Skip to content

Instantly share code, notes, and snippets.

@ryoppippi
Last active May 29, 2017 08:43
Show Gist options
  • Save ryoppippi/f451bb0e9a5ff39da6d7bb45a645f2d0 to your computer and use it in GitHub Desktop.
Save ryoppippi/f451bb0e9a5ff39da6d7bb45a645f2d0 to your computer and use it in GitHub Desktop.
Lecture8-1.ipynb
Display the source blob
Display the rendered blob
Raw
{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "Solve the following initial value problem over the interval from t=0 to 2, where y(0)=1. Output the values y(2). Optionally, display all your results on the same graph.\n\ndy/dt=yt3-1.5y\n\nusing\n\n(a) Euler's method with h=0.5 and h=0.25\n\n(b) Midpoint method with h=0.5\n\n(c) Fourth-order RK method with h=0.5."
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "import matplotlib.pyplot as plt\nimport numpy as np\ndef f_d(t, y):\n return y*t*t*t-1.5*y",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "def euler(h):\n t = [0.0]\n y = [1.0]\n while t[-1] < 2:\n y.append(h*f_d(t[-1], y[-1]) + y[-1])\n t.append(t[-1]+h)\n return (t, y)",
"execution_count": 2,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t1, y1 = euler(0.5)\nt2, y2 = euler(0.25)\nt3, y3 = euler(0.000001)\nprint(y1[-1])\nprint(y2[-1])\nplt.plot(t1,y1,\"b\")\nplt.plot(t2,y2,\"g\")\nplt.plot(t3,y3,\"y\")\nplt.text(2, y1[-1], '0.5', ha = 'center') \nplt.text(2, y2[-1], '0.25', ha = 'center')\nplt.text(2, y2[-1], '0.000001', ha = 'center') \nplt.show()",
"execution_count": 3,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "0.113525390625\n0.529694828397087\n"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAD8CAYAAAB0IB+mAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAAAElFTkSuQmCC\n",
"text/plain": "<matplotlib.figure.Figure at 0x10d0c1588>"
},
"metadata": {},
"output_type": "display_data"
}
]
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "def midpoint(h):\n t = [0.0]\n y = [1.0]\n while t[-1] < 2:\n y.append(h*f_d(t[-1]+h/2, y[-1]+f_d(t[-1], y[-1])*h/2) + y[-1])\n t.append(t[-1]+h)\n return (t, y)",
"execution_count": 4,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t4, y4 = midpoint(0.5)\nprint(y4[-1])\nplt.plot(t4, y4)\nplt.show()",
"execution_count": 5,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "1.591801757973883\n"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nyl1EJAap3EVEYpDKXUQkBqncRURi0P8Hfi//0SIZIQEAAAAASUVORK5CYII=\n",
"text/plain": "<matplotlib.figure.Figure at 0x112bec9e8>"
},
"metadata": {},
"output_type": "display_data"
}
]
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "def RK_forth(h):\n t = [0.0]\n y = [1.0]\n while t[-1] < 2:\n k1 = h*f_d(t[-1], y[-1])\n k2 = h*f_d(t[-1]+h/2, y[-1] + k1/2)\n k3 = h*f_d(t[-1]+h/2, y[-1] + k2/2)\n k4 = h*f_d(t[-1]+h, y[-1] + k3)\n y.append(y[-1] + k1/6 + k2/3 + k3/3 + k4/6)\n t.append(t[-1]+h)\n return (t, y)",
"execution_count": 6,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "t5, y5 = RK_forth(0.5)\nprint(y5[-1])\nplt.plot(t5,y5)\nplt.show()",
"execution_count": 7,
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": "2.5130724732170258\n"
},
{
"data": {
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAD8CAYAAACMwORRAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nAAAASUVORK5CYII=\n",
"text/plain": "<matplotlib.figure.Figure at 0x11e94e198>"
},
"metadata": {},
"output_type": "display_data"
}
]
}
],
"metadata": {
"kernelspec": {
"name": "python3",
"display_name": "Python 3",
"language": "python"
},
"language_info": {
"name": "python",
"version": "3.6.0",
"mimetype": "text/x-python",
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"pygments_lexer": "ipython3",
"nbconvert_exporter": "python",
"file_extension": ".py"
},
"toc": {
"threshold": 4,
"number_sections": true,
"toc_cell": false,
"toc_window_display": false,
"toc_section_display": "block",
"sideBar": true,
"navigate_menu": true,
"moveMenuLeft": true,
"widenNotebook": false,
"colors": {
"hover_highlight": "#DAA520",
"selected_highlight": "#FFD700",
"running_highlight": "#FF0000"
},
"nav_menu": {
"height": "12px",
"width": "252px"
}
},
"varInspector": {
"window_display": true,
"cols": {
"lenName": 16,
"lenType": 16,
"lenVar": 40
},
"kernels_config": {
"python": {
"library": "var_list.py",
"delete_cmd_prefix": "del ",
"delete_cmd_postfix": "",
"varRefreshCmd": "print(var_dic_list())"
},
"r": {
"library": "var_list.r",
"delete_cmd_prefix": "rm(",
"delete_cmd_postfix": ") ",
"varRefreshCmd": "cat(var_dic_list()) "
}
},
"types_to_exclude": [
"module",
"function",
"builtin_function_or_method",
"instance",
"_Feature"
]
},
"gist": {
"id": "",
"data": {
"description": "Lecture8-1.ipynb",
"public": true
}
}
},
"nbformat": 4,
"nbformat_minor": 2
}
Sign up for free to join this conversation on GitHub. Already have an account? Sign in to comment