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hw5 - Department of Chemical Engineering University of...

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Department of Chemical Engineering University of California, Santa Barbara Chemical Engineering 132B Computational Methods in Chemical Engineering Fall 2011 Homework #5 Homework due: Friday, 18 November 2011 1. Solve problem 1 on pages 349-350 in Bradie . 2. By hand, derive the Chebyshev differentiation matrix for N = 2, i.e. [ D 2 ]. Confirm your result by using the supplied function chebD.m . 3. Develop global approximants for the function y ( x ) = sin(2 x ) cos(5 x ) and its derivative over the interval x [0 , 1] by using 17 data points sampled from the function ( N = 16). (a) Interpolate the function using equally spaced points, and cubic spline interpolation. Assess the maximum error of the approximant over the interval. (b) Interpolate the function using Chebyshev points, and Chebyshev global interpolation. Assess the maximum error of the approximant over the interval x [0 , 1]. Note that you will have to rescale the interval to [ - 1 , 1] to do this! (c) Using second-order finite differences and the function data, obtain a global approximation for the derivative of the function. Assess the maximum error of the approximant over [0 , 1]. (d) Using Chebyshev differentiation and the function data, obtain a global approximation for the derivative of the function. Assess the maximum error of the approximant over the interval [0 , 1].
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