Solving a hard BVP with continuation

problem7.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from scipy.integrate import solve_bvp"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mu = 1e-2\n",
    "eps = 1e-2\n",
    "gamma = 1.1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def fun(x, y, eps, mu):\n",
    "    return np.vstack((\n",
    "        y[2],\n",
    "        y[3],\n",
    "        mu / eps**4 * (y[0] - y[1] + y[0] * y[1] - gamma * (1 - 0.5 * x**2)),\n",
    "        y[0] / mu * (1 - 0.5 * y[0])\n",
    "    ))\n",
    "\n",
    "def bc(ya, yb):\n",
    "    return np.array([ya[2], ya[3], yb[0], 0.7 * yb[1] + yb[3] + 0.7])\n",
    "\n",
    "S = np.array([\n",
    "    [0, 0, 0, 0],\n",
    "    [0, 0, 0, 0],\n",
    "    [0, 0, -3, 0],\n",
    "    [0, 0, 0, -3]\n",
    "])\n",
    "\n",
    "x = np.linspace(0, 1, 10)\n",
    "y = np.zeros((4, x.size))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Iteration    Max residual    Total nodes    Nodes added  \n",
      "       1          4.07e+00          10             14       \n",
      "       2          9.38e-03          24              9       \n",
      "       3          1.59e-03          33              3       \n",
      "       4          9.56e-04          36              0       \n",
      "Solved in 4 iterations, number of nodes 36, maximum relative residual 9.56e-04.\n"
     ]
    }
   ],
   "source": [
    "fun_1 = lambda x, y: fun(x, y, 1e-1, 1e-1)\n",
    "res_1 = solve_bvp(fun_1, bc, x, y, S=S, verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x107e5c860>]"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nREqYkoCISAlTEhARKWH/D4PBd8aa2aExAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107b80828>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res_1.x, res_1.y[0] * res_1.x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Iteration    Max residual    Total nodes    Nodes added  \n",
      "       1          3.71e-02          36             19       \n",
      "       2          8.36e-03          55             19       \n",
      "       3          2.71e-03          74              1       \n",
      "       4          9.38e-04          75              0       \n",
      "Solved in 4 iterations, number of nodes 75, maximum relative residual 9.38e-04.\n"
     ]
    }
   ],
   "source": [
    "fun_2 = lambda x, y: fun(x, y, 0.5e-1, 0.5e-1)\n",
    "res_2 = solve_bvp(fun_2, bc, res_1.x, res_1.y, S=S, verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x107cb24e0>]"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107e78320>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res_2.x, res_2.x * res_2.y[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Iteration    Max residual    Total nodes    Nodes added  \n",
      "       1          1.88e+01          75             94       \n",
      "       2          3.22e-01          169            37       \n",
      "       3          4.67e-02          206            21       \n",
      "       4          2.68e-03          227             4       \n",
      "       5          9.71e-04          231             0       \n",
      "Solved in 5 iterations, number of nodes 231, maximum relative residual 9.71e-04.\n"
     ]
    }
   ],
   "source": [
    "fun_3 = lambda x, y: fun(x, y, 1e-2, 1e-2)\n",
    "res_3 = solve_bvp(fun_3, bc, res_2.x, res_2.y, S=S, verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10770bb00>]"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nEZEUUwiIiKSYQkBEJMX+DyBbsvr2g4oJAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107e91e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res_3.x, res_3.x * res_3.y[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Iteration    Max residual    Total nodes    Nodes added  \n",
      "       1          4.94e-02          231            52       \n",
      "       2          2.79e-02          283            24       \n",
      "       3          3.42e-03          307             2       \n",
      "       4          9.87e-04          309             0       \n",
      "Solved in 4 iterations, number of nodes 309, maximum relative residual 9.87e-04.\n"
     ]
    }
   ],
   "source": [
    "fun_4 = lambda x, y: fun(x, y, 0.5e-2, 0.5e-2)\n",
    "res_4 = solve_bvp(fun_4, bc, res_3.x, res_3.y, S=S, verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x10776f2e8>]"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nA9t9Exm/rnr8AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x107cea400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res_4.x, res_4.x * res_4.y[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Iteration    Max residual    Total nodes    Nodes added  \n",
      "       1          5.20e-01          309            125      \n",
      "       2          8.65e-02          434            62       \n",
      "       3          4.93e-02          496            40       \n",
      "       4          2.00e-03          536             9       \n",
      "       5          1.61e-03          545             3       \n",
      "       6          1.28e-03          548             1       \n",
      "       7          1.10e-03          549             1       \n",
      "       8          9.87e-04          550             0       \n",
      "Solved in 8 iterations, number of nodes 550, maximum relative residual 9.87e-04.\n"
     ]
    }
   ],
   "source": [
    "fun_5 = lambda x, y: fun(x, y, 1e-3, 1e-3)\n",
    "res_5 = solve_bvp(fun_5, bc, res_4.x, res_4.y, S=S, verbose=2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x107eaac18>]"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYEAAAEACAYAAABVtcpZAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1077359e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(res_5.x, res_5.x * res_5.y[0])"
   ]
  },
  {
   "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": "3.4.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}