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ComputerProb2 - Sep 12 2006 ATMS 502 CS 505 CSE 566 Jewett...

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1 Sep. 12, 2006 ATMS 502 - CS 505 - CSE 566 Jewett Computer Problem 2 2- and 3-time-level multi-method comparison and evaluation Due : beginning of class – Thursday, Sep. 28. Turn in : your code (printed out, and also emailed to me), and plotted results (on paper). Problem being solved: linear advection equation. Boundary condition: periodic; c>0. Evaluation: you will overlay the true solution with each of your numerical results, as well as compute error statistics following Takacs (1985, eqn. 6.1-6.7). Schemes: there are three: 1. Lax-Wendroff (from computer problem 1) u j n + 1 = u j n " # 2 u j + 1 n " u j " 1 n ( ) + $ u j + 1 n " 2 u j n + u j " 1 n ( ) 2. Takacs (1985, eqn. 4.3) u j n + 1 = u j n " # 2 u j + 1 n " u j " 1 n ( ) + # 2 2 u j + 1 n " 2 u j n + u j " 1 n ( ) " $# # " 1 ( ) u j + 1 n " 3 u j n + 3 u j " 1 n " u j " 2 n ( ) 3. Leapfrog (3-time-level) u j n + 1 = u j n " 1 " # u j + 1 n " u j " 1 n ( ) (no Asselin filtering) Note the additional boundary term (j-2) above; you will have to change your array dimensions. For all of the above, " = c # t # x , and $ = 1 + " 6 ; all problems are linear.
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