n",
    "\n",
    "Рассмотрим следующую задачу.\n",
    "\n",
    "**Пример 4.** \n",
    "Человек бросает камень массы $m$\n",
    "вертикально вверх с начальной скоростью $v_0$.\n",
    "Предположим, что бросок проведен на высоте $h$.\n",
    "Сила сопротивления воздуха пропорциональна квадрату скорости с коэффициентом\n",
    "пропорциональности $\\kappa$. \n",
    "Требуется определить высоту камня над землей как функцию времени.\n",
    "В частности, необходимо установить, на какой высоте камень будет через\n",
    "время $T$.\n",
    "\n",
    "Пусть ось $Ox$ проходит через точку бросания камня и\n",
    "направлена вертикально вверх. Точка $O$ на этой оси расположена на земле.\n",
    "Обозначим $x(t)$ - расстояние от земли до камня в момент времени $t$.\n",
    "Тогда проекция скорости на ось $Ox$ равна $x'$,\n",
    "а проекция ускорения - $x''$.\n",
    "Используя второй закон Ньютона,\n",
    "получаем следующее *дифференциальное уравнение $2$-го порядка*:\n",
    "$$\n",
    "mx'' = -\\kappa x' |x'| - mg,      \\tag{7}\n",
    "$$\n",
    "где $g=9.8$ м/с - ускорение свободного падения.\n",
    "(порядок у уравнения $2$-й, так как оно содержит\n",
    "$2$-ю производную неизвестной функции $x(t)$).\n",
    "В момент времени $t=0$ камень находился на высоте $h$\n",
    "и имел скорость $v_0$,\n",
    "поэтому\n",
    "$$\n",
    "     x(0) = h, \\qquad  x'(0) = v_0.  \\tag{8}\n",
    "$$\n",
    "Требуется найти функцию $x(t)$, удовлетворяющую уравнению (7)\n",
    "и начальным условиям (8).\n",
    "\n",
    "Сейчас мы приведем полученное уравнение к системе двух уравнений первого порядка. \n",
    "Обозначим $v(t)$ - скорость камня в момент времени $t$.\n",
    "Так как $x'=v$ и $x''=v'$, то уравнение (7) и начальные\n",
    "условия (8) можно записать в виде\n",
    "$$\n",
    "\\left\\{\n",
    "   \\begin{array}{l}\n",
    "       x' = v,          \\\\\n",
    "       v' = -\\frac{\\kappa}{m} v |v| - g,\n",
    "   \\end{array}\n",
    "\\right.\n",
    "\\qquad\n",
    "   \\begin{array}{l}\n",
    "        x(0) = h, \\\\  v(0) = v_0.\n",
    "   \\end{array}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "В общем случае уравнение $n$-го порядка\n",
    "$$\n",
    "   x^{(n)} = f(t,x,x',\\dots,x^{(n-1)})\n",
    "$$\n",
    "путем введения новых зависимых переменных \n",
    "$$\n",
    "   y_1(t) = x,~ y_2(t) = x',~ y_3(t) = x'',~ \\dots,~ y_n(t) = x^{(n-1)}\n",
    "$$\n",
    "приводится к системе\n",
    "$$\n",
    "   \\left\\{\n",
    "      \\begin{array}{lcllllll}\n",
    "         y_1'     & = &      &      & y_2, &      &       &       \\\\\n",
    "         y_2'     & = &      &      &      & y_3, &       &       \\\\\n",
    "         \\dots                                                    \\\\\n",
    "         y_{n-1}' & = &      &      &      &      &       & y_n,  \\\\\n",
    "         y_n'     & = & f(t, & y_1, & y_2, & y_3, & \\dots,& y_n).\n",
    "      \\end{array}\n",
    "   \\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Пример 4.** *(продолжение)*\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def stone(t, y):\n",
    "    return [y[1], -k*y[1]*np.abs(y[1])/m-g]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "t0 = 0\n",
    "T = 2\n",
    "g = 9.8\n",
    "k = .01\n",
    "m = .3\n",
    "t  = np.linspace(t0, T, 500) \n",
    "h = .7\n",
    "v0 = 10\n",
    "\n",
    "sol = integrate.solve_ivp(stone, [t0, T], [h, v0], t_eval=t)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Построим графики зависимости высоты $x$ от времени $t$ и скорости $x'$ от $t$, а также график зависимости $x$ от $x'$ - это так называемая *фазовая траектория*."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1152x360 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (16, 5))\n",
    "\n",
    "plt.subplot(1, 3, 1)\n",
    "plt.plot(t, sol.y[0,:])\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x')\n",
    "plt.grid()\n",
    "\n",
    "plt.subplot(1, 3, 2)\n",
    "plt.plot(t, sol.y[1,:])\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('dx/dt')\n",
    "plt.grid()\n",
    "\n",
    "plt.subplot(1, 3, 3)\n",
    "plt.plot(sol.y[0,:], sol.y[1,:])\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('dx/dt')\n",
    "plt.grid()\n",
    "pass"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 6. События\n",
    "\n",
