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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Wave equation\n",
      "==\n",
      "\n",
      "We are seeking the solution for equation\n",
      "$$\\frac{\\partial^2 u}{\\partial t^2} = c^2\\frac{\\partial^2 u}{\\partial x^2}$$"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline\n",
      "from pylab import *\n",
      "from numpy import *"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#dimensions of the computational domain:\n",
      "maxx = 10.\n",
      "maxt = 40.\n",
      "\n",
      "#wave velocity\n",
      "v = 0.5"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We discretize the simulation domain:\n",
      "$$t_n = t_0 + n\\Delta t$$\n",
      "$$x_i = x_0 + i\\Delta x$$\n",
      "and seek for the numerical approximation $U^n_i$ to the actual solution $U(t_n, x_i)$ on the grid points"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#discretization parameters\n",
      "nx = 100   # number of unknown grid points in spatial direction\n",
      "CFL = 1.0  # Courant Friedrichs Lewy (CFL) condition v*dt/dx\n",
      "\n",
      "def wave_init(maxx, maxt, v, nx, CFL):\n",
      "    #choose time step according to CFL condition\n",
      "    dx = maxx/(nx+1)\n",
      "    dt = CFL*dx/v\n",
      "    nt = int(maxt/dt)+1\n",
      "    \n",
      "    #define array for storing the solution\n",
      "    U = zeros((nt, nx+2))\n",
      "    \n",
      "    x = arange(nx+2)*dx\n",
      "    t = arange(nt)*dt\n",
      "    return U, dx, dt, x, t"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We may replace the derivatives in wave equation by second differences in the following way\n",
      "$$\\frac{U^{n-1}_i - 2U^n_i + U^{n+1}_i}{\\Delta t^2} = c^2\\frac{U^n_{i-1} - 2U^n_i + U^n_{i+1}}{\\Delta x^2}$$\n",
      "to obtain explicit equation for propagation in time:\n",
      "$$U^{n+1}_i = 2U^n_i - U^{n-1}_i + \\frac{c^2\\Delta t^2}{\\Delta x^2} (U^n_{i-1} - 2U^n_i + U^n_{i+1}).$$\n",
      "We define a function for propagating the solution over the array U, assuming that U[0:2, xint] is the initial condition and U[:,[0,-1]] are the boundary conditions."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def wave_solve(U, dx, dt, nx, nt):\n",
      "    xint = arange(1, nx+1)\n",
      "    for it in range(1,nt-1):\n",
      "        d2x = U[it, xint-1] - 2*U[it, xint] + U[it, xint+1]\n",
      "        U[it+1,xint] = 2*U[it,xint] - U[it-1, xint] + d2x/dx**2*dt**2*v**2"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL*1)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# use gaussian pulse as initial condition\n",
      "U0 = exp(-(x-maxx/3)**2/2.)*2\n",
      "U[0,:] = U0\n",
      "U[1,:] = U0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "wave_solve(U, dx, dt, nx, len(t))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "<matplotlib.collections.QuadMesh at 0x7f27c0bcd278>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
