{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1 - integration of infinite intervals\n", "\n", "Calculate the value of the following integral using Gaussian quadrature: $$I=\\int_0^\\infty e^{-t^2}dt$$ The value of this integral is known analytically: $I=\\frac{1}{2}\\sqrt{\\pi}=0.886226925453\\ldots$. \n", "\n", "To solve the integral numerically, make the change of variables $z=t/(1+t)$. The integral becomes $$I=\\int_0^1 \\frac{e^{-z^2/(1-z)^2}}{(1-z)^2}dz .$$ \n", "\n", "1. Plot the functions $ f(x)=e^{-t^2} $ and $i(z)=\\frac{e^{-z^2/(1-z)^2}}{(1-z)^2}$.\n", "2. Change your Gauss-Legendre integration program from last week to solve this integral. \n", "3. Plot the value of the integral and/or the integration error as a function of integration points.\n", "\n", "## Talking points\n", "\n", "1. What do you observe?\n", "2. How many points do you need for 0.1% accuracy and how many for $10^{-6}$% accuracy? " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1.1a\n", "\n", "Plot the function $ f(x)=e^{-t^2}$." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from numpy import linspace,exp\n", "import matplotlib.pyplot as plt \n", "\n", "# start and end points\n", "a = 0.0\n", "b = 4.0\n", "points = 100\n", "\n", "# Set up lists for plotting\n", "y = []\n", "x = linspace(a,b,points)\n", "\n", "# generate the function values\n", "for xi in x:\n", " val = exp(-xi**2)\n", " y.append(val)\n", "\n", "# Make the graph\n", "plt.rc('font',size=16) # set the font size\n", "plt.plot(x,y)\n", "plt.xlabel('x')\n", "plt.ylabel('f(x)')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1.1b\n", "\n", "Plot the function $i(z)=\\frac{e^{-z^2/(1-z)^2}}{(1-z)^2}$." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from numpy import linspace,exp\n", "import matplotlib.pyplot as plt \n", "\n", "# start and end points\n", "a = 0.0\n", "b = 0.99\n", "points = 30\n", "\n", "# Set up lists for plotting\n", "y = []\n", "x = linspace(a,b,points)\n", "\n", "# generate the function values\n", "for xi in x:\n", " denom = (1.0-xi)**2\n", " val = exp(-(xi**2)/denom)/denom\n", " y.append(val)\n", "\n", "# Make the graph\n", "plt.rc('font',size=16) # set the font size\n", "plt.plot(x,y)\n", "plt.xlabel('z')\n", "plt.ylabel('i(z)')\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 1.2 \n", "\n", "Change your Gauss-Legendre integration program from last week to solve this integral. Plot the value of the integral and/or the integration error as a function of integration points.\n" ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from numpy import linspace,exp,sqrt,pi\n", "from gaussxw import gaussxwab\n", "import matplotlib.pyplot as plt \n", "\n", "# define function, bounds and value of integral\n", "def f(z):\n", " return exp(-z**2/(1-z)**2)/(1-z)**2\n", "a = 0.0\n", "b = 1.0\n", "val = 0.5*sqrt(pi)\n", "\n", "# Set up lists for plotting\n", "y = []\n", "x = []\n", "err1 = 0.1\n", "err2 = 1E-6\n", "\n", "# define settings