{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "

Leapfrog, Lax-Friedrichs and Lax-Wendroff Schemes (Heaviside Input)


\n", "" ], "text/plain": [ "" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.display import HTML \n", "s=\"\"\"

Leapfrog, Lax-Friedrichs and Lax-Wendroff Schemes (Heaviside Input)


\n", "\"\"\";\n", "h=HTML(s); h" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "***\n", "# Understand the Problem\n", "\n", "## Question\n", "\n", "* What is the 1D velocity for the **1D Wave Equation** for flow with a step function for the initial conditions?\n", "\n", "## Initial Conditions\n", "\n", "* `t = 0s` and `x = 0m to 2m` $\\Rightarrow$ ` u = 1m/s`\n", "\n", "* `t = 0s` and `x = 2m to 4m` $\\Rightarrow$ `u = 0m/s`\n", "\n", "## Boundary Conditions\n", "\n", "* `x = 0m` $\\Rightarrow$ ` u = 1m/s`\n", "\n", "* `y = 2m` $\\Rightarrow$ ` u = 0m/s`\n", "\n", "\n", "## Governing Equation\n", "\n", "* The Wave Equation described as follows:\n", "\n", "$$ {\\partial u \\over \\partial t} + c {\\partial u \\over \\partial x} = 0 $$\n", "\n", "\n", "\n", "***" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Formulate the Problem\n", "\n", "## Input Data:\n", "\n", "The Wave Equation **does have a temporal component**, so we use `nt`\n", "\n", "* `nt` = ? (number of temporal points)\n", "* `nx` = 51 (number of x spatial points)\n", "* `tmax` = 1.0\n", "* `xmax` = 4\n", "* `c` = 1.0\n", "\n", "Formulate `nt` based on the CFL Condition `sigma = c (dt / dx) = 1`\n", "\n", "## Initial Conditions:\n", "\n", "* $\\forall (x, t) \\quad t = 0 \\land x \\le 2 \\rightarrow u(x,0) = 2 $\n", "* $\\forall (x, t) \\quad t = 0 \\land x \\gt 2 \\rightarrow u(x,0) = 0 $\n", "\n", "## Velocity Boundary Conditions:\n", "\n", "* $\\forall (x, t) \\quad x = 0 \\rightarrow u(0,t) = 2 $\n", "\n", "* $\\forall (x, t) \\quad x = 4 \\rightarrow u(4,t) = 0 $\n", "\n", "## Output Data:\n", "\n", "* $\\forall (x, t) \\quad \\ u(x,t) = ? $\n", "\n", "***\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Design Algorithm to Solve Problem using Upwind Scheme\n", "\n", "## Space-time discretisation:\n", "\n", "* i $\\rightarrow$ index of grid in x\n", "* n $\\rightarrow$ index of time\n", "\n", "## Upwind Numerical scheme\n", "\n", "* For the **one** first derivative of velocity in time: 1st order FD in time\n", "* For the **one** first derivative of velocity in space: 1st order BD in space\n", "\n", "\n", "## Discrete equation\n", "\n", "$$ {{u_i^{n+1} - u_i^n} \\over {\\Delta t}} + c {{u_i^n - u_{i-1}^n} \\over \\Delta x}=0 $$\n", "\n", "## Transpose\n", "\n", "$$ u_i^{n+1} = u_i^n - c{\\Delta t \\over \\Delta x}(u_i^n - u_{i-1}^n) $$\n", "\n", "## Analytical solution\n", "\n", "This is simply the wave travelling in the x-direction\n", "\n", "$$ u_i^{n+1} = u_{i-1}^n $$\n", "\n", "We must limit the number of timesteps used for the analytical solution, proportional to the value of $\\sigma$ in order to compare with the numerical solution. Simply limit $t_{max}$ to $\\sigma \\times t_{max}$\n", "\n", "## Pseudo-code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " #Constants\n", " xmax = 4.0\n", " nx = 51\n", " dx = xmax/(nx-1)\n", " tmax = 1.0\n", " sigma = 1.0\n", " dt = (dx / sigma)\n", " nt = int(tmax/dt + 1)\n", " \n", " #Boundary Conditions\n", " for n between 0 and nt\n", " u(0,n)=1\n", " u(nx-1,n)=0 \n", "\n", " #Initial Conditions\n", " for i between 1 and nx-2\n", " if(i < (nx-1)/2)\n", " u(i,0) = 1\n", " else\n", " u(i,0) = 0\n", "\n", " #Iteration\n", " for n between 0 and nt-1\n", " for i between 1 and nx-2\n", " u(i,n+1) = u(i,n)-c*(dt/dx)*(u(i,n)-u(i-1,n)" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def initial_and_boundary_conditions(nx, nt):\n", " \n", " # Initialise data structures\n", " import numpy as np\n", " u = np.zeros((nx,nt))\n", " \n", " # Boundary conditions\n", " u[0,:] = 1.0\n", " u[nx-1,:] = 0.0\n", "\n", " half = int((nx-1)/2)\n", "\n", " # Initial conditions \n", " u[0:half,0] = 1.0\n", " \n", " return u" ] }, { "cell_type": "code", "execution_count": 88, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def analytical(sigma, nx, tmax, xmax, c):\n", " \n", " # Increments\n", " # dt = tmax/(nt-1)\n", " # dx = (c * dt) / sigma\n", " dx = xmax/(nx-1)\n", " dt = ((dx*sigma) / c)\n", " nt = int(sigma*tmax/dt + 1)\n", "\n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions(nx, nt)\n", "\n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", " \n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt-1):\n", " u[i:nx-1, n+1] = u[i-1:nx-2, n]\n", " \n", " return u, x, nt" ] }, { "cell_type": "code", "execution_count": 79, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def upwind_convection(sigma, nx, tmax, xmax, c):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt = ((dx * sigma) / c)\n", " nt = int(tmax/dt + 1)\n", "\n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions(nx, nt)\n", "\n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", " \n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt-1):\n", " u[i:nx-1, n+1] = u[i:nx-1, n]-sigma*(u[i:nx-1, n]-u[i-1:nx-2, n])\n", " #u[i:nx-1, n+1] = 0.5*(u[i-1:nx-2, n]+u[i+1:nx, n])-0.5*sigma*(u[i+1:nx, n]-u[i-1:nx-2, n])\n", " return u, x, nt" ] }, { "cell_type": "code", "execution_count": 103, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def plot(u,x,NT,u_analytical, x_analytical, NT2):\n", " \"\"\"\n", " Plots the 1D velocity field\n", " \"\"\"\n", "\n", " import matplotlib.pyplot as plt\n", " import matplotlib.cm as cm\n", " plt.figure()\n", " ax=plt.subplot(111)\n", " colour=iter(cm.rainbow(np.linspace(0,4,NT))) \n", " for n in range(0,NT,4):\n", " c=next(colour)\n", " ax.plot(x,u[:,n],linestyle='-',c=c,label='n='+str(n))\n", " ax.plot(x_analytical,u_analytical[:,NT2-1],linestyle='--',c='k',label='n='+str(NT2-1)+' analytical') \n", " box=ax.get_position()\n", " ax.set_position([box.x0, box.y0, box.width*2,box.height*2])\n", " ax.legend( bbox_to_anchor=(1.02,1), loc=2)\n", " plt.ylim([-0.5,1.5])\n", " plt.xlim([0.0,5.0])\n", " plt.xlabel('x (m)')\n", " plt.ylabel('u (m/s)')\n", " plt.show()\n" ] }, { "cell_type": "code", "execution_count": 145, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u00, x00, nt00 = analytical(1.0, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 146, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u0, x0, nt0 = upwind_convection(1.0, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 147, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "(101, 41)" ] }, "execution_count": 147, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u11.shape" ] }, { "cell_type": "code", "execution_count": 148, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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37oPc0TQL4cNwzmXD/hoAIB92bZFuHy/9ry35X+uh1zv021fbdceUoryvtTDV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\nAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(u0,x0,nt0, u00, x00,nt00)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* If the value of $\\sigma = 1$ then the new velocity simply equals the old velocity. \n", "* The phase angle is zero, so there is no diffusion or dispersion error" ] }, { "cell_type": "code", "execution_count": 149, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u11, x11, nt11 = analytical(0.5, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 150, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u1, x1, nt1 = upwind_convection(0.5, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 151, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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YO9fw6KPdh6/h4XjJmi11PYeMyUEfkzPSuH9nz6tnAJem5fFU+27aerig5JAJ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\n8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(u1,x1,nt1,u11,x11,nt11)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* The jump is diffused by the numerical diffusion arising from the first order truncation error\n", "* The amount of diffusion is increasing as we move through time (as n increases)\n", "* The numerical speed with which the solution moves through the domain is also reduced" ] }, { "cell_type": "code", "execution_count": 152, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u22, x22, nt22 = analytical(0.25, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 153, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u2, x2, nt2 = upwind_convection(0.25, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 154, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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AN36ydzv7Q40A9HVGM8GVyMO1WznYLuQ2DqY5TuLZ0CbqrPB1GQS5ltN4kw2s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\nTO85jciJiIiIiIj4GAU5ERERERERH6MgJyIiIiIi4mMU5ERER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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(u2,x2,nt2,u22, x22, nt22)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Clearly, the smaller Courant Number reduces the speed at which the solution travels through the domain\n", "* At these very low frequencies, there is not much more added diffusion between $\\sigma = 0.50$ and $\\sigma = 0.25$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Design Algorithm to Solve Problem using Leapfrog Scheme\n", "\n", "## Space-time discretisation:\n", "\n", "* i $\\rightarrow$ index of grid in x\n", "* n $\\rightarrow$ index of time\n", "\n", "## Lax Friedrichs scheme\n", "\n", "* For the **one** first derivative of velocity in time: 2nd order CD in time\n", "* For the **one** first derivative of velocity in space: 2nd order CD in space\n", "\n", "* Use upwind to initialise the leapfrog scheme\n", "\n", "## Discrete equation\n", "\n", "$$ {{u_i^{n+1} - u_i^{n-1}} \\over {2 \\Delta t}} + c {{u_{i-1}^n - u_{i-1}^n} \\over {2 \\Delta x}}=0 $$\n", "\n", "## Transpose\n", "\n", "$$ u_i^{n+1} = u_i^{n-1} - {{c \\Delta t} \\over \\Delta x} (u_{i+1}^n - u_{i-1}^n) $$\n", "\n", "## Pseudo-code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " #Constants\n", " xmax = 4.0\n", " nx = 51\n", " dx = xmax/(nx-1)\n", " tmax = 1.0\n", " sigma = 1.0\n", " dt = (dx / sigma)\n", " nt = int(tmax/dt + 1)\n", " \n", " #Boundary Conditions\n", " for n between 0 and nt\n", " u(0,n)=1\n", " u(nx-1,n)=0 \n", "\n", " #Initial Conditions\n", " for i between 1 and nx-2\n", " if(i < (nx-1)/2)\n", " u(i,0) = 1\n", " else\n", " u(i,0) = 0\n", "\n", " #Initialise using Upwind\n", " n = 0\n", " for i between 1 and nx-2\n", " u(i,n+1) = u(i,n)-c*(dt/dx)*(u(i,n)-u(i-1,n)\n", " \n", " #Proceed Using Leapfrog\n", " for n between 1 and nt-1\n", " for i between 1 and nx-2\n", " u(i,n+1) = u(i,n-1)-c*(dt/dx)*(u(i+1,n)-u(i-1,n)" ] }, { "cell_type": "code", "execution_count": 126, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def leapfrog_convection(sigma, nx, tmax, xmax, c):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt = ((dx * sigma) / c)\n", " nt = int(tmax/dt + 1)\n", "\n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions(nx, nt)\n", " \n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", " \n", " # Initialise using Upwind\n", " n = 0\n", " i = 1\n", " u[i:nx-1, n+1] = u[i:nx-1, n]-sigma*(u[i:nx-1, n]-u[i-1:nx-2, n])\n", " \n", " # Proceed using Leapfrog\n", " for n in range(1, nt-1):\n", " u[i:nx-1, n+1] = u[i:nx-1, n-1]-sigma*(u[i+1:nx, n]-u[i-1:nx-2, n])\n", " \n", " return u, x, nt" ] }, { "cell_type": "code", "execution_count": 155, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u44, x44, nt44 = analytical(0.5, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 156, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u4, x4, nt4 = leapfrog_convection(0.5, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 157, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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JdiSNrZWJFEUWleBgkDMpZmqs53M4viNtC6LbpNKvxClX7VO+pw76ufHtXZzf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HIxudLVLjndQK6fM3JCCCEGPwnkhBBiCDMdrB8ASCQUtTXOyiU7M3KOrvV52JbUC8rCyqPVIwdu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\nvQe9vLS0VLm5uS1vZOdKl35Xuu+Flrf/5RxpxtQ2P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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(u4,x4,nt4,u44, x44, nt44)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Oscillatory, behind the wave, more accurate than Lax-Friedrichs" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Design Algorithm to Solve Problem using Lax Friedrichs Scheme\n", "\n", "## Space-time discretisation:\n", "\n", "* i $\\rightarrow$ index of grid in x\n", "* n $\\rightarrow$ index of time\n", "\n", "## Lax Friedrichs scheme\n", "\n", "$$ u_i^{n+1} = {1 \\over 2} (u_{i-1}^n + u_{i+1}^n) - {\\sigma \\over 2}(u_{i+1}^n - u_{i-1}^n) $$\n", "\n", "## Pseudo-code" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " #Constants\n", " xmax = 4.0\n", " nx = 51\n", " dx = xmax/(nx-1)\n", " tmax = 1.0\n", " sigma = 1.0\n", " dt = (dx / sigma)\n", " nt = int(tmax/dt + 1)\n", " \n", " #Boundary Conditions\n", " for n between 0 and nt\n", " u(0,n)=1\n", " u(nx-1,n)=0 \n", "\n", " #Initial Conditions\n", " for i between 1 and nx-2\n", " if(i < (nx-1)/2)\n", " u(i,0) = 1\n", " else\n", " u(i,0) = 0\n", "\n", " #Iteration\n", " for n between 0 and nt-1\n", " for i between 1 and nx-2\n", " u(i,n+1) = 0.5*(u(i-1,n)+u(i+1,n))-0.5*sigma*(u(i+1,n)-u(i-1,n)" ] }, { "cell_type": "code", "execution_count": 132, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def lax_friedrichs_convection(sigma, nx, tmax, xmax, c):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt = ((dx * sigma) / c)\n", " nt = int(tmax/dt + 1)\n", "\n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions(nx, nt)\n", "\n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt-1):\n", " u[i:nx-1, n+1] = 0.5*(u[i-1:nx-2, n]+u[i+1:nx, n])-0.5*sigma*(u[i+1:nx, n]-u[i-1:nx-2, n])\n", "\n", " return u, x, nt" ] }, { "cell_type": "code", "execution_count": 158, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u55, x55, nt55 = analytical(0.5, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 159, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u5, x5, nt5 = lax_friedrichs_convection(0.5, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 160, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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yexGJawrk5ESL9Jmz8CdMERGJRZmpcMAP5/exU1lvsq0m/BLMI6U6bIxKcvKv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\nf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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(u5,x5,nt5,u55, x55, nt55)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* Numerical dissipation and odd-even decoupling\n", "* Amount of diffusion is still increasing with increasing n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Design Algorithm to Solve Problem using Lax Wendroff Scheme\n", "\n", "## Space-time discretisation:\n", "\n", "* i $\\rightarrow$ index of grid in x\n", "* n $\\rightarrow$ index of time\n", "\n", "## Lax Wendroff scheme\n", "\n", "$$ u_i^{n+1} = u_i^n - {\\sigma \\over 2}(u_{i+1}^n - u_{i-1}^n) + {\\sigma^2 \\over 2} (u_{i+1}^n - 2u_i^n + u_{i-1}^n) $$" ] }, { "cell_type": "code", "execution_count": 138, "metadata": { "collapsed": false }, "outputs": [], "source": [ "def lax_wendroff_convection(sigma, nx, tmax, xmax, c):\n", " \"\"\"\n", " Returns the velocity field and distance for 1D linear convection\n", " \"\"\"\n", " # Increments\n", " dx = xmax/(nx-1)\n", " dt = ((dx * sigma) / c)\n", " nt = int(tmax/dt + 1)\n", "\n", " # Initial and Boundary Conditions\n", " u = initial_and_boundary_conditions(nx, nt)\n", "\n", " # X Loop\n", " x = np.zeros(nx)\n", " x = np.linspace(0.0,xmax,nx)\n", "\n", " i = 1\n", " # Loop - must loop as NumPy cannot be used for dependency reasons\n", " for n in range(0,nt-1):\n", " u[i:nx-1, n+1] = (u[i:nx-1, n] - 0.5*sigma*(u[i+1:nx, n] - u[i-1:nx-2, n]) +\n", " 0.5*(sigma**2)*(u[i+1:nx, n] - 2.0*u[i:nx-1, n] + u[i-1:nx-2, n]))\n", "\n", " return u, x, nt" ] }, { "cell_type": "code", "execution_count": 161, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u66, x66, nt66 = analytical(0.5, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 162, "metadata": { "collapsed": false }, "outputs": [], "source": [ "u6, x6, nt6 = lax_wendroff_convection(0.5, 101, 1.0, 5.0, 1.0)" ] }, { "cell_type": "code", "execution_count": 163, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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n7P1xzUxPCLc/frtas4mDYT+5hjtukCuigjzSsGCQabFTFk5kRu7YINcYtW3I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\nBwAAAAAOQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot(u6,x6,nt6,u66, x66, nt66)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "* This more accurately represents the step change\n", "* However, there is an oscillatory response" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "kernelspec": { "display_name": "Python [default]", "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": "3.5.2" } }, "nbformat": 4, "nbformat_minor": 0 }