    "В последнем примере нам бы хотелось, по-видимому, завершить процесс интегрирования в тот момент, когда камень окажется на земле, т.е. $x(t)$ не станет равным нулю. Также было бы интересно (по ходу вычислений) определить, находится ли камень в своей наивысшей точке, т.е. $x'(t)=0$. Отслеживать такого сорта *события* можно с помощью одноименного механизма (*events*), реализуемого в функции `solve_ivp`.\n",
    "\n",
    "События связываются с обращением в нуль некоторых индикаторных функций.\n",
    "Эти функции могут зависеть от значений функций $y_1, y_2, \\dots, y_n$ и от значений переменной $t$. \n",
    "В процессе интегрирования уравнения решатель `solve_ivp` выявляет события и вызывает пользовательский обработчик.\n",
    "\n",
    "Решатель может обрабатывать несколько типов событий.\n",
    "Для каждого такого типа пользователь должен написать функцию вида\n",
    "`event_function(t, y)`, вычисляющую свою индикаторную функцию. \n",
    "Кроме этого можно задать два атрибута этой функции:\n",
    "\n",
    "- `terminal` - булево значение: если его значение `True`, то при возникновении события интегрирование уровнения завершается; \n",
    "   по умолчанию - процесс интегрирования не останавливается;  \n",
    "- `direction` - вещественное число: \n",
    "   - если положительно, то считается, что событие совершается только в случае, \n",
    "     если значение индикаторной функции не только обратилось в нуль, но возрастает в этот момент;\n",
    "   - если отрицательно, то событие совершается только в случае, \n",
    "     если значение индикаторной функции обратилось в нуль и убывает;\n",
    "   - если равно нулю, то считается, что событие совершается, если индикаторная функция обратилась в ноль \n",
    "     и не важно, как она менялась в этот момент.\n",
    "\n",
    "Значения времени, в которые происходили события, возвращаются в `sol.t_events`.\n",
    "\n",
    "Заметим, что если вы ожидаете, что интегрирование закончится в результате наступления некоторого события, то в качестве конечного момента времени можно указать `np.Inf`.\n",
    "\n",
    "**Пример 4.** (*продолжение*)\n",
    "\n",
    "Будем отслеживать два события: камень достиг наивысшей точки ($x'=0$) и камень оказался на земле ($x=0$, $x$ убывает).\n",
    "\n",
    "В случае, если происзходит второе событие, процесс интегрирования завершается.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def event_highest(t, y):\n",
    "    return y[1] # событие случается, если y[1] = x' = 0\n",
    "\n",
    "def event_ground(t, y):\n",
    "    return y[0] # событие случается, если y[0] = x = 0\n",
    "\n",
    "event_ground.terminal  = True\n",
    "event_ground.direction = -1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Вызываем решатель:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "t0 = 0\n",
    "g = 9.8\n",
    "k = .01\n",
    "m = .3\n",
    "h = .7\n",
    "v0 = 10\n",
    "\n",
    "sol = integrate.solve_ivp(stone, [t0, np.Inf], [h, v0], dense_output=True, events=[event_highest, event_ground])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_highest = sol.t_events[0][0]\n",
    "x_highest = sol.sol(t_highest)[0]\n",
    "\n",
    "t_ground  = sol.t_events[1][0]\n",
    "v_ground  = sol.sol(t_ground)[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Камень в наивысшей точке: t =  0.9218 c, x =  5.0918\n",
      "Камень на земле:          t =  1.9707 c, v = -9.1986\n"
     ]
    }
   ],
   "source": [
    "print('Камень в наивысшей точке: t = {:7.4f} c, x = {:7.4f}'.format(t_highest, x_highest))\n",
    "print('Камень на земле:          t = {:7.4f} c, v = {:7.4f}'.format(t_ground,  v_ground))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "t  = np.linspace(t0, t_ground, 500) \n",
    "\n",
    "plt.plot(t, sol.sol(t)[0])\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Пример 5.** (*продолжение*)\n",
    "\n",
    "Парашютист прыгает с парашютом из самолета на расстоянии $H$ от земли.\n",
    "На расстоянии $h$ от земли он раскрывает парашют.\n",
    "Найдем время спуска и скорость приземления.\n",
    "\n",
    "Движение парашютися описывается таким же дифференциальным уравнением, что и движение камня, но с другими начальными условиями и меняющимся коэффициентом сопротивления $\\kappa$:\n",
    "$$\n",
    "mx'' = -\\kappa x' |x'| - mg, \\qquad x(t_0) = H, \\qquad x'(t_0) = 0, \\qquad \n",
    "\\kappa = \n",
    "         \\left\\{\n",
    "             \\begin{array}{ll}\n",
    "                  \\kappa_0,       & \\mbox{если } x  >  h, \\\\\n",
    "                  \\kappa_{\\rm p}, & \\mbox{если } x \\le h.\n",
    "             \\end{array}\n",
