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@nmayorov
Created January 21, 2018 12:02
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Interpolation errors of ODE solvers
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"from scipy.integrate import solve_ivp"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"import numpy as np"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def fun_sin(t, y):\n",
" return np.array([y[1], -y[0]])"
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"def sol_sin(t):\n",
" return np.vstack((np.sin(t), np.cos(t)))"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {
"collapsed": false
},
"outputs": [],
"source": [
"res = solve_ivp(fun_sin, [0, 4 * np.pi], [0, 1], dense_output=True)"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"t_test = np.linspace(0, 4 * np.pi, 100)"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.text.Text at 0x10e763400>"
]
},
"execution_count": 9,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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1XXD2+5AYa0RhplXucBTp8mDd8sdsIUc0ZZgs05jsP9cFe58HVosBxTmJcoej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\nERGRB/8fKHaqlBjxbCEAAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x103aaa128>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t_test, res.sol(t_test)[0])\n",
"plt.xlabel('t')\n",
"plt.ylabel('y1')"
]
},
{
"cell_type": "code",
"execution_count": 10,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"error = res.sol(t_test) - sol_sin(t_test)"
]
},
{
"cell_type": "code",
"execution_count": 11,
"metadata": {
"collapsed": true
},
"outputs": [],
"source": [
"error_points = res.y - sol_sin(res.t)"
]
},
{
"cell_type": "code",
"execution_count": 12,
"metadata": {
"collapsed": false
},
"outputs": [
{
"data": {
"text/plain": [
"<matplotlib.legend.Legend at 0x10efec080>"
]
},
"execution_count": 12,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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aXJHnUKAWERERuQLX/tM1vH8a4If9GRgGtKl7PwALfl6Aw3CYXJVnUKAWERER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VpHFD2Ts9XkQp1+Kp29J/ditVjp2qirqVnMdveIU2BzgtOGr6+hMl0NWYzq9juRSXJycggODsbh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\nIiIiUgYq1CIiIiIiZaBCLSIiIiJSBv8Pq9zNf9SJnz0AAAAASUVORK5CYII=\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x10b436198>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(t_test, error[0], label='y1')\n",
"plt.plot(res.t, error_points[0], 'bx')\n",
"plt.plot(t_test, error[1], 'g', label='y2')\n",
"plt.plot(res.t, error_points[1], 'gx')\n",
"plt.xlabel('t')\n",
"plt.ylabel('error')\n",
"plt.legend()"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {
"collapsed": true
},
"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": "3.6.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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