{
 "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",
   "execution_count": 1,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:46:39.881245Z",
     "start_time": "2022-05-02T11:46:39.875631Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.078724Z",
     "iopub.status.busy": "2024-06-14T19:44:32.078632Z",
     "iopub.status.idle": "2024-06-14T19:44:32.352871Z",
     "shell.execute_reply": "2024-06-14T19:44:32.352438Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.078701Z"
    }
   },
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "from pylab import *\n",
    "from numpy import *"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:46:39.983661Z",
     "start_time": "2022-05-02T11:46:39.883380Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.353669Z",
     "iopub.status.busy": "2024-06-14T19:44:32.353532Z",
     "iopub.status.idle": "2024-06-14T19:44:32.355393Z",
     "shell.execute_reply": "2024-06-14T19:44:32.355199Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.353660Z"
    }
   },
   "outputs": [],
   "source": [
    "#dimensions of the computational domain:\n",
    "maxx = 10.\n",
    "maxt = 40.\n",
    "\n",
    "#wave velocity\n",
    "v = 0.5"
   ]
  },
  {
   "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",
   "execution_count": 3,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:46:40.187127Z",
     "start_time": "2022-05-02T11:46:39.985227Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.355794Z",
     "iopub.status.busy": "2024-06-14T19:44:32.355704Z",
     "iopub.status.idle": "2024-06-14T19:44:32.357967Z",
     "shell.execute_reply": "2024-06-14T19:44:32.357783Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.355786Z"
    }
   },
   "outputs": [],
   "source": [
    "#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"
   ]
  },
  {
   "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",
   "execution_count": 4,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:46:40.354224Z",
     "start_time": "2022-05-02T11:46:40.188745Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.358322Z",
     "iopub.status.busy": "2024-06-14T19:44:32.358241Z",
     "iopub.status.idle": "2024-06-14T19:44:32.360104Z",
     "shell.execute_reply": "2024-06-14T19:44:32.359927Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.358315Z"
    }
   },
   "outputs": [],
   "source": [
    "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"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:46:40.465471Z",
     "start_time": "2022-05-02T11:46:40.355532Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.360437Z",
     "iopub.status.busy": "2024-06-14T19:44:32.360362Z",
     "iopub.status.idle": "2024-06-14T19:44:32.362037Z",
     "shell.execute_reply": "2024-06-14T19:44:32.361863Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.360431Z"
    }
   },
   "outputs": [],
   "source": [
    "U, dx, dt, x, t = wave_init(maxx, maxt, v, nx, CFL*1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:46:40.561415Z",
     "start_time": "2022-05-02T11:46:40.466581Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.362686Z",
     "iopub.status.busy": "2024-06-14T19:44:32.362607Z",
     "iopub.status.idle": "2024-06-14T19:44:32.364209Z",
     "shell.execute_reply": "2024-06-14T19:44:32.364038Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.362679Z"
    }
   },
   "outputs": [],
   "source": [
    "# use gaussian pulse as initial condition\n",
    "U0 = exp(-(x-maxx/3)**2/2.)*2\n",
    "U[0,:] = U0\n",
    "U[1,:] = U0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:46:40.675594Z",
     "start_time": "2022-05-02T11:46:40.562614Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.364544Z",
     "iopub.status.busy": "2024-06-14T19:44:32.364468Z",
     "iopub.status.idle": "2024-06-14T19:44:32.368096Z",
     "shell.execute_reply": "2024-06-14T19:44:32.367933Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.364537Z"
    }
   },
   "outputs": [],
   "source": [
    "wave_solve(U, dx, dt, nx, len(t))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:46:40.944877Z",
     "start_time": "2022-05-02T11:46:40.676917Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.368412Z",
     "iopub.status.busy": "2024-06-14T19:44:32.368340Z",
     "iopub.status.idle": "2024-06-14T19:44:32.433069Z",
     "shell.execute_reply": "2024-06-14T19:44:32.432820Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.368406Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.QuadMesh at 0x7adfc8d46510>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pcolormesh(U, rasterized=True, vmin=-2, vmax=2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What happens if the CFL condition is violated by a small relative amount, say $10^{-3}$?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:46:41.078821Z",
     "start_time": "2022-05-02T11:46:40.946228Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.433389Z",
     "iopub.status.busy": "2024-06-14T19:44:32.433304Z",
     "iopub.status.idle": "2024-06-14T19:44:32.495295Z",
     "shell.execute_reply": "2024-06-14T19:44:32.495047Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.433382Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.QuadMesh at 0x7adfc91d2840>"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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)"
   ]
  },
  {
   "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",
   "execution_count": 10,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:46:41.236817Z",
     "start_time": "2022-05-02T11:46:41.080846Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.495672Z",
     "iopub.status.busy": "2024-06-14T19:44:32.495594Z",
     "iopub.status.idle": "2024-06-14T19:44:32.555634Z",
     "shell.execute_reply": "2024-06-14T19:44:32.555383Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.495666Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.QuadMesh at 0x7adfc8351130>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:46:41.240362Z",
     "start_time": "2022-05-02T11:46:41.238100Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.556063Z",
     "iopub.status.busy": "2024-06-14T19:44:32.555958Z",
     "iopub.status.idle": "2024-06-14T19:44:32.557632Z",
     "shell.execute_reply": "2024-06-14T19:44:32.557464Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.556056Z"
    }
   },
   "outputs": [],
   "source": [
    "#let's take every 10th frame into animation\n",
    "Un = U[:-10:10,:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:48:44.815570Z",
     "start_time": "2022-05-02T11:48:44.809100Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.557961Z",
     "iopub.status.busy": "2024-06-14T19:44:32.557882Z",
     "iopub.status.idle": "2024-06-14T19:44:32.560713Z",
     "shell.execute_reply": "2024-06-14T19:44:32.560542Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.557954Z"
    }
   },
   "outputs": [],
   "source": [
    "plt.ioff()\n",
    "from matplotlib import animation\n",
    "#from matplotlib.animation import FuncAnimation\n",
    "#from JSAnimation.IPython_display import display_animation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "ExecuteTime": {
     "end_time": "2022-05-02T11:55:05.840963Z",
     "start_time": "2022-05-02T11:55:05.426987Z"
    },
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.561054Z",
     "iopub.status.busy": "2024-06-14T19:44:32.560976Z",
     "iopub.status.idle": "2024-06-14T19:44:32.944045Z",
     "shell.execute_reply": "2024-06-14T19:44:32.943792Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.561048Z"
    }
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "\n",
       "<link rel=\"stylesheet\"\n",
       "href=\"https://maxcdn.bootstrapcdn.com/font-awesome/4.4.0/css/font-awesome.min.css\">\n",
       "<script language=\"javascript\">\n",
       "  function isInternetExplorer() {\n",
       "    ua = navigator.userAgent;\n",
       "    /* MSIE used to detect old browsers and Trident used to newer ones*/\n",
       "    return ua.indexOf(\"MSIE \") > -1 || ua.indexOf(\"Trident/\") > -1;\n",
       "  }\n",
       "\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",
