{ "cells": [ { "cell_type": "markdown", "id": "honest-procurement", "metadata": {}, "source": [ "# Прикладные дифференциальные уравнения\n", "## Занятие 1\n", "*Илья Щуров*\n", "\n", "Факультет компьютерных наук, Прикладная математики и информатика, 2021-22 учебный год\n", "\n", "[Страница курса](http://math-info.hse.ru/2021-22/Прикладные_дифференциальные_уравнения)" ] }, { "cell_type": "markdown", "id": "damaged-territory", "metadata": {}, "source": [ "## Задача 1\n", "Реализовать [метод Эйлера](https://ode.mathbook.info/chapter/label/chap:2:auto/#label_sec_2_euler)." ] }, { "cell_type": "code", "execution_count": 1, "id": "relevant-savings", "metadata": {}, "outputs": [], "source": [ "import numpy as np" ] }, { "cell_type": "code", "execution_count": 2, "id": "demonstrated-hudson", "metadata": {}, "outputs": [], "source": [ "def euler(f, t0, x0, T, steps):\n", " \"\"\"\n", " Решает уравнение \\dot x = f(t, x) с начальным условием\n", " x(t0) = x0\n", " \n", " Возвращает np.array([[t0, x0], [t1, x1], ..., [t_steps, x_steps]]),\n", " где t_steps == T\n", " \"\"\"\n", " points = [[t0, x0]]\n", " x = x0\n", " delta_t = (T - t0) / steps\n", " for i in range(steps):\n", " t = t0 + delta_t * (i + 1)\n", " x = x + delta_t * f(t, x)\n", " points.append([t, x])\n", " return np.array(points)\n", "\n", "\n", "def x_identity(t, x):\n", " return x\n", "\n", "\n", "assert euler(x_identity, 0, 1, 5, 10).shape == (11, 2)" ] }, { "cell_type": "code", "execution_count": 3, "id": "sealed-syntax", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "\n", "%matplotlib inline\n", "\n", "t0 = 0\n", "x0 = 1\n", "T = 2\n", "for steps in [2, 5, 10, 100]:\n", " solution = euler(x_identity, t0, x0, T, steps)\n", " plt.plot(\n", " solution[:, 0], solution[:, 1], label=f\"Euler approximation, {steps} steps\"\n", " )\n", "t_true = np.linspace(t0, T, 500)\n", "plt.plot(t_true, x0 * np.exp(t_true), label=\"True solution\")\n", "plt.legend()" ] }, { "cell_type": "markdown", "id": "elect-philip", "metadata": {}, "source": [ "### Задача 2\n", "Решить уравнение\n", "$$\\dot x = x ^ 2$$ \n", "с начальным условием $x(0)=1$ на отрезке $[0, 3]$, построить график." ] }, { "cell_type": "code", "execution_count": 4, "id": "annual-algorithm", "metadata": { "scrolled": true }, "outputs": [ { "ename": "OverflowError", "evalue": "(34, 'Result too large')", "output_type": "error", "traceback": [ "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m", "\u001b[0;31mOverflowError\u001b[0m Traceback (most recent call last)", "\u001b[0;32m\u001b[0m in \u001b[0;36m\u001b[0;34m\u001b[0m\n\u001b[1;32m 3\u001b[0m \u001b[0mT\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m1.1\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m 4\u001b[0m \u001b[0msteps\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m200\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 5\u001b[0;31m \u001b[0msolution\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0meuler\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m 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\u001b[0meuler\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;32mlambda\u001b[0m \u001b[0mt\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m\u001b[0;34m:\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mt0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mT\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msteps\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m 6\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0msolution\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msolution\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mlabel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34mf\"Euler approximation, {steps} steps\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n", "\u001b[0;31mOverflowError\u001b[0m: (34, 'Result too large')" ] } ], "source": [ "t0 = 0\n", "x0 = 1\n", "T = 1.1\n", "steps = 200\n", "solution = euler(lambda t, x: x ** 2, t0, x0, T, steps)\n", "plt.plot(solution[:, 0], solution[:, 1], label=f\"Euler approximation, {steps} steps\")" ] }, { "cell_type": "markdown", "id": "recent-lotus", "metadata": {}, "source": [ "Вопрос: что случилось?" ] }, { "cell_type": "markdown", "id": "stupid-plant", "metadata": {}, "source": [ "### Задача 3: логистический рост популяции\n", "$$\\dot x = (1 - x)x$$" ] }, { "cell_type": "code", "execution_count": 5, "id": "serious-signal", "metadata": {}, "outputs": [ { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t0 = 0\n", "x0 = 1\n", "T = 10\n", "steps = 200\n", "for x0 in [0, 0.001, 0.01, 0.1, 0.3, 0.5, 0.7, 1, 1.5]:\n", " solution = euler(lambda t, x: (1 - x) * x, t0, x0, T, steps)\n", " plt.plot(solution[:, 0], solution[:, 1], color=\"C0\")" ] }, { "cell_type": "markdown", "id": "honey-pioneer", "metadata": {}, "source": [ "### Задача 4\n", "Адаптировать функцию `euler`, чтобы она могла работать с многомерными фазовыми пространствами" ] }, { "cell_type": "code", "execution_count": 6, "id": "excited-mouse", "metadata": {}, "outputs": [], "source": [ "\n", "def euler_multidim(f, t0, x0, T, steps):\n", " \"\"\"\n", " Решает уравнение \\dot x = f(t, x) с начальным условием\n", " x(t0) = x0\n", " \n", " Возвращает tpoints, xpoints\n", " tpoints == [t0, t1, ..., t_steps],\n", " xpoints == [x0, x1, ..., x_steps]\n", " где t_steps == T\n", " \"\"\"\n", " tpoints = [t0]\n", " xpoints = [x0]\n", " x = x0\n", " delta_t = (T - t0) / steps\n", " for i in range(steps):\n", " t = t0 + delta_t * (i + 1)\n", " x = x + delta_t * f(t, x)\n", " tpoints.append(t)\n", " xpoints.append(x)\n", " return np.array(tpoints), np.array(xpoints)" ] }, { "cell_type": "markdown", "id": "blocked-tiger", "metadata": {}, "source": [ "### Задача 5\n", "Построить и визуализировать решение [модели Лотки — Волтерры](https://ru.wikipedia.org/wiki/Модель_Лотки_—_Вольтерры):\n", "\n", "$$\\dot x = x - xy,\\quad \\dot y = -y + xy,$$\n", "где $x$ — число кроликов, $y$ — число лис." ] }, { "cell_type": "code", "execution_count": 7, "id": "falling-incentive", "metadata": {}, "outputs": [], "source": [ "def lotka_volterra(t, x):\n", " rabbits, foxes = x\n", " return np.array([rabbits - foxes * rabbits, -foxes + foxes * rabbits])" ] }, { "cell_type": "code", "execution_count": 8, "id": "arctic-fundamental", "metadata": {}, "outputs": [], "source": [ "t, x = euler_multidim(lotka_volterra, 0, np.array([0.2, 0.2]), 15, 5000)" ] }, { "cell_type": "code", "execution_count": 9, "id": "stuffed-sweden", "metadata": {}, "outputs": [], "source": [ "import plotly.graph_objects as go" ] }, { "cell_type": "code", "execution_count": 10, "id": "young-economy", "metadata": {}, "outputs": [ { "data": { "text/html": [ " \n", " " ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "application/vnd.plotly.v1+json": { "config": { "plotlyServerURL": "https://plot.ly" }, "data": [ { "mode": "lines", "type": "scatter3d", "x": [ 0, 0.003, 0.006, 0.009000000000000001, 0.012, 0.015, 0.018000000000000002, 0.021, 0.024, 0.027, 0.03, 0.033, 0.036000000000000004, 0.039, 0.042, 0.045, 0.048, 0.051000000000000004, 0.054, 0.057, 0.06, 0.063, 0.066, 0.069, 0.07200000000000001, 0.075, 0.078, 0.081, 0.084, 0.08700000000000001, 0.09, 0.093, 0.096, 0.099, 0.10200000000000001, 0.105, 0.108, 0.111, 0.114, 0.117, 0.12, 0.123, 0.126, 0.129, 0.132, 0.135, 0.138, 0.14100000000000001, 0.14400000000000002, 0.147, 0.15, 0.153, 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x[:, 0], label=\"rabbits\")\n", "plt.plot(x[:, 1], label=\"foxes\")\n", "plt.legend()" ] }, { "cell_type": "code", "execution_count": 12, "id": "martial-settlement", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'foxes')" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot(x[:, 0], x[:, 1])\n", "plt.xlabel(\"rabbits\")\n", "plt.ylabel(\"foxes\")" ] }, { "cell_type": "code", "execution_count": 13, "id": "practical-better", "metadata": {}, "outputs": [], "source": [ "### FROM: https://stackoverflow.com/a/27666700/3025981\n", "\n", "import matplotlib.lines as mlines\n", "import matplotlib.patches as mpatches\n", "\n", "def add_arrow_to_line2D(\n", " axes, line, arrow_locs=[0.2, 0.4, 0.6, 0.8],\n", " arrowstyle='-|>', arrowsize=1, transform=None):\n", " \"\"\"\n", " Add arrows to a matplotlib.lines.Line2D at selected locations.\n", "\n", " Parameters:\n", " -----------\n", " axes: \n", " line: Line2D object as returned by plot command\n", " arrow_locs: list of locations where to insert arrows, % of total length\n", " arrowstyle: style of the arrow\n", " arrowsize: size of the arrow\n", " transform: a matplotlib transform instance, default to data coordinates\n", "\n", " Returns:\n", " --------\n", " arrows: list of arrows\n", " \"\"\"\n", " if not isinstance(line, mlines.Line2D):\n", " raise ValueError(\"expected a matplotlib.lines.Line2D object\")\n", " x, y = line.get_xdata(), line.get_ydata()\n", "\n", " arrow_kw = {\n", " \"arrowstyle\": arrowstyle,\n", " \"mutation_scale\": 10 * arrowsize,\n", " }\n", "\n", " color = line.get_color()\n", " use_multicolor_lines = isinstance(color, np.ndarray)\n", " if use_multicolor_lines:\n", " raise NotImplementedError(\"multicolor lines not supported\")\n", " else:\n", " arrow_kw['color'] = color\n", "\n", " linewidth = line.get_linewidth()\n", " if isinstance(linewidth, np.ndarray):\n", " raise NotImplementedError(\"multiwidth lines not supported\")\n", " else:\n", " arrow_kw['linewidth'] = linewidth\n", "\n", " if transform is None:\n", " transform = axes.transData\n", "\n", " arrows = []\n", " for loc in arrow_locs:\n", " s = np.cumsum(np.sqrt(np.diff(x) ** 2 + np.diff(y) ** 2))\n", " n = np.searchsorted(s, s[-1] * loc)\n", " arrow_tail = (x[n], y[n])\n", " arrow_head = (np.mean(x[n:n + 2]), np.mean(y[n:n + 2]))\n", " p = mpatches.FancyArrowPatch(\n", " arrow_tail, arrow_head, transform=transform,\n", " **arrow_kw)\n", " axes.add_patch(p)\n", " arrows.append(p)\n", " return arrows\n", "### END FROM" ] }, { "cell_type": "code", "execution_count": 14, "id": "floral-description", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Text(0, 0.5, 'foxes')" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ax = plt.gca()\n", "line, = plt.plot(x[:, 0], x[:, 1])\n", "add_arrow_to_line2D(ax, line, arrowsize=2, arrowstyle='->')\n", "plt.xlabel(\"rabbits\")\n", "plt.ylabel(\"foxes\")" ] }, { "cell_type": "markdown", "id": "expressed-audit", "metadata": {}, "source": [ "## Домашнее задание №1\n", "### Задача 1\n", "Изучите с помощью компьютерной симуляции, как зависит ошибка метода Эйлера от длины шага $\\Delta t = (T-t_0) / N$, где $N$ — количество шагов? Возьмите уравнение с известным решением (например, $\\dot x = x$) и для какого-то фиксированного начального условия и фиксированного $T$ найдите точное решение $x(T)$ и его приближение $x_{Euler}(t; N)$ для $N$ шагов. Постройте график $|x(T) - x_{Euler}(t; N)|$ как функции от $N$ при больших $N$. Умножьте ошибку на $N$ и на $N^2$ и постройте графики получающихся функций. Возьмите логарифм ошибки и поделите его на логарифм $N$, постройте график этой функции при больших $N$. Сделайте вывод о скорости уменьшения ошибки в терминах $O$-больших или $\\Theta$ от $N$ и $\\Delta t$." ] }, { "cell_type": "markdown", "id": "grateful-salon", "metadata": {}, "source": [ "### Задача 2\n", "Модифицируйте функцию `euler_multidim` таким образом, чтобы она обрабатывала случай `T < t_0`." ] }, { "cell_type": "markdown", "id": "super-subscriber", "metadata": {}, "source": [ "### Задача 3\n", "Найдите все положения равновесия в модели Лотки — Вольтерры. Покажите, что существует единственное положение равновесия в области $x>0$, $y>0$. Изучите с помощью компьютерных экспериментов, как ведут себя решения вблизи этого положения равновесия и вдалеке от него. Является ли на ваш взгляд это положение равновесия устойчивым? Объясните, почему. В каких случаях решения похожи на решения уравнения осциллятора (близки к гармоническим колебаниям)? В каких случаях не похожи? Зависит ли период от выбора начального условия? Как вы думаете, как объясняются эти результаты?" ] }, { "cell_type": "code", "execution_count": null, "id": "expensive-macedonia", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "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": "3.6.10" } }, "nbformat": 4, "nbformat_minor": 5 }