    "         \\right.\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def parachute(t, y):\n",
    "    if y[0] > h: # т.е. x > h\n",
    "        k = k0\n",
    "    else:\n",
    "        k = kp\n",
    "    return [y[1], -k*y[1]*np.abs(y[1])/m-g] # т.е. [x', -k x' |x'|/m - g]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [],
   "source": [
    "def event_parachute(t, y):\n",
    "    return y[0] - h # событие случается, если y[0] = x = h (раскрывается парашют)\n",
    "\n",
    "def event_ground(t, y):\n",
    "    return y[0] # событие случается, если y[0] = x = 0 (приземление парашютиста)\n",
    "\n",
    "event_ground.terminal  = True\n",
    "event_ground.direction = -1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "t0 = 0    # начальный момент времени\n",
    "H  = 4000 # исходная высота\n",
    "v0 = 0    # начальная скорость\n",
    "h  = 700  # высота, на которой раскрывается парашют\n",
    "m  = 120  # общая масса\n",
    "k0 = .24  # коэффициент сопротивления воздуха для парашютиста до раскрытия парашюта\n",
    "kp = 45   # коэффициент сопротивления воздуха с раскрытым парашютом\n",
    "g  = 9.8  # ускорение свободного падения\n",
    "\n",
    "sol = integrate.solve_ivp(parachute, [t0, np.Inf], [H, v0], dense_output=True, events=[event_parachute, event_ground])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [],
   "source": [
    "t_parachute = sol.t_events[0][0]\n",
    "v_parachute = sol.sol(t_parachute)[1]\n",
    "\n",
    "t_ground    = sol.t_events[1][0]\n",
    "v_ground    = sol.sol(t_ground)[1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Раскрытие парашюта: t = 52.0920 c, v = -69.7971\n",
      "Приземление:        t = 187.9550 c, v = -5.1147\n"
     ]
    }
   ],
   "source": [
    "print('Раскрытие парашюта: t = {:7.4f} c, v = {:7.4f}'.format(t_parachute, v_parachute))\n",
    "print('Приземление:        t = {:7.4f} c, v = {:7.4f}'.format(t_ground,    v_ground))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x432 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "t = np.linspace(t0, t_ground, 500) \n",
    "x, v = sol.sol(t)\n",
    "\n",
    "plt.figure(figsize = (6, 6))\n",
    "\n",
    "plt.subplot(2, 1, 1)\n",
    "plt.plot(t, x)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('x')\n",
    "plt.grid()\n",
    "\n",
    "plt.subplot(2, 1, 2)\n",
    "plt.plot(t, v)\n",
    "plt.xlabel('t')\n",
    "plt.ylabel('dx/dt')\n",
    "plt.grid()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Замечание.** \n",
    "В условиях падения с учетом сопротивления воздуха скорость нарастает, но вместе с этим увеличивается сопротивление (пропорциональное квадрату этой скорости). В результате скорость перестает меняться, когда достигает (с математической точки зрения - асимптотически) некоторой устоявшейся скорости. Т.е. через какое-то время начинает падать с постоянной скоростью. Это хорошо видно на графике для зависимости скорости от времени. Скорости, конечно, различны и зависят от того считаем ли мы ее до или после раскрытия парашюта.\n",
    "\n",
    "Заметим, что устоявшуюся скорость можно вычислить, положив в уравнении $x''=0$. Получаем\n",
    "$$\n",
    "mx'' = -\\kappa x' |x'| - mg = 0,\n",
    "$$\n",
    "откуда для устоявшейся скорости получаем\n",
    "$$\n",
    "|x'|=\\sqrt{\\frac{mg}{\\kappa}}.\n",
    "$$\n",
    "Для нашего случая эти скорости равны"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(70.0, 5.11207720338155)"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.sqrt(m*g/k0), np.sqrt(m*g/kp) "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "что практически совпадает со значениями, найденными через численное решение уравнения. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Выводы\n",
    "\n",
    "- Дифференциальные уравнения – один из основных инструментов математического моделирования.\n",
    "- Огромное количество дифференциальных уравнений не удается решить аналитически и их приходится решать численно.\n",
    "- Задача Коши - это задача нахождения решения системы дифференциальных уранвнений, при известных начальных условиях.\n",
    "- Разработаны многие методы численного решения задачи Коши, однако некоторые системы не удается решать с приемлемой точностью.\n",
    "- Обыкновенные дифференциальные уравнения высших порядков сводятся к системам дифференциальных уравнений 1-го порядка."
   ]
  }
 ],
 "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": "3.7.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}