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Gaf0tYVr/iBhzdOPzIkcekQaEHII/EOLT9e2Tk5gODmgwuE2W/23Ke0D1ozWg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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f27c1481710>"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "What happens if the CFL condition is violated by a small relative amount, say $10^{-3}$?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "CFL = 1.001\n",
      "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL)\n",
      "U0 = exp(-(x-maxx/3)**2/2.)*2\n",
      "U[0,:] = U0\n",
      "U[1,:] = U0\n",
      "wave_solve(U, dx, dt, nx, len(t))\n",
      "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "<matplotlib.collections.QuadMesh at 0x7f27c0b78f98>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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9yXvOZ0Ya/p5TIE+mTRFnQpJt3l8m5uw+9cFy9LXhEoe/7VxZlruA/4MpgcnU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\nfRAEQQcQYR8EQdAB/Avnn+om2CTNgAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f27c0c26d30>"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The unstable high-frequency oscillations quickly grow larger that the solution of interest "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We may also animate the solution. Let us first recalculate with correct CFL condition:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "CFL = 1.\n",
      "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL)\n",
      "U0 = exp(-(x-maxx/3)**2/2.)*2\n",
      "U[0,:] = U0\n",
      "U[1,:] = U0\n",
      "wave_solve(U, dx, dt, nx, len(t))\n",
      "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "<matplotlib.collections.QuadMesh at 0x7f27c0ae1f28>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Gaf0tYVr/iBhzdOPzIkcekQaEHII/EOLT9e2Tk5gODmgwuE2W/23Ke0D1ozWg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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f27c0b4aeb8>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#let's take every 10th frame into animation\n",
      "Un = U[:-10:10,:]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from matplotlib import animation\n",
      "from JSAnimation.IPython_display import display_animation"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig = figure();\n",
      "ax = axes(xlim=(0,maxx),ylim=(-3,3));\n",
      "line, = ax.plot([],[],lw=2);\n",
      "\n",
      "def animate(data):\n",
      "    line.set_data(x,data)\n",
      "    return line,\n",
      "\n",
      "anim = animation.FuncAnimation(fig, animate, frames=Un, interval=100)\n",
      "display_animation(anim, default_mode='loop')"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Define the Animation class */\n",
        "  function Animation(frames, img_id, slider_id, interval, loop_select_id){\n",
        "    this.img_id = img_id;\n",
        "    this.slider_id = slider_id;\n",
        "    this.loop_select_id = loop_select_id;\n",
        "    this.interval = interval;\n",
        "    this.current_frame = 0;\n",
        "    this.direction = 0;\n",
        "    this.timer = null;\n",
        "    this.frames = new Array(frames.length);\n",
