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@ryoppippi
Created May 29, 2017 10:33
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Lecture8-2
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{
"cells": [
{
"metadata": {},
"cell_type": "markdown",
"source": "Solve the following problem with the fourth-order Runge-Kutta method:\n\ny''+0.5y'+7y=0\n\nwith y(0)=4 and y'(0)=0. Solve from x=0 to 5 with h=0.5. Plot your results.\n\n\nIt can be transformed that\ny'' = -0.5y'-7y\nTherefore,"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "import matplotlib.pyplot as plt\nimport numpy as np\ndef y_d_vector(x, u):\n return np.array([-0.5*u[0]-7*u[1], u[0]])",
"execution_count": 1,
"outputs": []
},
{
"metadata": {
"collapsed": true,
"trusted": true
},
"cell_type": "code",
"source": "def solution(h, tbegin, tend, y0, y_0, f):\n y = np.array([[y_0, y0]])\n x = [tbegin]\n yy = [y0]\n while x[-1] < tend:\n k1 = h*f(x[-1], y[-1])\n k2 = h*f(x[-1]+h/2, y[-1] + k1/2)\n k3 = h*f(x[-1]+h/2, y[-1] + k2/2)\n k4 = h*f(x[-1]+h, y[-1] + k3)\n y0 = y[-1] + k1/6 + k2/3 + k3/3 + k4/6\n y = np.vstack((y,y0))\n yy.append(y0[1])\n x.append(x[-1]+h)\n return (x, yy)",
"execution_count": 2,
"outputs": []
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "x, y = solution(0.5, 0, 5, 4, 0,y_d_vector)\nprint(y[-1])\nplt.plot(x,y)\nplt.show()",
"execution_count": 3,
"outputs": [
{
"output_type": "stream",
"text": "0.909684093525\n",
"name": "stdout"
},
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x10feac4a8>",
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NA/Mn8vDCdKPjXNFCm5V756bx8/dPcqxB9vIXnmf8rJOPWWSzYndo9la3Gh3Fb5Sca+er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\nCJORYhdCCJORYhdCCJP5/3c39Le0o9wFAAAAAElFTkSuQmCC\n"
},
"metadata": {}
}
]
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "x, y = solution(0.001, 0, 50, 4, 0, y_d_vector)\nplt.plot(x,y)\nplt.show()",
"execution_count": 4,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x1131e2358>",
"image/png": 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OljqsbU/gcH8SZ3c0ulpPnYhoNtRase8E8AEAj3kwltNWbrpjutRjL396sbCB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\ngg==\n"
},
"metadata": {}
}
]
},
{
"metadata": {},
"cell_type": "markdown",
"source": "減衰振動だ!"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "この式は、抵抗力を含む単振動の式と見ることができる。"
},
{
"metadata": {},
"cell_type": "markdown",
"source": "では、抵抗力の大きさを反対に、すなわちどんどん振動が大きくなるようにしてみると"
},
{
"metadata": {
"trusted": true
},
"cell_type": "code",
"source": "def y_d_vector2(x, u):\n return np.array([0.5*u[0]-7*u[1], u[0]])\n\nx, y = solution(0.001, 0, 50, 4, 0, y_d_vector2)\nplt.plot(x,y)\nplt.show()",
"execution_count": 5,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": "<matplotlib.figure.Figure at 0x1132fbf60>",
"image/png": 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},
"metadata": {}
}
]
}
],
"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": "be410853adbcefb61f66157aacea5d07",
"data": {
"description": "Lecture8-2",
"public": true
}
},
"_draft": {
"nbviewer_url": "https://gist.github.com/be410853adbcefb61f66157aacea5d07"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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