       "    var slider = document.getElementById(this.slider_id);\n",
       "    slider.max = this.frames.length - 1;\n",
       "    if (isInternetExplorer()) {\n",
       "        // switch from oninput to onchange because IE <= 11 does not conform\n",
       "        // with W3C specification. It ignores oninput and onchange behaves\n",
       "        // like oninput. In contrast, Microsoft Edge behaves correctly.\n",
       "        slider.setAttribute('onchange', slider.getAttribute('oninput'));\n",
       "        slider.setAttribute('oninput', null);\n",
       "    }\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 =\n",
       "            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() {\n",
       "        t.anim_step_forward();\n",
       "    }, 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() {\n",
       "        t.anim_step_reverse();\n",
       "    }, this.interval);\n",
       "  }\n",
       "</script>\n",
       "\n",
       "<style>\n",
       ".animation {\n",
       "    display: inline-block;\n",
       "    text-align: center;\n",
       "}\n",
       "input[type=range].anim-slider {\n",
       "    width: 374px;\n",
       "    margin-left: auto;\n",
       "    margin-right: auto;\n",
       "}\n",
       ".anim-buttons {\n",
       "    margin: 8px 0px;\n",
       "}\n",
       ".anim-buttons button {\n",
       "    padding: 0;\n",
       "    width: 36px;\n",
       "}\n",
       ".anim-state label {\n",
       "    margin-right: 8px;\n",
       "}\n",
       ".anim-state input {\n",
       "    margin: 0;\n",
       "    vertical-align: middle;\n",
       "}\n",
       "</style>\n",
       "\n",
       "<div class=\"animation\">\n",
       "  <img id=\"_anim_img066ff86f472d4fdca3d168c2af8adc6f\">\n",
       "  <div class=\"anim-controls\">\n",
       "    <input id=\"_anim_slider066ff86f472d4fdca3d168c2af8adc6f\" type=\"range\" class=\"anim-slider\"\n",
       "           name=\"points\" min=\"0\" max=\"1\" step=\"1\" value=\"0\"\n",
       "           oninput=\"anim066ff86f472d4fdca3d168c2af8adc6f.set_frame(parseInt(this.value));\">\n",
       "    <div class=\"anim-buttons\">\n",
       "      <button title=\"Decrease speed\" aria-label=\"Decrease speed\" onclick=\"anim066ff86f472d4fdca3d168c2af8adc6f.slower()\">\n",
       "          <i class=\"fa fa-minus\"></i></button>\n",
       "      <button title=\"First frame\" aria-label=\"First frame\" onclick=\"anim066ff86f472d4fdca3d168c2af8adc6f.first_frame()\">\n",
       "        <i class=\"fa fa-fast-backward\"></i></button>\n",
       "      <button title=\"Previous frame\" aria-label=\"Previous frame\" onclick=\"anim066ff86f472d4fdca3d168c2af8adc6f.previous_frame()\">\n",
       "          <i class=\"fa fa-step-backward\"></i></button>\n",
       "      <button title=\"Play backwards\" aria-label=\"Play backwards\" onclick=\"anim066ff86f472d4fdca3d168c2af8adc6f.reverse_animation()\">\n",
       "          <i class=\"fa fa-play fa-flip-horizontal\"></i></button>\n",
       "      <button title=\"Pause\" aria-label=\"Pause\" onclick=\"anim066ff86f472d4fdca3d168c2af8adc6f.pause_animation()\">\n",
       "          <i class=\"fa fa-pause\"></i></button>\n",
       "      <button title=\"Play\" aria-label=\"Play\" onclick=\"anim066ff86f472d4fdca3d168c2af8adc6f.play_animation()\">\n",
       "          <i class=\"fa fa-play\"></i></button>\n",
       "      <button title=\"Next frame\" aria-label=\"Next frame\" onclick=\"anim066ff86f472d4fdca3d168c2af8adc6f.next_frame()\">\n",
       "          <i class=\"fa fa-step-forward\"></i></button>\n",
       "      <button title=\"Last frame\" aria-label=\"Last frame\" onclick=\"anim066ff86f472d4fdca3d168c2af8adc6f.last_frame()\">\n",
       "          <i class=\"fa fa-fast-forward\"></i></button>\n",
       "      <button title=\"Increase speed\" aria-label=\"Increase speed\" onclick=\"anim066ff86f472d4fdca3d168c2af8adc6f.faster()\">\n",
       "          <i class=\"fa fa-plus\"></i></button>\n",
       "    </div>\n",
       "    <form title=\"Repetition mode\" aria-label=\"Repetition mode\" action=\"#n\" name=\"_anim_loop_select066ff86f472d4fdca3d168c2af8adc6f\"\n",
