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hw3 - (c Solve it numerically using a spectral method based...

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Department of Chemical Engineering University of California, Santa Barbara ChE 230A Fall 2006 Instructor: Glenn Fredrickson Homework #3 Homework Due: Thursday, Oct. 19, 2006 1. Prepare solutions to the following problems in your Riley, Hobson, and Bence text: 13.1, 13.5, 13.9, 13.22, and 13.24. 2. Consider the following boundary value problem: d 2 φ ( x ) dx 2 = 2 x 2 (1 - x ) 2 , x (0 , 1) φ (0) = φ (1) = 0 (a) Solve it exactly by variation of parameters. (b) Solve it formally by a sine Fourier series expansion.
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Unformatted text preview: (c) Solve it numerically using a spectral method based on the sine DFT. (Note that Mathematica has a built in version of a sine FFT algorithm.) (d) Check your results by numerically comparing the exact result obtained in (a) with your truncated sine FS expansion from (b) and with your numerical results from (c). Can you see a difference in the execution time of the latter two approaches? Can you explain it?...
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