Differential Equations Lecture Work Solutions 322

Differential Equations Lecture Work Solutions 322 - 2....

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2. Prove that the CFL condition is the stability requirement when the Lax Wendrof method is applied to solve the simple 1-D wave equation. The diference equation is o± the ±orm: u n +1 j = u n j c t 2∆ x u n j +1 u n j 1 + c 2 (∆ t ) 2 2(∆ x ) 2 u n j +1 2 u n j + u n j 1 Substitute a Fourier mode as be±ore we get λ =1 ν 2 e e | {z } 2 i sin β + ν 2 2 e 2+ e | {z } 2cos β 2 Take the absolute value | λ | 2 = 1+ ν 2 (cos β 1) | {z } = Re ( λ )
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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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