        "\n",
        "    for (var i=0; i<frames.length; i++)\n",
        "    {\n",
        "     this.frames[i] = new Image();\n",
        "     this.frames[i].src = frames[i];\n",
        "    }\n",
        "    document.getElementById(this.slider_id).max = this.frames.length - 1;\n",
        "    this.set_frame(this.current_frame);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.get_loop_state = function(){\n",
        "    var button_group = document[this.loop_select_id].state;\n",
        "    for (var i = 0; i < button_group.length; i++) {\n",
        "        var button = button_group[i];\n",
        "        if (button.checked) {\n",
        "            return button.value;\n",
        "        }\n",
        "    }\n",
        "    return undefined;\n",
        "  }\n",
        "\n",
        "  Animation.prototype.set_frame = function(frame){\n",
        "    this.current_frame = frame;\n",
        "    document.getElementById(this.img_id).src = this.frames[this.current_frame].src;\n",
        "    document.getElementById(this.slider_id).value = this.current_frame;\n",
        "  }\n",
        "\n",
        "  Animation.prototype.next_frame = function()\n",
        "  {\n",
        "    this.set_frame(Math.min(this.frames.length - 1, this.current_frame + 1));\n",
        "  }\n",
        "\n",
        "  Animation.prototype.previous_frame = function()\n",
        "  {\n",
        "    this.set_frame(Math.max(0, this.current_frame - 1));\n",
        "  }\n",
        "\n",
        "  Animation.prototype.first_frame = function()\n",
        "  {\n",
        "    this.set_frame(0);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.last_frame = function()\n",
        "  {\n",
        "    this.set_frame(this.frames.length - 1);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.slower = function()\n",
        "  {\n",
        "    this.interval /= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
        "  }\n",
        "\n",
        "  Animation.prototype.faster = function()\n",
        "  {\n",
        "    this.interval *= 0.7;\n",
        "    if(this.direction > 0){this.play_animation();}\n",
        "    else if(this.direction < 0){this.reverse_animation();}\n",
        "  }\n",
        "\n",
        "  Animation.prototype.anim_step_forward = function()\n",
        "  {\n",
        "    this.current_frame += 1;\n",
        "    if(this.current_frame < this.frames.length){\n",
        "      this.set_frame(this.current_frame);\n",
        "    }else{\n",
        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.first_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.last_frame();\n",
        "        this.reverse_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.last_frame();\n",
        "      }\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.anim_step_reverse = function()\n",
        "  {\n",
        "    this.current_frame -= 1;\n",
        "    if(this.current_frame >= 0){\n",
        "      this.set_frame(this.current_frame);\n",
        "    }else{\n",
        "      var loop_state = this.get_loop_state();\n",
