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Unformatted text preview: MATH 445 COMPUTER PROJECT 2 DUE WEDNESDAY, DECEMBER 2, 2009 AT THE LECTURE You are free to use any programming language or environment and any help you want. Please, use at least a 10pt font, and do not submit more than 12 pages of printouts for this assignment. Points can be taken off for using very small letters or producing too many pages of output. The objective of this assignment is to see how implicit numerical schemes work for parabolic and hyperbolic equations. Problem 1. Consider the heat equation u t ( x,t ) = 0 . 25 u xx ( x,t ) , < t 2 , < x < 1 , with u (0 ,t ) = u (1 ,t ) = 0 and u ( x, 0) = 20 x, x 1 / 2 20(1 x ) , 1 / 2 x 1 . Solve it numerically by the CrankNicholson method taking h = k = 0 . 1. Plot a 3D graph of the result. Then compare the result with the Fourier series solution (use your judgement as to how many terms to keep in the Fourier series: this is your only chance to get to the exact solution as close as possible)....
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This note was uploaded on 10/06/2009 for the course MATH 445 taught by Professor Friedlander during the Fall '07 term at USC.
 Fall '07
 Friedlander
 Math

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