Differential Equations Lecture Work Solutions 329

Differential Equations Lecture Work Solutions 329 - 1....

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1. Determine the errors in amplitude and phase for β =90 if the MacCormack scheme is applied to the wave equation for 10 time steps with ν = . 5 . Recall that | G | = 1 ν 2 (1 cos β ) sin β = ± [1 ν 2 (1 cos β )] 2 +( ν sin β ) 2 Given that β =90 then cos β =0ands in β = 1. Substitute these values and the given ν = . 5in | G | ,wehave | G | = ± [1 . 5 2 (1 0)] 2 +( . 5 · 1) 2 = ± [1 . 25] 2 + . 25 = s 9 16 + 1 4 = s 13 16 After 10 steps | G | 10 = s 13 16 10 = ² 13
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.

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