        "      if(loop_state == \"loop\"){\n",
        "        this.last_frame();\n",
        "      }else if(loop_state == \"reflect\"){\n",
        "        this.first_frame();\n",
        "        this.play_animation();\n",
        "      }else{\n",
        "        this.pause_animation();\n",
        "        this.first_frame();\n",
        "      }\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.pause_animation = function()\n",
        "  {\n",
        "    this.direction = 0;\n",
        "    if (this.timer){\n",
        "      clearInterval(this.timer);\n",
        "      this.timer = null;\n",
        "    }\n",
        "  }\n",
        "\n",
        "  Animation.prototype.play_animation = function()\n",
        "  {\n",
        "    this.pause_animation();\n",
        "    this.direction = 1;\n",
        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_forward();}, this.interval);\n",
        "  }\n",
        "\n",
        "  Animation.prototype.reverse_animation = function()\n",
        "  {\n",
        "    this.pause_animation();\n",
        "    this.direction = -1;\n",
        "    var t = this;\n",
        "    if (!this.timer) this.timer = setInterval(function(){t.anim_step_reverse();}, this.interval);\n",
        "  }\n",
        "</script>\n",
        "\n",
        "<div class=\"animation\" align=\"center\">\n",
        "    <img id=\"_anim_imgQWCWSTYSPQEEBVYZ\">\n",
        "    <br>\n",
        "    <input id=\"_anim_sliderQWCWSTYSPQEEBVYZ\" type=\"range\" style=\"width:350px\" name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\" onchange=\"animQWCWSTYSPQEEBVYZ.set_frame(parseInt(this.value));\"></input>\n",
        "    <br>\n",
        "    <button onclick=\"animQWCWSTYSPQEEBVYZ.slower()\">&#8211;</button>\n",
        "    <button onclick=\"animQWCWSTYSPQEEBVYZ.first_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,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\"></button>\n",
        "    <button onclick=\"animQWCWSTYSPQEEBVYZ.previous_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAgyTCyQ6wAAANRJREFUKM9jYBjO4AiUfgzFGGAp4+yayUvX6jMwMDCsYmBgOCS4OAOrSYmMgcc8/pd5Q3irC+Neh/1AlmeBMVgZmP8yMLD8/c/cqv9r90whzv/MX7Eq/MfAwMDIwCuZdfSV8U8WDgZGRmYGrAoZGRgY/jO8b3sj/J2F6T8j4z80pzEhmIwMjAxsSbqqlkeZGP//Z8SlkJnhPwMjwx/Guoe1NhmRwk+YGH5jV8jOwMPHzcDBysAwh8FrxQwtPU99HrwBXsnAwMDAsJiBgYGBoZ1xmKYqALHhMpn1o7igAAAAAElFTkSuQmCC\"></button>\n",
        "    <button onclick=\"animQWCWSTYSPQEEBVYZ.reverse_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,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\"></button>\n",
        "    <button onclick=\"animQWCWSTYSPQEEBVYZ.pause_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAkR91DQ2AAAAKtJREFUKM9jYCANTEVib2K4jcRbzQihGWEC00JuNjN8Z2Q0Zo3VYWA4lL005venH9+c3ZK5IfIsMIXMBtc12Bj+MMgxMDAwMPzWe2TBzPCf4SLcZCYY4/9/RgZGBiaYFf8gljFhKiQERhUOeoX/Gf8y/GX4y/APmlj+Mfxj+MfwH64Qnnq0zr9fyfLrPzP3eQYGBobvk5x4GX4xMIij23gdib0cRWYHiVmAAQDK5ircshCbHQAAAABJRU5ErkJggg==\"></button>\n",