for convergence loop\n", "factor = 2\n", "initial = 2\n", "increments = 8\n", "\n", "# convergence loop\n", "N = initial\n", "for i in range(1,increments):\n", " N = N*factor\n", " z,w = gaussxwab(N,a,b)\n", " s = 0.0\n", " for k in range(N):\n", " s += w[k]*f(z[k])\n", " error = abs((val-s)/val*100) # compute error\n", " y.append(error)\n", " x.append(N)\n", "\n", "# Make the graph\n", "plt.rc('font',size=16) # set the font size\n", "plt.plot(x,y)\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.plot(x,y,\"ko\")\n", "plt.xlabel('Number of integration points')\n", "plt.ylabel('Integration error in %')\n", "plt.hlines(err1,x[0],x[increments-2],linestyles='dashed',colors='k')\n", "plt.hlines(err2,x[0],x[increments-2],linestyles='dashed',colors='k')\n", "plt.hlines(1E-14,x[0],x[increments-2],linestyles='dashed',colors='k')\n", "plt.text(50, err1+4E-2, '0.1% error')\n", "plt.text(50, err2+4E-7, '1E-6% error')\n", "plt.text(5, 1E-14+4E-14, 'machine precision')\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2 - multi dimensional integrals\n", "\n", "Calculate the double integral $\\DeclareMathOperator\\erf{erf} \\int_{-1}^1\\int_{-1}^1 e^{(-x^2-y^2)} dx dy = \\pi \\erf(1)^2$ numerically. \n", "\n", "1. Plot the functions $ e^{(-x^2-y^2)}$.\n", "2. Adapt your Gauss-Legendre integration program to solve this integral. \n", "3. Plot the value of the integral and/or the integration error as a function of integration points.\n", "\n", "## Talking points\n", "\n", "1. What do you observe?\n", "2. How many points do you need for 0.1% accuracy and how many for $10^{-6}$% accuracy?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2.1\n", "\n", "Plot the functions $ e^{(-x^2-y^2)}$." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "import matplotlib.pyplot as plt\n", "from mpl_toolkits.mplot3d import Axes3D\n", "from matplotlib import cm\n", "\n", "f = lambda x,y: exp(-x**2-y**2)\n", "\n", "fig = plt.figure(figsize=(12,6))\n", "\n", "ax = fig.add_subplot(1,2,1,projection='3d')\n", "\n", "xvalues = np.linspace(-1,1,100)\n", "yvalues = np.linspace(-1,1,100)\n", "xgrid, ygrid = np.meshgrid(xvalues, yvalues)\n", "zvalues = f(xgrid, ygrid)\n", "\n", "surf = ax.plot_surface(xgrid, ygrid, zvalues, rstride=5, cstride=5, linewidth=0, cmap=cm.plasma)\n", "\n", "ax = fig.add_subplot(1,2,2)\n", "\n", "plt.contourf(xgrid, ygrid, zvalues, 30, cmap=cm.plasma)\n", "fig.colorbar(surf, aspect=18)\n", "plt.tight_layout()\n", "\n", "None" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 2.2\n", "\n", "Adapt your Gauss-Legendre integration program to solve the integral $ \\int_{-1}^1 \\int_{-1}^1 e^{(-x^2-y^2)} dx dy$. Plot the value of the integral and/or the integration error as a function of integration points." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from numpy import linspace,exp,sqrt,pi\n", "from math import erf\n", "from gaussxw import gaussxwab\n", "import matplotlib.pyplot as plt \n", "\n", "# define function, bounds and value of integral\n", "def f(x,y):\n", " return exp(-x**2-y**2)\n", "ax = -1.0\n", "bx = 1.0\n", "ay = -1.0\n", "by = 1.0\n", "\n", "val = pi*erf(1)**2\n", "\n", "# print('val: ',val)\n", "\n", "# Set up lists for plotting\n", "y = []\n", "x = []\n", "err1 = 0.1\n", "err2 = 1E-6\n", "\n", "# define settings for convergence loop\n", "factor = 1\n", "initial = 1\n", "increments = 10\n", "\n", "# convergence loop\n", "N = initial\n", "for i in range(1,increments):\n", " N = N+factor\n", " zx,wx = gaussxwab(N,ax,bx)\n", " zy,wy = gaussxwab(N,ay,by)\n", " s = 0.0\n", " for k in range(N): # x integration\n", " for j in range(N): # y integration\n", " s += wx[k]*wy[j]*f(zx[k],zy[j])\n", " error = abs((val-s)/val*100) # compute error\n", " # print('N: ',N,' integral: ',s,' error: ',error)\n", " y.append(error)\n", " x.append(N)\n", "\n", "# Make the graph\n", "plt.rc('font',size=16) # set the font size\n", "plt.plot(x,y)\n", "plt.xscale('log')\n", "plt.yscale('log')\n", "plt.plot(x,y,\"ko\")\n", "plt.xlabel('Number of integration points')\n", "plt.ylabel('Integration error in %')\n", "plt.hlines(err1,x[0],x[increments-2],linestyles='dashed',colors='k')\n", "plt.hlines(err2,x[0],x[increments-2],linestyles='dashed',colors='k')\n", "plt.hlines(1E-14,x[0],x[increments-2],linestyles='dashed',colors='k')\n", "plt.text(6, err1+4E-2, '0.1% error')\n", "plt.text(2, err2+5E-7, '1E-6% error')\n", "plt.text(2, 1E-14+4E-14, 'machine precision')\n", "\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 3 - numeric differentiation\n", "\n", "Calculate the derivative of $f(x)=x^3-2x^2+x-1$ numerically with the forward $\\left( \\frac{df}{dx} \\approx \\frac{f(x+h)-f(x)}{h}\\right)$ or the backward difference $\\left( \\frac{df}{dx} \\approx \\frac{f(x)-f(x-h)}{h} \\right)$ method. \n", "\n", "1. Use the forward and backward difference rule to calculate $f'(x)$ for $h=0.1$ and $h=0.01$.\n", "2. Plot the analytic derivative and your numeric derivatives in the same graph. \n", "3. Plot the difference between the analytic and the numeric derivatives.\n", "\n", "## Talking points\n", "\n", "1. What do you observe?\n", "2. How does the error in the numeric derivatives behave with $x$ and $h$?\n", "3. How can we do better?\n", "\n", "\n", "## Exercise 3.1 and 3.2\n", "\n", "Calculate the derivative of $f(x)=x^3-2x^2+x-1$ numerically. Use the forward and backward difference rule to calculate $f'(x)$ for $h=0.1$ and $h=0.01$. Plot the analytic derivative and your numeric derivatives in the same graph. " ] }, { "cell_type": "code", "execution_count": 56, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from numpy import linspace\n", "import matplotlib.pyplot as plt \n", "\n", "# define function, bounds and value of integral\n", "def f(x):\n", " return x**3-2*x**2+x-1\n", "def g(x):\n", " return 3*x**2-4*x+1\n", "\n", "a = 0.0\n", "b = 2.0\n", "points = 30\n", "h = 0.1\n", "\n", "# Set up lists for plotting\n", "y = []\n", "x = linspace(a,b,points)\n", "fda = []\n", "bda = []\n", "\n", "# generate the function values\n", "for xi in x: \n", " fd = (f(xi+h)-f(xi))/h\n", " fda.append(fd)\n", " bd = (f(xi)-f(xi-h))/h\n", " bda.append(bd)\n", " y.append(g(xi))\n", "\n", "# Make the graph\n", "plt.rc('font',size=16) # set the font size\n", "plt.plot(x,y,\"k\")\n", "plt.plot(x,fda,\"bo\",label='forward difference')\n", "plt.plot(x,bda,\"ro\",label='backward difference')\n", "plt.xlabel('x')\n", "plt.ylabel('df/dx')\n", "plt.legend(loc=\"upper left\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 3.3 \n", "\n", "Plot the difference between the analytic and the numeric derivatives." ] }, { "cell_type": "code", "execution_count": 65, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from numpy import linspace\n", "import matplotlib.pyplot as plt \n", "\n", "# define function, bounds and value of integral\n", "def f(x):\n", " return x**3-2*x**2+x-1\n", "def g(x):\n", " return 3*x**2-4*x+1\n", "\n", "a = 0.0\n", "b = 2.0\n", "points = 30\n", "h1 = 0.1\n", "h2 = 0.01\n", "\n", "# Set up lists for plotting\n", "y = []\n", "x = linspace(a,b,points)\n", "fda1 = []\n", "bda1 = []\n", "fda2 = []\n", "bda2 = []\n", "\n", "# generate the function values\n", "for xi in x: \n", " fd = (f(xi+h1)-f(xi))/h1\n", " fda1.append(fd-g(xi))\n", " fd = (f(xi+h2)-f(xi))/h2\n", " fda2.append(fd-g(xi))\n", " bd = (f(xi)-f(xi-h1))/h1\n", " bda1.append(bd-g(xi))\n", " bd = (f(xi)-f(xi-h2))/h2\n", " bda2.append(bd-g(xi))\n", " y.append(g(xi))\n", "\n", "# Make the graph\n", "plt.rc('font',size=16) # set the font size\n", "#plt.plot(x,y,\"k\")\n", "plt.plot(x,fda1,\"b-\",label='forward')\n", "plt.plot(x,bda1,\"r-\",label='backward')\n", "plt.plot(x,fda2,\"b--\")\n", "plt.plot(x,bda2,\"r--\")\n", "plt.xlabel('x')\n", "plt.ylabel('difference')\n", "plt.legend(loc=\"upper left\")\n", "plt.text(1.5,0.2,'h=0.1',color=\"blue\")\n", "plt.text(1.5,0.07,'h=0.01',color=\"blue\")\n", "plt.text(1.5,-0.23,'h=0.1',color=\"red\")\n", "plt.text(1.5,-0.1,'h=0.01',color=\"red\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 4 - central difference method\n", "\n", "Calculate the derivative of $f(x)=x^3-2x^2+x-1$ numerically with the central difference $\\left( \\frac{df}{dx}\\approx\\frac{f((x+h/2)-f(x-h/2)}{h}\\right) $ method. \n", "\n", "1. Use the central difference rule to calculate $f'(x)$ for $h=0.1$ and $h=0.01$.\n", "2. Plot the analytic and your numeric derivative in the same graph. \n", "3. Plot the difference between the analytic and the numeric derivative.\n", "\n", "## Talking points\n", "\n", "1. What do you observe?\n", "2. How does the error in the numeric derivatives now behave with $x$ and $h$?\n", "\n", "## Exercise 4.1 and 4.2\n", "\n", "Use the central difference rule to calculate $f'(x)$ for $h=0.1$ and $h=0.01$. Plot the analytic and your numeric derivative in the same graph." ] }, { "cell_type": "code", "execution_count": 67, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from numpy import linspace\n", "import matplotlib.pyplot as plt \n", "\n", "# define function, bounds and value of integral\n", "def f(x):\n", " return x**3-2*x**2+x-1\n", "def g(x):\n", " return 3*x**2-4*x+1\n", "\n", "a = 0.0\n", "b = 2.0\n", "points = 30\n", "h = 0.1\n", "\n", "# Set up lists for plotting\n", "y = []\n", "x = linspace(a,b,points)\n", "cda = []\n", "\n", "# generate the function values\n", "for xi in x: \n", " cd = (f(xi+0.5*h)-f(xi-0.5*h))/h\n", " cda.append(cd)\n", " y.append(g(xi))\n", "\n", "# Make the graph\n", "plt.rc('font',size=16) # set the font size\n", "plt.plot(x,y,\"k\")\n", "plt.plot(x,cda,\"bo\",label='central difference')\n", "plt.xlabel('x')\n", "plt.ylabel('df/dx')\n", "plt.legend(loc=\"upper left\")\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Exercise 4.3\n", "\n", "Plot the difference between the analytic and the numeric derivative." ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "data": { "image/png": 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pD8l0UY8UEduRrEEckjoApwFPR0SmB/gkSSL7Tk78GcBr6SjGcjidJGm9XKb1mVk7VV9fz4gRI9hzzz3p3bs3kydPZsuW5g96bmho4Mknn2TMmDFbkxbAmDFjqKmpYebMfGPkttltt1JSQ+WV0uN6lOQ+rtkt2N4dJE9LninpSpJf/NcA7wBTM5Uk9QbeJJntYjJARCyQNA2YIqkjycjA84C+ZCWpiFgp6RaSpzV/BMwnSW5DyRlyL6k/23pinYHekkann5+PiPfTttxHMux+KUlv7hTgTGBqRLzZgv1hZi0wfjwsWNC2bRg4EKZMadk6TjnlFMaNG8dFF13Eo48+ysSJE+nZsyfjxo0DKPoaWIcOya/0N998k40bN3LYYYdtt7xTp07069ePxYvLdeKpbZSSuP4ZuFfSFpKbeHe4VhQRy5paQUR8LGkoyYwT95GcbptFMuXTuqyqAnZnxx7hOOA64FqSYekLgeERMT+n3hXAOuBCtk35NCYiHs2pNwaYmPX5uPQF8DXgOeCj9LtOAD5HkmxfB/4Bz4hvZmVwySWXbE1Sxx9/PLNnz+aBBx7YWpbda2pK5rL+6tXJr+euXXccrN2tW7ety6tVKYkrc5pwEtv/ss+2e6GVpHMSfrtAneXkGQUYERuAi9NXU/GfkiS3awvUm0TyfZqqsxo4uak6ZtY2WtrT2VmMGLHdTHocdthhvPLKK1s/v/xyaVckMgks302+O94pVH1KSVxn4YEIZmZl163b9oOta2tr2bhx49bPAwcObNb68vWs1qxZw4AB+cbIVY+iE1dE3NOK7TAzs0aUeqqwX79+1NbWsmjRou2Wb9y4kWXLlnHqqYUmKtq5lTxzRvrIkP4kz9+aGxEfl71VZma2VamnCmtqahg+fDgPPfQQkyZN2jpoY8aMGWzatImRI0e2RjMrpqTEJel8kutb+5KcNvxrYL6k/wRmR8Q/lb2FZmbtXF1dXckxkyZNYsiQIYwZM4bzzz+f5cuXc9lllzF69GgGDRq0td69997LWWedxaxZszj22GO3ls+YMQOAefPmAfDEE0/QvXt3unfvvl29tlB04pKUmeboLuBptn/+1m9JBlw4cZmZ7QQGDhzIU089xYQJExgxYgR777033/ve97j++uu3q7dlyxY+/fTTHQZt5J5O/OEPfwjAsccey3PPPdeqbS9ExY4wkfQ68EhETJC0O8kjRuoiYn76MMk7I2K/Vmxr1aqrq4u5c+e2dTPMqtrrr7/OF77whbZuhpVRoX9TSfMiYofuZim3R/cFnmpk2cck91WZmZm1qlIS1yqgTyPLDiF5IrKZmVmrKiVxPQpcnT3PIBCS9gUuAv6znA0zMzPLp5TEdSXJo0xeA54hGVX4TyTTH30KTC5768zMzHIUnbgi4i8kz566gWSW9jdJRiXeBgyJiA9bpYVmZmZZihoOL6kG+Bnw7xFxDcmM7mZmZhVXVI8rIj4BziV59IeZmVmbKeUa1yvA4a3VEDMzs2KUkrguAS6VdJLyzZVvZmZWAaXMVTgd2BuYCWyWtJLtH3MSEdG7nI0zMzPLVUqPaxbwa+Be4N9JhsTPynrNLnvrzMx2YZMmTUISmzdvbpX1v/DCC3z5y1+mc+fO7Lffflx88cVs2LChqNh33nmH0aNHs/fee7PXXnvxrW99i7fffnu7Oh999BGXXnopxx13HHvttReSKjKPYSnP4zqzFdthZmZl9Oqrr3LCCScwbNgwHnvsMerr67nssstYsWIF06ZNazJ2/fr1DB06lNraWn71q18hiSuvvJKvfe1rvPrqq+yxxx4A/OUvf+Guu+7iqKOO4oQTTuDhhx+uxFcr/XlcZma285s4cSIHHHAA06dP3/ogypqaGsaOHcuECRM46qijGo294447WLZsGUuWLOGggw4C4IgjjuDggw9m6tSpXHzxxQD07t1761OWn3nmmYolrlJOFSLpi5IelrRK0mZJR6Xl10sa3jpNNDPbtdXX1zNixAj23HNPevfuzeTJk9myZUuz19fQ0MCTTz7JmDFjtnt68pgxY6ipqWHmzJlNxj/yyCMMHjx4a9IC6Nu3L0cfffR2sW01Tq+U53F9heS61jKSa1wXZC3eAvw98GRZW2dm1pTx42HBgrZtw8CBMGVKi1ZxyimnMG7cOC666CIeffRRJk6cSM+ePRk3bhxA0dfAMk86fvPNN9m4cSOHHXbYdss7depEv379WLx4cZPrWbRoEaNGjdqhfMCAAUyfPr2otrSmUk4V3kjyWJOTgd3ZPnHNB75XvmaZmbUfl1xyydYkdfzxxzN79mweeOCBrWXZvaamZJ6vmDl917Vr1x3qdOvWbevyxqxevbrR2DVr1hTVltZUSuI6CvhWRISk3KdPrgK6l69ZZmZFaGFPZ2cxYsSI7T4fdthhvPLKK1s/v/zyyyWtL5PA8p3KK+Hhwc2ObW2lJK6NQJdGln0e8CS7ZmbN0K1bt+0+19bWsnHjxq2fBw4c2Kz15etZrVmzhgEDBjQZ37Vr10Zj8/XEKq2UwRkvAOMl7Z5Vlkm/38f3cZmZtYqOHTsW9cro168ftbW1LFq0aLv1bNy4kWXLltG/f/8mtzdgwIAdYgEWL15cMLYSSulxXQW8CCwEZpAkrbGSbgYGAX9d/uaZmVmppwpramoYPnw4Dz30EJMmTdo6aGPGjBls2rSJkSNHNhk/cuRILr30UpYtW8aBBybPDl6+fDkvvvgiN954Y/O+RBmVcgPyQknHADcBVwAiGaDxW+DYiFjSOk00M2vf6urqSo6ZNGkSQ4YMYcyYMZx//vksX76cyy67jNGjRzNo0KCt9e69917OOussZs2axbHHHgvA2WefzW233caoUaO49tprkcRVV11Fz549Offcc7fbzhNPPMHHH3/M73//ewCef/55Vq1axR577MGJJ57Ygm/dhIho9AWMBPbOU94J+F9Al6biG1lnT5Ie24fAWuBhoFeRsZ1IEue7wAbgJeCYPPV2Ay4HlpNcm1sIfDtPvbEk01i9RdKDvKeJbZ9MMkP+xrT+lcDuxbR70KBBYWYts3jx4rZuQtlNnDgxgGhoaNiufOzYsdG7d+8Wr//555+PwYMHR21tbfTo0SMuvPDC+Pjjj7erc/fddwcQzz777Hblb731VnzrW9+Kz3zmM7HnnnvGqFGjor6+fodt9O7dO9Lfn9u9iml/oX9TYG7k+Z2qaGKUiKRPSZ5u/Lvsn5uXIkFSlzSJbEp/8QdwLcmgjyMi4uMC8f8GjAAuI7mf7HzgxLRdC7LqXQdcStIznAf8HXA2cFJEPJ5V779JRkPOBU4F/iPyTG0laRjwOHAn8ADwReB64NaImFDoe9fV1cXcuXMLVTOzJrz++ut84QtfaOtmWBkV+jeVNC8iduhuFjpVuI5kRnhITg221NnAgcAhEbE0bdirwBskD6q8ubFASUcCpwNnRcTdadnzwCJgMknvEEk9SJLWjRHx8zT8WUkHkdyL9njWaodFxJY0rqmZP24EXoiIc7LWtydwpaRbIuLPxe4AMzNrmUKJax4wVdJv0s9XSXq/kboREd8vsL6RwJxM0kqD6iW9CIyiicSVxjYAW2eHjIjNkh4EfiKpNiI2AcOAGuD+nPj7gbsk9Y2I+jS+4JwqknoCA4FzchbdB/yUpMd3d6H1mJlZeRRKXOcBtwDHkJzW+xvgk0bqFnNn2gCS53nlWkRyqq5QbH1ErM8TWwMclP48gORU5NI89QD6A/VFtDV7uwCvZRemCXd9uj4zM6uQJhNXJCMFvwEgaQvwzZZc4wK6AfnmC1kNFLqrranYzPLM+wex48W73HrFytTPt+01ja1P0jmkvbRevXqVuEkzM2tMkzcgpzPBZ6YHHkcymq+l8vXMirl+piJji61XrExcSeuMiNsjoi4i6rp392xYZuXQ1GAyqy4t+bcsNHPGKOCz6c93kUzt1BKN9VC6kr9Hk211E7GZ5Zn3rtpxoq3cesVqqqe2TzPWZ2bN0LFjx6Kf3ms7vw0bNhQ9eXCuQonrPWBw+nNjPZlSZK5B5eoPND3PfhLbNx1Snxv7CduuaS0CaoF+eepRxHbybRdy2i2pD8kw/lLXZ2bN0KNHD1asWMH69evd86piEcH69etZsWIFPXr0aNY6Cg3OeAi4JZ3WKYA5TTw4LCKi0PoeAX4u6cCIWAZbE8DRwE+KiP0pySCOX6WxHYDTgKfTEYWQPBPsE+A7af2MM4DXMiMKixURb0tamK7vlznrawCeKGV9ZtY8e+21FwB/+tOfaGhoaOPWWEt07NiRz33uc1v/TUtVKNFcRDI/YX9gInAPsKJZW0rcQTJN1ExJmRuQrwHeAaZmKknqDbwJTI6IyQARsUDSNGCKpI4kIwPPA/qSJBXSeisl3QJcLukjkmeFnQYMJTn1SdZ2+rOtJ9YZ6C1pdPr5+YjIDP3/R+AxSVPZdgPylSQ3IPseLrMK2WuvvZr9y852HYVGFQYwHUDSmSS/qBc2d2MR8bGkoSRD7O8jOf04CxgfEeuyqorkYZW5pzLHAdeRzLaxD8ksHMMjYn5OvStIbp6+ENgPWAKMiYhHc+qNIUnIGcelL4CvAc+l7X48TWgTgTNJTqFen7bFzMwqqMkpn6w8POWTmVnpmjXlUzob/PyIWJf+3KSI+E2hOmZmZi1R6BrXcySjCn+X/txY9ywz4nD3RpabmZmVRaHE9TXg9fTnobR8OLyZmVmLFBqc8XzWz8+1emvMzMwKKHSNa3YJ64qI+HoL22NmZtakQqcKd2P704OHkAwvX04yJPxzQB+SOQyXlL95ZmZm2yt0qvC4zM+STgZuBQZnzxAv6Uskz8i6tXWaaGZmtk2huQqzXQNclftYk4j4H2ASyU3BZmZmraqUxHUw0