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 = 0 and sin β = 1. Substitute these values and the given ν = . 5 in | G | , we have | G | = [1 . 5 2 (1 0)] 2 + ( . 5 · 1) 2 = [1 . 25] 2 + . 25 = 9 16 + 1 4 = 13 16 After 10 steps | G | 10 = 13 16 10 = 13 16 5 . 354
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