Differential Equations Lecture Work Solutions 324

Differential Equations Lecture Work Solutions 324 - 4. In...

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4. In attempting to solve a simple PDE, a system of Fnite-di±erence equations of the form u n +1 j = 1+ νν 0 01 + - ν + ν u n j . Investigate the stability of the scheme. ²or the stability, we need || A || ≤ 1orthat | eig ( A ) |≤ 1. To compute the eigenvalues we need to solve 1+ ν λν 0 + ν ν + ν λ =0 or (1 + ν λ ) 3 ν 3 So ν λ = ν νe 2 πi/ 3 4 πi/ 3 λ = 1 ν 1 e 2 πi/ 3 ν 1 e 4 πi/ 3 Note that the last two eigenvalues are complex conjugate of each other. