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@ischurov
Created November 2, 2020 10:10
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euler.ipynb
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{
"cells": [
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "import numpy as np",
"execution_count": 1,
"outputs": []
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Рассмотрим уравнение\n\n$$\\dot{\\mathbf{x}}= \\mathbf F(t, \\mathbf{x}), \\quad \\mathbf{x}(t) \\in \\mathbb R^n,\\quad \\mathbf F\\colon \\mathbb R\\times \\mathbb R^n \\to \\mathbb R^n$$"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Пример: модель Лотки — Вольтерра.\n\n$x$ — кролики, $y$ — лисы.\n\n$$\\dot x = \\alpha x - \\beta x y,\\quad \\dot y = -\\gamma y + \\delta x y$$"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def rhs(t, X): # X = (x, y)\n x, y = X\n # x = X[0]; y = X[1]\n # пусть 𝛼 = 𝛽 = 𝛾 = 𝛿 = 1\n return np.array([x - x * y, -y + x * y])",
"execution_count": 81,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "rhs(2, np.array([0.3, 0.4]))",
"execution_count": 82,
"outputs": [
{
"data": {
"text/plain": "array([ 0.18, -0.28])"
},
"execution_count": 82,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Решаем задачу Коши:\n\nНачальное условие:\n\n$$\\mathbf{x}(t_0)=\\mathbf{x}_0$$\n\nЭйлеровские приближения:\n\n$$\\mathbf{x}_{n+1}=\\mathbf{x}_n + \\Delta t \\cdot {\\mathbf F}(t_{n}, \\mathbf{x}_n),$$\n$$t_{n+1}=t_n + \\Delta t,$$\n$$\\Delta t = (T-t_0) / n$$"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Реализация\nДля дальнейшего нам понадобятся некоторые факты о питоне и функциях из `numpy`.\n\nФункция `np.linspace(a, b, steps, retstep=True)` возвращает массив точек из `steps` точек, разбивая отрезок $[a, b]$ на несколько (`steps-1`) равных частей, `retstep=True` показывает, что нужно возвращать также длину части (шаг)."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "np.linspace(-1, 2, 5, retstep=True)",
"execution_count": 79,
"outputs": [
{
"data": {
"text/plain": "(array([-1. , -0.25, 0.5 , 1.25, 2. ]), 0.75)"
},
"execution_count": 79,
"metadata": {},
"output_type": "execute_result"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "циклы в питоне работают так:"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "for a in [1, 2, 15, 3]:\n print(f\"a = {a}\")",
"execution_count": 80,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "a = 1\na = 2\na = 15\na = 3\n"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Теперь можно приступать к реализации"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def euler(rhs, t0, X0, T, n):\n t, DeltaT = np.linspace(t0, T, n + 1, retstep=True)\n # получили массив моментов времени\n # мы хотим сделать n шагов, значит\n # нужно получить n + 1 точку, \n # первая равна t0\n # последняя совпадает с T\n \n X = [X0]\n # X — это список, в который мы будем записывать найденные x_n\n # с самого начала запишем в него первый элемент (начальное условие)\n \n X_cur = X0\n # значение X в текущий момент времени\n for t_cur in t[:-1]: \n # t[:-1] — все элементы массива t, кроме последнего\n # последний момент времени равен T, но в этот момент\n # ничего считать уже не надо, поэтому мы его выкинем\n \n X_cur = X_cur + DeltaT * rhs(t_cur, X_cur)\n X.append(X_cur)\n # добавить X_cur в список X\n \n # вернём пару — массив моментов времени и массив значений x_n\n return t, np.array(X)",
"execution_count": 83,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def X_rhs(t, X):\n return X",
"execution_count": 47,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "import matplotlib.pyplot as plt\n%matplotlib inline",
"execution_count": 48,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.plot([1, 2, 5], [2, 3, 1], 'o-')\n# рисование картинок",
"execution_count": 84,
"outputs": [
{
"data": {
"text/plain": "[<matplotlib.lines.Line2D at 0x7fdc596c09b0>]"
},
"execution_count": 84,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "for n in [3, 10, 100]:\n t, X = euler(X_rhs, t0=0, X0=1, T=1, n=n)\n plt.plot(t, X, 'x-')\n # 'x-' означает, что точки нужно рисовать крестиками и соединять линиями\nplt.plot(t, np.exp(t))",
"execution_count": 85,
"outputs": [
{
"data": {
"text/plain": "[<matplotlib.lines.Line2D at 0x7fdc5951c160>]"
},
"execution_count": 85,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def X_sq_rhs(t, X):\n return X ** 2",
"execution_count": 49,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "for n in [3, 10, 100, 1000]:\n t, X = euler(X_sq_rhs, t0=0, X0=1, T=0.95, n=n)\n plt.plot(t, X, 'x-')\nplt.plot(t, 1 / (1 - t))",
"execution_count": 59,
"outputs": [
{
"data": {
"text/plain": "[<matplotlib.lines.Line2D at 0x7fdc81535c50>]"
},
"execution_count": 59,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "for n in [3, 10, 100]:\n t, X = euler(X_sq_rhs, t0=0, X0=1, T=1.2, n=n)\n plt.plot(t, X, 'x-')\nplt.plot(t, 1 / (1 - t))",
"execution_count": 86,
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": "/Users/user/miniconda3/envs/featurevis-py3.6/lib/python3.6/site-packages/ipykernel_launcher.py:2: RuntimeWarning: overflow encountered in double_scalars\n \n"
},
{
"data": {
"text/plain": "[<matplotlib.lines.Line2D at 0x7fdc5954feb8>]"
},
"execution_count": 86,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "что-то пошло не так: мы попытались с помощью метода Эйлера посчитать значение решения в точках, где оно не определено; решение ушло на бесконечность (при маленьком шаге это приводит к переполнениям)."
},
{
"metadata": {},
"cell_type": "markdown",
"source": "### Решение уравнения Лотки — Волтерра"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t, X = euler(rhs, X0=np.array([0.1, 0.4]), t0=0, T=50, n=100000)\n",
"execution_count": 87,
"outputs": [
{
"data": {
"text/plain": "Text(0, 0.5, 'лисы')"
},
"execution_count": 87,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "Решения являются функцией $\\mathbb R \\to \\mathbb R^2$, её график лежит в трёхмерном пространстве. Как правило, для автономных уравнений (правая часть не зависит от $t$) достаточно представлять себе картинку в фазовом пространстве (в данном случае, $\\mathbb R^2$)."
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.plot(X[:, 0], X[:, 1])\nplt.xlabel(\"кролики\")\nplt.ylabel(\"лисы\")",
"execution_count": 89,
"outputs": [
{
"data": {
"text/plain": "Text(0, 0.5, 'лисы')"
},
"execution_count": 89,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "plt.plot(t, X[:, 0], label='кролики')\nplt.plot(t, X[:, 1], label='лисы')\nplt.legend()",
"execution_count": 102,
"outputs": [
{
"data": {
"text/plain": "<matplotlib.legend.Legend at 0x7fdc5ebf7d68>"
},
"execution_count": 102,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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\n",
"text/plain": "<Figure size 432x288 with 1 Axes>"
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
]
}
],
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3",
"language": "python"
},
"language_info": {
"name": "python",
"version": "3.6.10",
"mimetype": "text/x-python",
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"gist": {
"id": "",
"data": {
"description": "euler.ipynb",
"public": false
}
}
},
"nbformat": 4,
"nbformat_minor": 4
}
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