Skip to content

Instantly share code, notes, and snippets.

@PavelEprines
Created April 23, 2019 19:41
Show Gist options
  • Save PavelEprines/965b198de24b2ee35b4da25c9baf350a to your computer and use it in GitHub Desktop.
Save PavelEprines/965b198de24b2ee35b4da25c9baf350a to your computer and use it in GitHub Desktop.
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"# try to solve x'' + 1000x + x^3 = 0"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"n = 10000\n",
"h = 1/n"
]
},
{
"cell_type": "code",
"execution_count": 99,
"metadata": {},
"outputs": [],
"source": [
"x = np.zeros(n)\n",
"t = np.linspace(0, 10, n)\n",
"u = np.zeros(n)\n",
"x[0]=1\n",
"u[0]=0\n",
"E = np.zeros(n)"
]
},
{
"cell_type": "code",
"execution_count": 57,
"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": [
"for i in range(n -1): # метод эйлера\n",
" x[i+1] = x[i] + h*u[i]\n",
" u[i+1] = u[i] - x[i + 1]**3 - x[i + 1]\n",
"plt.plot(t,x)\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 140,
"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": [
"x1 = np.zeros(n)\n",
"t1 = np.linspace(0, 10, n)\n",
"u1 = np.zeros(n)\n",
"x1[0]=1\n",
"u1[0]=0\n",
"for i in range(n -1):\n",
" u1[i+1] = u1[i] - (x1[i]**3 + 1000*x1[i])*h\n",
" x1[i+1] = x1[i] + h*u1[i+1]\n",
"plt.plot(t1,x1)\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 143,
"metadata": {},
"outputs": [],
"source": [
"for i in range(n - 1):\n",
" E[i] = (u1[i])**2 +1000*x1[i]**2 + x1[i]**2/2"
]
},
{
"cell_type": "code",
"execution_count": 145,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f4aa8e39cf8>]"
]
},
"execution_count": 145,
"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"
}
],
"source": [
"plt.plot(t1[:-1], E[:-1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Незначительные рсциляции энергии"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"## Рунге-Кутта "
]
},
{
"cell_type": "code",
"execution_count": 146,
"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": [
"x2 = np.zeros(n)\n",
"t2 = np.linspace(0, 10, n)\n",
"u2 = np.zeros(n)\n",
"x2[0]=1\n",
"u2[0]=0\n",
"for i in range(n -1):\n",
" w = u2[i] - h*0.5*(x2[i +1]**3 + 1000*x2[i+1])\n",
" q = x2[i] + h*0.5*u2[i]\n",
" u2[i+1] = u2[i] - (1000*q + q**3)*h\n",
" x2[i+1] = x2[i]+ h*w\n",
" \n",
" \n",
"plt.plot(t2,x2)\n",
"plt.grid()\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 148,
"metadata": {},
"outputs": [],
"source": [
"E2 = np.zeros(n)"
]
},
{
"cell_type": "code",
"execution_count": 149,
"metadata": {},
"outputs": [],
"source": [
"for i in range(n - 1):\n",
" E2[i] = (u2[i])**2 +1000*x2[i]**2 + x2[i]**2/2"
]
},
{
"cell_type": "code",
"execution_count": 151,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f4aa92d87f0>]"
]
},
"execution_count": 151,
"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"
}
],
"source": [
"plt.plot(t2[:-1], E2[:-1])"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Расходится немного, печалька "
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment