{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Explicit Trapezoidal Method\n", "\n", "Our goal is to implement the explicit trapezoidal method and compare its error to that of the forward Euler method.\n", "\n", "The explicit trapezoidal incorporates the forward Euler method ($\\widehat{y_{FE}}$) and is defined\n", "\n", "The method is\n", "\n", "\\begin{equation*}\n", "\\widehat{y}(t + \\Delta t) = \\widehat{y}(t) + \\Delta t \\cdot \\frac{f(t,\\widehat{y}(t))+f(t+\\Delta t, \\widehat{y_{FE}}))}{2}\n", "\\end{equation*}\n", "\n", "where \n", "\n", "\\begin{equation*}\n", "\\widehat{y_{FE}}(t + \\Delta t) = \\widehat{y}(t) + \\Delta t \\cdot f(t,\\widehat{y}(t))\n", "\\end{equation*}\n", "\n", "We first need the degradation model and the forward Euler method (for comparison)." ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "import scipy.integrate\n", "\n", "def degradation_model( t, y, params ):\n", " y1 = y[0]\n", " y2 = y[1]\n", " dydt = np.zeros( (2,) )\n", " dydt[0] = -params[0] * y1\n", " dydt[1] = -params[1] * y2\n", " return dydt" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [], "source": [ "def forwardEuler( fn, t, y0, params ):\n", " \"\"\" [t,y] = forwardEuler( fn, t, y0, params )\n", " Given a function handle fn for dydt, find the value of\n", " y at timepoints t, given y(0) = y0.\n", " fn takes t, y, and params as input.\n", " t is 1-dimensional (NT,)\n", " y is 2-dimensional (NY,NT)\n", " \"\"\"\n", " y = np.zeros( (y0.size,t.size) )\n", " y[:,0] = y0;\n", " for i in range(1,t.size):\n", " h = t[i]-t[i-1];\n", " yprime = fn(t[i-1],y[:,i-1],params);\n", " y[:,i] = y[:,i-1] + h*yprime;\n", " \n", " return (t,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Implement Explicit Trapezoidal Method\n", "\n", "Implement the method so that is uses the same interface as Forward Euler.\n", "\n", "So you don't need to scan up, I retype the methor here:\n", "\n", "\\begin{equation*}\n", "\\widehat{y}(t + \\Delta t) = \\widehat{y}(t) + \\Delta t \\cdot \\frac{f(t,\\widehat{y}(t))+f(t+\\Delta t, \\widehat{y_{FE}}))}{2}\n", "\\end{equation*}\n", "\n", "where \n", "\n", "\\begin{equation*}\n", "\\widehat{y_{FE}}(t + \\Delta t) = \\widehat{y}(t) + \\Delta t \\cdot f(t,\\widehat{y}(t))\n", "\\end{equation*}" ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [], "source": [ "def explicitTrapezoidal( fn, t, y0, params ):\n", " \"\"\"[t,y] = explicitTrapezoidal( fn, t, y0, params )\n", " Given a function handle fn for y', find the value of\n", " y at timepoints t, assuming y(0) = y0.\n", " fn takes t, y, and params as input.\n", " t is 1-dimensional (NT,)\n", " y is 2-dimensional (NY,NT)\n", " \"\"\"\n", " y = np.zeros( (y0.size,t.size) )\n", " y[:,0] = y0;\n", " for i in range(1,t.size):\n", " h = t[i]-t[i-1];\n", " yprime = fn(t[i-1],y[:,i-1],params);\n", " yhatFE = y[:,i-1] + h*yprime;\n", " yprimehatFE = fn(t[i],yhatFE,params);\n", " y[:,i] = y[:,i-1] + h/2*(yprime+yprimehatFE);\n", "\n", " return (t,y)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Run and plot result from Explicit Trapezoidal method.\n", "\n", "Run both the forward Euler and explicit trapezoidal methods on the degradation model with degradation rates (2,5) and initial conditions (1,1) with time steps from 0 to 4 with a step of 0.1.\n", "\n", "Then plot the true solution (solid lines), forward Euler's solution (dashed lines), and explicit trapezoidal's solution (dotted lines).\n", "\n", "Then plot the difference over time between the true solution and forward Euler's solution (dashed lines) and then the difference over time between the true solution and explicit trapezoidal's solution (dotted lines)." ] }, { "cell_type": "code", "execution_count": 81, "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import matplotlib.pyplot as plt\n", "params = np.array([2,5])\n", "y0 = np.array([1,1])\n", "t = np.arange(0,4,0.1)\n", "(tFE,yFE) = forwardEuler( degradation_model, t, y0, params)\n", "tru_y1 = y0[0]*np.exp(-params[0]*t)\n", "tru_y2 = y0[1]*np.exp(-params[1]*t)\n", "tru_y = np.vstack( ( tru_y1, tru_y2) )\n", "\n", "(t,y) = explicitTrapezoidal( degradation_model, t, y0, params)\n", "plt.figure( figsize = (8,4) )\n", "plt.subplot(2,1,1)\n", "plt.plot(t, tru_y.T )\n", "plt.plot(tFE, yFE.T);\n", "plt.plot(t,y.T)\n", "plt.subplot( 2, 1, 2 )\n", "plt.plot( t, tru_y.T-yFE.T, '--' )\n", "plt.gca().set_prop_cycle(None) # this resets the color cycle\n", "plt.plot( t, tru_y.T-y.T, ':');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Error vs Step Size\n", "\n", "Determine how the error changes with the time step for both forward Euler and Explicit Trapezoidal. Plot two figures - one with the simulations and one with the errors. Compute the error using one method: Compute the Euclidean distance between the true solution and the approximate solution (2-norm of the difference) at each time point, then take the mean across time.\n", "\n", "Make an array of time steps. For each time step, plot each solution in a separate subfigure, and keep track of the error in an array. Then plot the errors in a second figure, with each error computation in a separate subfigure." ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# range from smallest timestep that doesn't take way too long to run to largest time step with qualitatively correct answer.\n", "dts = np.linspace(1e-4,0.2,10)\n", "err1 = np.zeros( (dts.size,) )\n", "err2 = np.zeros( (dts.size,) )\n", "params = (2,5)\n", "y0 = np.array((1,1))\n", "\n", "plt.figure(figsize=(8,12))\n", "for i in range(dts.size):\n", " t = np.arange(0,4,dts[i])\n", " sol = scipy.integrate.solve_ivp(fun=degradation_model, t_span=(0,150), y0=y0, method='LSODA', rtol=1e-8, atol=1e-8, t_eval=t, args=[params] )\n", " (t,y) = forwardEuler( degradation_model, t, y0, params)\n", " plt.subplot( dts.size, 1, i+1 )\n", " plt.plot( t, sol.y.T )\n", " plt.gca().set_prop_cycle(None) # this resets the color cycle\n", " plt.plot( t, y.T, '--')\n", " err1[i] = np.mean(scipy.linalg.norm( sol.y-y, 2, axis=0) )\n", " plt.gca().set_prop_cycle(None) # this resets the color cycle\n", " (t,y) = explicitTrapezoidal( degradation_model, t, y0, params)\n", " plt.plot( t, y.T, ':')\n", " err2[i] = np.mean(scipy.linalg.norm( sol.y-y, 2, axis=0) )\n", "plt.tight_layout()\n", " \n", "plt.figure()\n", "plt.plot( dts, err1, '.-' );\n", "plt.plot( dts, err2, '.-' );\n", "plt.legend( ['FE Error','ET Error']);\n", "plt.xlabel( 'Size of Time Step');\n", "plt.ylabel( 'Error');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Bonus Code\n", "This is the code Stephanie used to generate the illustration figure for her lecture notes." ] }, { "cell_type": "code", "execution_count": 83, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Illustrate one step of the explicit trapezoidal method\n", "\n", "def degradation_model1D( t, y, params ):\n", " dydt = -params[0] * y;\n", " return dydt\n", "fn = degradation_model1D\n", "\n", "# set up the usual problem, with a faster degradation rate \n", "# to exaggerate the differences somewhat.\n", "y0 = 1\n", "params = (5,)\n", "h = 0.1 # step size\n", "t0 = 0 # first time step\n", "\n", "# one step of trapezoidal method\n", "yprime = fn(t0,y0,params);\n", "yhatFE = y0 + h*yprime;\n", "yprimehatFE = fn(t0+h,yhatFE,params);\n", "yhat = y0 + h*(yprime+yprimehatFE)/2;\n", "\n", "# To get the curvature, compute the true solution over 10\n", "# steps within this single step.\n", "tru_t = np.linspace(0,h,10)\n", "tru_y = y0*np.exp(-params[0]*tru_t)\n", "\n", "# Plot the true solution, along with the interdediate estimate\n", "# and the slopes.\n", "plt.plot( tru_t, tru_y, 'k' );\n", "plt.plot( [t0, t0+h], [y0, yhatFE]);\n", "plt.plot( [t0+h-0.02,t0+h+0.02], [yhatFE-0.02*yprimehatFE,yhatFE+0.02*yprimehatFE]);\n", "plt.plot( [t0,t0+h],[y0,yhat]);\n", "plt.annotate( \"y0=%0.2f\\nf(y0)=%0.2f\"% (y0,yprime), (t0,y0), (t0+0.03,y0-0.05), \n", " xycoords='data', arrowprops={'arrowstyle':'->'});\n", "plt.annotate( \"y1=%0.2f\\nf(y0)=%0.2f\"% (tru_y[-1],fn(t0+h,tru_y[-1],params)), (t0+h,tru_y[-1]), (t0+h+0.03,y1-0.05), \n", " xycoords='data', arrowprops={'arrowstyle':'->'});\n", "plt.annotate( \"yhatFE=%0.2f\\nf(yhatFE)=%0.2f\"% (yhatFE,yprimehatFE), (t0+h,yhatFE), (t0+h-0.04,yhatFE-0.05), \n", " xycoords='data', arrowprops={'arrowstyle':'->'});\n", "plt.annotate( \"yhat=%0.2f\"% (yhat), (t0+h,yhat), (t0+h-0.02,yhat+0.1), \n", " xycoords='data', arrowprops={'arrowstyle':'->'});\n", "plt.annotate( \"slope of blue line = %0.2f\" % yprime, (0.005,0.7))\n", "plt.annotate( \"slope of green line = %0.2f\" % ((yprime+yprimehatFE)/2), (0.05,0.85) );\n", "plt.xlabel( \"Time\");" ] } ], "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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 4 }