        "    <button onclick=\"animQWCWSTYSPQEEBVYZ.play_animation()\"><img class=\"anim_icon\" src=\"data:image/png;base64,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\"></button>\n",
        "    <button onclick=\"animQWCWSTYSPQEEBVYZ.next_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABQAAAAUCAQAAAAngNWGAAAAAXNSR0IArs4c6QAAAAJiS0dEAP+Hj8y/AAAACXBIWXMAAAsTAAALEwEAmpwYAAAAB3RJTUUH3QURCAkd/uac8wAAAMhJREFUKM9jYBie4DEUQ8B+fEq3+3UrMzAwMFxjYGBgYJizYubaOUxYFUaXh/6vWfRfEMIL/+//P5gZJoei4/f/7wxnY1PeNUXdE2RgYGZgYoCrY2BBVsjKwMDAwvCS4f3SG/dXxm5gYESSQ1HIwvCPgZmB8f8Pxv+Kxxb/YfiPJIdi9T8GJgaG/38ZFd4Fx0xUYsZt4h8GBgb2D2bLy7KnMTAwMEIxFoVCXIYr1IoDnkF4XAysqNIwUMDAwMDAsADKS2NkGL4AAIARMlfNIfZMAAAAAElFTkSuQmCC\"></button>\n",
        "    <button onclick=\"animQWCWSTYSPQEEBVYZ.last_frame()\"><img class=\"anim_icon\" src=\"data:image/png;base64,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\"></button>\n",
        "    <button onclick=\"animQWCWSTYSPQEEBVYZ.faster()\">+</button>\n",
        "  <form action=\"#n\" name=\"_anim_loop_selectQWCWSTYSPQEEBVYZ\" class=\"anim_control\">\n",
        "    <input type=\"radio\" name=\"state\" value=\"once\" > Once </input>\n",
        "    <input type=\"radio\" name=\"state\" value=\"loop\" checked> Loop </input>\n",
        "    <input type=\"radio\" name=\"state\" value=\"reflect\" > Reflect </input>\n",
        "  </form>\n",
        "</div>\n",
        "\n",
        "\n",
        "<script language=\"javascript\">\n",
        "  /* Instantiate the Animation class. */\n",
        "  /* The IDs given should match those used in the template above. */\n",
        "  (function() {\n",
        "    var img_id = \"_anim_imgQWCWSTYSPQEEBVYZ\";\n",
        "    var slider_id = \"_anim_sliderQWCWSTYSPQEEBVYZ\";\n",
        "    var loop_select_id = \"_anim_loop_selectQWCWSTYSPQEEBVYZ\";\n",
        "    var frames = new Array(0);\n",
        "    \n",
        "  frames[0] = 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\"\n",
        "  frames[1] = 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Wp07d9bSpUvVrl079enTR3PnzlV6evqB5xzpTaiokH7/e+nf/k1auFAqK7P9CQl20mdenn3q5A8UDVV1tV0Z/PXX7QNe7YhErVNOkXr0sPU9e/a0SwSlpzOZqT4gwE6y9957Tw8++KDy8/MlSVOnTpUkTZw48cBzvvsmfPWVnWg8f771tGpDS7I/wlGjpKuu4rpcwOGUlEgFBXai9Ntv21Wiv6tRIxut6NTJto4d7ZjaOefYidXNmsW6ahwLTwGWGLqAY7Ft2zalpaUduJ+amqo//vGPhzxv61b7BLlwoR2o3r+/7rHevaURI+yqyOefH4uqAb/atrWJHVdfbff37rWJTqtX22klH35o63/WbofTvLl9QGzb1rZWrWzdxlatpBYt7PEWLaTTTrMFsJOTLfSaNJGSkmL3s8IPlwEWOcqZFAdlnBIS7ED03/6tLbDbvv3JqQ1oCFq0kHJzbatVUSFt2mQBtmmTbVu2SH/+s92Wltp2uN7b92nUyIKscWObTHLqqTaMmZRUd5uYaM+rva3dEhLqbiORutvvfv3d7WAH7zv4sSM1RUz4OvlcBli7du1UXFx84H5xcbFSD7Pce2LiJHXoYBeOHDcuR8OH58SuSKCBadLEjoV163boY9GotHu3tGOHbV98YVeY3rXLzrUsLbVeXWmprRhSVma35eW2VVfbvoOH/nGiFPzf5o/LY2BVVVXq3Lmzli1bprPPPlsXXHDBYSdxlJdHOdEYcC4ateH/igo7J7N2q6y0/ZWVNnv44K26um6rqbGtutq+VzRq9w/3de323f+/dt/Bjx2p5fTXqta5+WaOgZ1UiYmJmj17ti677DJVV1dr/Pjx3wqvWoQX4F8kYsOEzAqOjZtvDl3B0XPZAzsanmbSAEC88NR2shY1AMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXHIXYK+++qoyMzPVqFEjFRYWhi4HABCIuwDLysrS/Pnzdckll4QuBQAQUGLoAn6oLl26hC4BABAH3PXAAACQ4rQHlpubq5KSkkP2T548WcOGDQtQEQAg3sRlgC1ZsuSEfJ9JkyYd+DonJ0c5OTkn5PsCQH1RUFCggoKC0GUck0g0Go2GLuJY9O/fX9OmTVOvXr0O+3gkEpHTHw0AgvHUdro7BjZ//nylpaVp1apVGjp0qC6//PLQJQEAAnDbA/s+nj5FAEC88NR2uuuBAQAgEWAAAKcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAldwF21113KT09Xd27d9eVV16p0tLS0CUBAAJwF2CDBg3Shg0btG7dOnXq1ElTpkwJXRIAIAB3AZabm6uEBCu7b9++2rp1a+CKAAAhuAuwgz3zzDMaMmRI6DIAAAEkhi7gcHJzc1VSUnLI/smTJ2vYsGGSpIcfflinnHKKrrnmmliXBwCIA3EZYEuWLDni488995wWL16sZcuWHfF5kyZNOvB1Tk6OcnJyTkB1AFB/FBQUqKCgIHQZxyQSjUajoYv4IfLz8zVhwgStWLFCrVu3/n+fF4lE5OxHA4DgPLWd7gKsY8eOqqysVMuWLSVJF154oZ544olDnufpTQCAeOGp7XQXYEfL05sAAPHCU9vpehYiAKDhIsAAAC4RYAAAlwgwAIBLBBgAwCUCDADgEgEGAHCJAAMAuESAAQBcIsAAAC4RYAAAlwgwAIBLBBgAwCUCDADgEgEGAHCJAAMAuESAAQBcIsAAAC4RYAAAlwgwAIBLBBgAwCUCDADgEgEGAHCJAAMAuESAAQBcIsAAAC4RYAAAlwgwAIBL7gLs/vvvV/fu3ZWdna0BAwaouLg4dEkAgADcBdjdd9+tdevW6YMPPtDw4cP14IMPhi4p7hUUFIQuIW7wWtThtajDa+GTuwA77bTTDnxdVlam1q1bB6zGB/446/Ba1OG1qMNr4VNi6AKOxX333acXXnhBTZs21apVq0KXAwAIIC57YLm5ucrKyjpke+211yRJDz/8sLZs2aLrr79ed955Z+BqAQAhRKLRaDR0Ecdqy5YtGjJkiD766KNDHotEIgEqAgD/vMSCuyHETZs2qWPHjpKkhQsXqkePHod9npc3AABwbNz1wEaOHKlPP/1UjRo1UocOHfTkk0+qTZs2ocsCAMSYuwADAECK00kcxys/P19dunRRx44d9cgjj4QuJ5ji4mL1799fmZmZ6tq1q2bNmhW6pKCqq6vVo0cPDRs2LHQpQe3du1cjR45Uenq6MjIyGvRM3ilTpigzM1NZWVm65ppr9M0334QuKWby8vKUkpKirKysA/t2796t3NxcderUSYMGDdLevXsDVvj96l2AVVdX67bbblN+fr4+/vhjzZ07V5988knosoJISkrS9OnTtWHDBq1atUqPP/54g30tJGnmzJnKyMho8BN8br/9dg0ZMkSffPKJPvzwQ6Wnp4cuKYiioiI99dRTKiws1Pr161VdXa158+aFLitmxo0bp/z8/G/tmzp1qnJzc7Vx40YNGDBAU6dODVTd0al3AbZ69Wqdf/75at++vZKSknT11Vdr4cKFocsKom3btsrOzpYkJScnKz09Xdu3bw9cVRhbt27V4sWLdcMNNzToCT6lpaVauXKl8vLyJEmJiYlq3rx54KrCOP3005WUlKTy8nJVVVWpvLxc7dq1C11WzFx88cU644wzvrVv0aJFGjt2rCRp7NixWrBgQYjSjlq9C7Bt27YpLS3twP3U1FRt27YtYEXxoaioSGvXrlXfvn1DlxLEnXfeqUcffVQJCfXuV/4H2bx5s84880yNGzdOPXv21I033qjy8vLQZQXRsmVLTZgwQeecc47OPvtstWjRQgMHDgxdVlA7d+5USkqKJCklJUU7d+4MXNGR1bu/5oY+PHQ4ZWVlGjlypGbOnKnk5OTQ5cTc66+/rjZt2qhHjx4NuvclSVVVVSosLNQtt9yiwsJCNWvWLO6HiU6Wzz77TDNmzFBRUZG2b9+usrIyvfTSS6HLihuRSCTu29N6F2Dt2rX71gr1xcXFSk1NDVhRWPv379eIESM0evRoDR8+PHQ5Qbz77rtatGiRzjvvPI0aNUrLly/XmDFjQpcVRGpqqlJTU9WnTx9JdlpKYWFh4KrCWLNmjS666CK1atVKiYmJuvLKK/Xuu++GLiuolJQUlZSUSJJ27NgR96co1bsA6927tzZt2qSioiJVVlbq5Zdf1hVXXBG6rCCi0ajGjx+vjIwM3XHHHaHLCWby5MkqLi7W5s2bNW/ePF166aV6/vnnQ5cVRNu2bZWWlqaNGzdKkpYuXarMzMzAVYXRpUsXrVq1ShUVFYpGo1q6dKkyMjJClxXUFVdcoTlz5kiS5syZE/cfet2txPF9EhMTNXv2bF122WWqrq7W+PHjG+wsq3feeUcvvviiunXrdmDFkilTpmjw4MGBKwsr3odFTrbHHntM1157rSorK9WhQwc9++yzoUsKonv37hozZox69+6thIQE9ezZUzfddFPosmJm1KhRWrFihXbt2qW0tDQ99NBDmjhxoq666io9/fTTat++vV555ZXQZR4RJzIDAFyqd0OIAICGgQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMCl/wXO/iaB0DBmdAAAAABJRU5ErkJggg==\"\n",
        "  frames[2] = 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\"\n",
        "  frames[3] = 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\"\n",
        "  frames[4] = 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\"\n",
        "  frames[5] = 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\"\n",
        "  frames[6] = 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\"\n",
        "  frames[7] = 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\"\n",
        "  frames[8] = 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\"\n",
        "  frames[9] = 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\"\n",
        "  frames[10] = 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\"\n",
        "  frames[11] = 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\"\n",
        "  frames[12] = 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\"\n",
        "  frames[13] = 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\"\n",
        "  frames[14] = 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\"\n",
        "  frames[15] = 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\"\n",
        "  frames[16] = 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        "  frames[17] = 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\"\n",
        "  frames[18] = 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\"\n",
        "  frames[19] = 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H5Z277bZhBMm2ASNTp2ClA80Wn/5i11+8qc/WbCtXbv/PklJNmTfvbt9TU+3BYc7d5ZOPpnrLEPzFGAuO/cbN25UWlra3u3U1FR9+OGH++13223S/fdLFRW2feGFto4hF2gCR0fnznbZybhxtl1eLv35z3bOubjYrrFcu9YWxF658sA/o00b6cQTpY4dpZQUu89Zu3bWWre2YcpWraTjj5eSk621aGGN4cqmxeXbHTnMWRZ33WVfzztP+uUvbQgDQMNp397+/s47r/axv/3NzkWvXm1Djp9/bj239eul0lK73cuXX35/wB1MYqL14I45prY1b24tKclaYqK1Zs32bwkJ1iKR/b9+X9vXvo/t+9zBDllMGqs7lwHWqVMnlZaW7t0uLS1Vamrqfvt17jxVZ51lwxJffZUnKa/BagRwYC1b2n30cnP3f27PHltQoKxM2rxZ+utfbbu83NqOHda2b7eRlYoK6euvbbr/zp22HNbXX1vD4Sr8/+aPy3NgNTU16tGjh95++22ddNJJGjBgwAEncezZE+PTDdBExGI2Q3LnTjvfvXu33a+vutpaVZUF3L4tGq1te/ZYi0btZ8VitY99s/3d9t1//5vH9n3uYEfYeDz6XnUV58COqsTERD388MM699xzFY1GNWnSpG+F1zcIL6DpiERqhwtRd1ddFbqCw+eyB3Y4PM2kAYB44enYyRK1AACXCDAAgEsEGADAJQIMAOASAQYAcIkAAwC4RIABAFwiwAAALhFgAACXCDAAgEsEGADAJQIMAOASAQYAcIkAAwC4RIABAFwiwAAALhFgAACXCDAAgEsEGADAJQIMAOASAQYAcIkAAwC4RIABAFwiwAAALhFgAACXCDAAgEsEGADAJQIMAOASAQYAcMldgL388svKyspSs2bNVFRUFLocAEAg7gIsOztbr7zyigYPHhy6FABAQImhCzhSPXv2DF0CACAOuOuBAQAgxWkPLD8/X2VlZfs9Pm3aNI0YMSJARQCAeBOXATZv3rx6+TlTp07d+31eXp7y8vLq5ecCQGNRWFiowsLC0GXUSSQWi8VCF1EXQ4YM0X333ad+/fod8PlIJCKnvxoABOPp2OnuHNgrr7yitLQ0LVq0SOeff77OO++80CUBAAJw2wM7FE+fIgAgXng6drrrgQEAIBFgAACnCDAAgEsEGADAJQIMAOASAQYAcIkAAwC4RIABAFwiwAAALhFgAACXCDAAgEsEGADAJQIMAOASAQYAcIkAAwC4RIABAFwiwAAALhFgAACXCDAAgEsEGADAJQIMAOASAQYAcIkAAwC4RIABAFwiwAAALhFgAACXCDAAgEsEGADAJXcBdsMNNygjI0N9+vTRqFGjtGPHjtAlAQACcBdg55xzjlasWKHi4mJ1795d06dPD10SACAAdwGWn5+vhAQre+DAgdqwYUPgigAAIbgLsH09+eSTGj58eOgyAAABJIYu4EDy8/NVVla23+PTpk3TiBEjJEl33323mjdvrosuuqihywMAxIG4DLB58+Yd9PmnnnpKb731lt5+++2D7jd16tS93+fl5SkvL68eqgOAxqOwsFCFhYWhy6iTSCwWi4Uu4kgUFBTo+uuv14IFC9S+ffvv3S8SicjZrwYAwXk6droLsPT0dFVVValt27aSpEGDBunRRx/dbz9PbwIAxAtPx053AXa4PL0JABAvPB07Xc9CBAA0XQQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwyV2A3XrrrerTp49ycnI0dOhQlZaWhi4JABCAuwCbMmWKiouLtXTpUo0cOVJ33HFH6JLiXmFhYegS4gavRS1ei1q8Fj65C7Djjjtu7/cVFRVq3759wGp84I+zFq9FLV6LWrwWPiWGLqAubrnlFj377LNq0aKFFi1aFLocAEAAcdkDy8/PV3Z29n7tjTfekCTdfffdWr9+vS677DJdd911gasFAIQQicVisdBF1NX69es1fPhwLV++fL/nIpFIgIoAwD8vseBuCHHNmjVKT0+XJL322mvKzc094H5e