NjTj1eSPMjRzMysVZWSuOqBcxtZdi7JdS8zM7NWVWhwRrafAv8m6TVgBtsGZ4wGDiVrolszM7PWUnTiiogHJa0iSWCXAx1JHuvxMjAsIma1ThPNzMy2KaXHRUQ8AzwjaTdgX2BVRGxplZaZmZnlUVLiykiT1coyt8XMzKygUgZnmJmZtTknLjMzqypOXGZmVlWcuMzMrKo4cZmZWVVx4jIzs6rixGVmZlXFicvMzKqKE5eZmVUVJy4zM6sqTlxmZlZVnLjMzKyqOHGZmVlVqXjiktRT0gxJH0paK+lhSb2KjO0k6SZJ70raIOklScfkqbebpMslLZe0UdJCSd9uZJ1nS/qDpE2Slkj6+zx17pEUeV5TSt4BZmbWIs16rElzSeoCzAY2AWOBAK4FnpV0RER8XGAVdwIjgMuAZcD5wFOShkTEgqx61wCXAlcA84C/A6ZLOikiHs9qz9nAVOAG4Bng68AvJCki/iVn2+8DI3PK3i3qi5uZWdkoIiq3MelC4GbgkIhYmpb1Bd4AfhwRNzcReySwADgrIu5OyzoAi4AlETEyLesBvAPcGBETs+JnAd0j4ois2D8BT0TE2Kx6d5EkqM9HRENadg9wfEQc0JzvXVdXF3Pnzm1OqJlZuyVpXkTU5ZZX+lThSGBOJmkBREQ98CIwqojYBmBaVuxm4EFgmKTatHgYUAPcnxN/P3B4migBhgDd89S7D/gs8JUiv5OZmVVQpRPXAOC1POWLgP5FxNZHxPo8sTXAQVn1NgFL89QjazsD0vfc9uTWy+ghaZWkzZL+n6QJknYv0GYzMyuzil7jAroBa/KUrwa6tiA2szzz/kHseA40Xz3yrDO3HiSnKOeRJLVOwCkk18UOBn6Qr7GSzgHOAejVq6ixJ2ZmVoRKJy5IBmTkUhFxKjK2lHqNtWc7ETElp+hxSeuA8ZJ+FhFv5Im5HbgdkmtchbZhZmbFqfSpwjVs35PJ6Er+3lS21U3EZpZn3rtKyk1U+eqRZ53dcpY35oH0fYcLh2Zm1noqnbgWse3aUrb+wOIiYvumQ+pzYz9h2zWtRUAt0C9PPbK2k7mWldue3HqNKbrHZmZm5VPpxPUIMFjSgZkCSX2Ao9NlhWI7AqdmxXYATgOejohNafGTJInsOznxZwCvpaMYAV4CVjVSbzXJSMemnE6StF4uUM/MzMqo0te47gAuAGZKupLkF/81JPddTc1UktQbeBOYHBGTASJigaRpwBRJHYF64DygL1nJJyJWSroFuFzSR8B8kuQ2lKwh9xHRIOkqkhuOV5DcgDwUOAv4UUR8ktWW+0iG3S8l6c2dApwJTI2IN8u6h8zMrEkVTVwR8bGkocAtJMlAwCxgfESsy6oqYHd27BGOA64jmW1jH2AhMDwi5ufUuwJYB1wI7AcsAcZExKM57flXSQFcQjIbx9vABRHxi6xqH5H0wCYAnyNJtq8D/wBk1zMzswqo6MwZ7ZVnzjAzK93OMnOGmZlZizhxmZlZVXHiMjOzquLEZWZmVcWJy8zMqooTl5mZVRUnLjMzqypOXGZmVlWcuMzMrKo4cZmZWVVx4jIzs6rixGVmZlXFicvMzKqKE5eZmVUVJy4zM6sqTlxmZlZVnLjMzKyqOHGZmVlVceIyM7Oq4sRlZmZVxYnLzMyqihOXmZlVFScuMzOrKk5cZmZWVZy4zMysqjhxmZlZVXHiMjOzqlLxxCWpp6QZkj6UtFbSw5J6FRnbSdJNkt6VtEHSS5KOyVNvN0mXS1ouaaOkhZK+3cg6z5b0B0mbJC2R9PeN1DtZ0ivp+t6SdKWk3Uv79mZm1lIVTVySugCzgUOBscB3gYOBZyXtUcQq7gTOBq4GTgLeBZ6SNDCn3jXAJOA24ERgDjBd0jdy2nM2MBX4NTAcmA78QtJ5OfWGpXVeTtd3K3AlcH0RbTYzszJSRFRuY9KFwM3AIRGxNC3rC7wB/Dgibm4i9khgAXBWRNydlnUAFgFLImJkWtYDeAe4MSImZsXPArpHxBFZsX8CnoiIsVn17gJGAp+PiIa07BVgbUQcm1XvapLk1Ssi/tzU966rq4u5c+cWsYdyjB8PCxaUHmdmtrMYOBCmTGlWqKR5EVGXW17pU4UjgTmZpAUQEfXAi8CoImIbgGlZsZuBB4FhkmrT4mFADXB/Tvz9wOFpogQYAnTPU+8+4LPAVyA5tQkMbKReR5IemJmZVUiHCm9vADAzT/ki4NQiYusjYn2e2BrgoPTnAcAmYGmeegD9gfq0HsBrTdR7trF6EVEvaX1ar3U0868UM7NdWaV7XN2ANXnKVwNdWxCbWZ55/yB2PAearx551llsvUxZtzzlSDpH0lxJc99///18VczMrBnaYjh8votqKiJORcaWUq+x9hRbr9F2R8TtEVEXEXXdu3cvsAkzMytWpRNXYz2UruTv0WRb3URsZnnmvauk3KSSrx551tmtyHoA+2QtNzOzCqh04spcg8rVH1hcRGzfdEh9buwnbLumtQioBfrlqUfWdjLXsnLbU1Q9SX2ALkW028zMyqjSiesRYLCkAzMFaQI4Ol1WKLYjWYM40iHtpwFPR8SmtPhJkkT2nZz4M4DX0lGMAC8Bqxqpt5pkpCMR8TawsJF6DcATBdptZmZlVOlRhXcAFwAzJV1Jct3oGpL7rqZmKknqDbwJTI6IyQARsUDSNGCKpI4kIwPPA/qSlVQiYqWkW4DLJX0EzCdJbkPJGnIfEQ2SriK54XgF8Exa5yzgRxHxSVa7/xF4TNJU4AHgiyT3cN1a6B4uMzMrr4omroj4WNJQ4BaS+6AEzALGR8S6rKoCdmfHHuE44DrgWpLrSwuB4RExP6feFcA64EJgP2AJMCYiHs1pz79KCuAS4DLgbeCCiPhFTr3HJY0GJgJnAu+RzJpxXYm7wMzMWqiiM2e0V82eOcPMrB1rbOYMJ64KkPQ+8FYzw/cluRZnxfH+Ko33V2m8v0rXkn3WOyJ2uJ/IiWsnJ2luvr84LD/vr9J4f5XG+6t0rbHP/DwuMzOrKk5cZmZWVZy4dn63t3UDqoz3V2m8v0rj/VW6su8zX+MyM7Oq4h6XmZlVFScuMzOrKk5cbUBST0kzJH0oaa2khyX1KjK2k6SbJL0raYOklyQd09ptbmst3GfRyGtgKze7TUg6QNI/p8fG+vS79ikytr0eXy3ZZ+3t+Bot6deS3kqPkSWSbpD0mSJiy3J8OXFVWDq7/WzgUGAs8F3gYOBZSXsUsYo7gbOBq4GTgHeBp3bV/yRQln0GcA8wJOf1/8re2J3DQcAYkkcF/bbE2HZ3fKVass+gfR1flwKfkszhOhz4F5J5Y/9bUqGcUp7jKyL8quCLZP7ET4GDssr6ApuBiwvEHkkyMfG4rLIOJHMxPtLW321n3Gdp3QCubevvUcH9tVvWzz9Iv3+fIuLa5fHVkn2W1m9vx1f3PGXfS/fD0CbiynZ8ucdVeSOBORGReX4YkTxq5UWyZq9vIrYBmJYVuxl4EBgmqbb8zd0ptGSftTsRsaWZoe31+GrJPmt3IuL9PMUvp+/7NxFatuPLiavyBgCv5SlfxLaHWDYVWx8R6/PE1pCc7tgVtWSfZZwnaVN6/WK2pK+Wr3m7jPZ6fJVDez++jk3fX2+iTtmOLyeuyutGch4912qgawtiM8t3RS3ZZwD3Az8EjgfOAT4LzJZ0XJnat6tor8dXS7Xr40vS/sBk4JmIaOoxGGU7vir9IElL5LvrW0XEqQWx1a7Z3zsivpv18beSZpL04K4FvlKGtu0q2vPx1Wzt+fiStCcwk+R687hC1SnT8eUeV+WtIf9fFl3J/9dIttVNxGaW74pass92EBEfAf8F/HUL27Wraa/HV1m1l+NLUifgEeBAYFhE/LFASNmOLyeuyltEcq43V39gcRGxfdPh4bmxnwBLdwzZJbRknzWmsb/+2rP2eny1hl36+JLUEfg18DfANyLi90WEle34cuKqvEeAwZIOzBSkNzoenS4rFNsRODUrtgNwGvB0RGwqe2t3Di3ZZzuQtBcwAvifcjVwF9Fej6+y2tWPr/RerX8Dvg6Miog5RYaW7/hq63sC2tsL2IPkL4vfkwzlHgksBJYBe2bV601y3vjqnPgHSU6P/SA9cGYAG4Gj2vq77Yz7jORmyTuA04HjSG5g/j3JX3hfbevv1or7bHT6+heSv/zPSz8f6+OrfPusPR5fWfvnWmBwzuuAShxfbb4T2uML6EXSzV4LfAT8Jzk3OwJ90oNjUk55Z+Bm4M/pP/j/AMe19XfaWfcZ8E2S+71WkdxD8heSv/z+pq2/Uyvvr2jk9ZyPr/Lts/Z4fAHLm9hXkypxfPmxJmZmVlV8jcvMzKqKE5eZmVUVJy4zM6sqTlxmZlZVnLjMzKyqOHGZmVlVceIyM7Oq4sRlZmZVxYnLzMyqihOXWTsiaQ9Jf5D0u3SG70z530raIun8tmyfWTE85ZNZOyPpi8Ac4JaI+ImkHsCrwO8iYmTbts6sMCcus3ZI0kXA/wX+lmSG88OBIyNiVZs2zKwITlxm7ZAkkTyldyhQA5wQEbPatlVmxfE1LrN2KJK/WO8DaoGFTlpWTZy4zNohSfsBU4D5wJGSLmzbFpkVz4nLrJ1JTxP+iuQpvSeQJLCfSTqiLdtlVixf4zJrZyRdAvwfYGhEPC+phmSUYS1QFxEb2rSBZgW4x2XWjqRD4a8HboiI5wEi4hPgf5M8bv3mtmudWXHc4zIzs6riHpeZmVUVJy4zM6sqTlxmZlZVnLjMzKyqOHGZmVlVceIyM7Oq4sRlZmZVxYnLzMyqyv8HJqld3PcAAr0AAAAASUVORK5CYII=\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from numpy import linspace\n", "import matplotlib.pyplot as plt \n", "\n", "# define function, bounds and value of integral\n", "def f(x):\n", " return x**3-2*x**2+x-1\n", "def g(x):\n", " return 3*x**2-4*x+1\n", "\n", "a = 0.0\n", "b = 2.0\n", "points = 30\n", "h1 = 0.1\n", "h2 = 0.01\n", "\n", "# Set up lists for plotting\n", "y = []\n", "x = linspace(a,b,points)\n", "cda1 = []\n", "cda2 = []\n", "\n", "# generate the function values\n", "for xi in x: \n", " cd = (f(xi+0.5*h1)-f(xi-0.5*h1))/h1\n", " cda1.append(cd-g(xi))\n", " cd = (f(xi+0.5*h2)-f(xi-0.5*h2))/h2\n", " cda2.append(cd-g(xi))\n", " y.append(g(xi))\n", "\n", "# Make the graph\n", "plt.rc('font',size=16) # set the font size\n", "#plt.plot(x,y,\"k\")\n", "plt.plot(x,cda1,\"b-\",label='h=0.1')\n", "plt.plot(x,cda2,\"r-\",label='h=0.01')\n", "plt.xlabel('x')\n", "plt.ylabel('difference')\n", "plt.legend(loc=\"best\")\n", "\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "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": "3.7.8" } }, "nbformat": 4, "nbformat_minor": 4 }