       "          class=\"anim-state\">\n",
       "      <input type=\"radio\" name=\"state\" value=\"once\" id=\"_anim_radio1_066ff86f472d4fdca3d168c2af8adc6f\"\n",
       "             >\n",
       "      <label for=\"_anim_radio1_066ff86f472d4fdca3d168c2af8adc6f\">Once</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"loop\" id=\"_anim_radio2_066ff86f472d4fdca3d168c2af8adc6f\"\n",
       "             checked>\n",
       "      <label for=\"_anim_radio2_066ff86f472d4fdca3d168c2af8adc6f\">Loop</label>\n",
       "      <input type=\"radio\" name=\"state\" value=\"reflect\" id=\"_anim_radio3_066ff86f472d4fdca3d168c2af8adc6f\"\n",
       "             >\n",
       "      <label for=\"_anim_radio3_066ff86f472d4fdca3d168c2af8adc6f\">Reflect</label>\n",
       "    </form>\n",
       "  </div>\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_img066ff86f472d4fdca3d168c2af8adc6f\";\n",
       "    var slider_id = \"_anim_slider066ff86f472d4fdca3d168c2af8adc6f\";\n",
       "    var loop_select_id = \"_anim_loop_select066ff86f472d4fdca3d168c2af8adc6f\";\n",
       "    var frames = new Array(20);\n",
       "    \n",
       "  frames[0] = \"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAoAAAAHgCAYAAAA10dzkAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90\\\n",
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       "jjvu0KpVq7Ro0SK7RzFSYWGh7rrrLn300UeKjIy0exyjBYNBDR06VNOnT5ckDRo0SGvXrtXs2bMJ\\\n",
       "wFb2yiuv6O9//7teeukl9evXTytWrNDkyZOVnp6uG2+80e7xIHO35wTgSUpJSZHL5Tpqb9/evXuP\\\n",
       "+ikCrWfSpEmaP3++Fi5cqIyMDLvHMdLSpUu1d+9eDRkyJLQsEAho4cKFmjlzpvx+v1wul40TmqNT\\\n",
       "p07q27dvo2V9+vTRG2+8YdNE5rr77rt177336pprrpEk9e/fX9u3b1deXh4BaLO0tDRJDXsCO3Xq\\\n",
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       "2j2SkXw+n3XXXXdZWVlZVmRkpNWtWzfrgQcesPx+v92jGeGTTz455jbixhtvtCzLsoLBoPXQQw9Z\\\n",
       "aWlpltvttkaNGmWtXr3a3qFbCdcBBAAAMAznAAIAABiGAAQAADAMAQgAAGAYAhAAAMAwBCAAAIBh\\\n",
       "CEAAAADDEIAAAACGIQABAAAMQwACAAAYhgAEAAAwDAEIAABgGAIQAADAMAQgAACAYQhAAAAAwxCA\\\n",
       "AAAAhiEAAQAADEMAAgAAGIYABAAAMAwBCAAAYBgCEAAAwDAEIAAAgGEIQAAAAMMQgAAAAIYhAAEA\\\n",
       "AAxDAAIAABiGAAQAADAMAQgAAGAYAhAAAMAwBCAAAIBhCEAAAADDEIAAAACG+f+TjOegxWnRbgAA\\\n",
       "AABJRU5ErkJggg==\\\n",
       "\"\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",
       "        anim066ff86f472d4fdca3d168c2af8adc6f = new Animation(frames, img_id, slider_id, 100.0,\n",
       "                                 loop_select_id);\n",
       "    }, 0);\n",
       "  })()\n",
       "</script>\n"
      ],
      "text/plain": [
       "<matplotlib.animation.FuncAnimation at 0x7adfc836f710>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "plt.rcParams[\"animation.html\"] = \"jshtml\"\n",
    "#%matplotlib notebook\n",
    "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",
    "animation.FuncAnimation(fig, animate, frames=Un, interval=100)"
   ]
  },
  {
   "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",
   "execution_count": 14,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.944529Z",
     "iopub.status.busy": "2024-06-14T19:44:32.944419Z",
     "iopub.status.idle": "2024-06-14T19:44:32.955787Z",
     "shell.execute_reply": "2024-06-14T19:44:32.955576Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.944522Z"
    }
   },
   "outputs": [],
   "source": [
    "plt.ion()\n",
    "plt.clf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "execution": {
     "iopub.execute_input": "2024-06-14T19:44:32.956190Z",
     "iopub.status.busy": "2024-06-14T19:44:32.956100Z",
     "iopub.status.idle": "2024-06-14T19:44:33.006011Z",
     "shell.execute_reply": "2024-06-14T19:44:33.005804Z",
     "shell.execute_reply.started": "2024-06-14T19:44:32.956182Z"
    }
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "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)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "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": "3.12.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}