3gAAQN2464GNGTNGn332mZo1a6Zu3bpp1qxZ6tChQ+iyAAANzF2AAQAgxekkjr9XQUGBevbsqfT0dN1zzz2hywmmtLRUQ4YMUVZWlnr16qUHH3wwdElBRaNR5ebmasSIEaFLCWr79u0aM2aMMjIylJmZ2aRn8k6fPl1ZWVnKzs7WRRddpN27d4cuqcFMnDhRKSkpys7O3vvYtm3blJ+fr+7du+ucc87R9u3bA1Z4aI0uwKLRqK655hoVFBRo5cqVeuGFF/Tpp5+GLiuIpKQk3X///VqxYoUWLVqkRx55pMm+FpI0c+ZMZWZmNvkJPtdee62GDx+uTz/9VJ988okyMjJClxRESUmJnnjiCRUVFWnZsmWKRqOaO3du6LIazIQJE1RQUPCtx2bMmKH8/HytXr1aQ4cO1YwZMwJVd3gaXYAtXrxYp5xyirp06aKkpCT99Kc/1WuvvRa6rCA6duyonJwcSVJycrIyMjK0adOmwFWFsWHDBr311lu6/PLLm/QEnx07dujdd9/VxIkTJUmJiYlq1apV4KrCOP7445WUlKTKykrV1NSosrJSnTp1Cl1WgznjjDPUpk2bbz32+uuva/z48ZKk8ePH69VXXw1R2mFrdAG2ceNGpaWl7d1OTU3Vxo0bA1YUH0pKSrRkyRINHDgwdClBXHfddbr33nuVkNDo/ssfkS+++EInnHCCJkyYoL59++qKK65QZWVl6LKCaNu2ra6//nqdfPLJOumkk9S6dWudffbZocsKasuWLUpJSZEkpaSkaMuWLYErOrhG99fc1IeHDqSiokJjxozRzJkzlZycHLqcBvfmm2+qQ4cOys3NbdK9L0mqqalRUVGRrr76ahUVFally5ZxP0x0tKxdu1YPPPCASkpKtGnTJlVUVOj5558PXVbciEQicX88bXQB1qlTp2+tUF9aWqrU1NSAFYVVXV2t0aNH65JLLtHIkSNDlxPEwoUL9frrr6tr164aO3as/vjHP2rcuHGhywoiNTVVqamp6t+/vyS7LKWoqChwVWF89NFH+vGPf6x27dopMTFRo0aN0sKFC0OXFVRKSorKysokSZs3b477S5QaXYCdeuqpWrNmjUpKSlRVVaUXX3xRF1xwQeiygojFYpo0aZIyMzM1efLk0OUEM23aNJWWluqLL77Q3LlzddZZZ+mZZ54JXVYQHTt2VFpamlavXi1Jmj9/vrKysgJXFUbPnj21aNEi7dy5U7FYTPPnz1dmZmbosoK64IIL9PTTT0uSnn766bj/0OtuJY5DSUxM1MMPP6xzzz1X0WhUkyZNarKzrN5//30999xz6t27994VS6ZPn65hw4YFriyseB8WOdoeeughXXzxxaqqqlK3bt00Z86c0CUF0adPH40bN06nnnqqEhIS1LdvX1155ZWhy2owY8eO1YIFC1ReXq60tDTdeeeduummm3ThhRdq9uzZ6tKli1566aXQZR4UFzIDAFxqdEOIAICmgQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMAlAgwA4BIBBgBwiQADALhEgAEAXCLAAAAuEWAAAJcIMACASwQYAMCl/wNL3tp4mp503AAAAABJRU5ErkJggg==\"\n",
        "\n",
        "\n",
        "    /* set a timeout to make sure all the above elements are created before\n",
        "       the object is initialized. */\n",
        "    setTimeout(function() {\n",
        "        animQWCWSTYSPQEEBVYZ = new Animation(frames, img_id, slider_id, 100, loop_select_id);\n",
        "    }, 0);\n",
        "  })()\n",
        "</script>\n"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 14,
       "text": [
        "<IPython.core.display.HTML at 0x7f27c0a28860>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Implementing time-dependent boundary conditions is simple. For example, vibrating with one end of the string looks like:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "maxt=60.\n",
      "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL)\n",
      "U[0,:] = 0\n",
      "U[1,:] = 0\n",
      "U[:,0] = sin(t*0.5)\n",
      "wave_solve(U, dx, dt, nx, len(t))\n",
      "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.collections.QuadMesh at 0x7f27c01b0710>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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C4KcA/KqI/DKyOMp/6JxbRib+TOznEL9dN7DUZLOPJgYX6vD3zwpsYS1Ay1vC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\nISFhFyCRfUJCQsIuQCL7hISEhF2A/x8YhI/Wug6gLAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x7f27c0b0f470>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    }
   ],
   "metadata": {}
  }
 ]
}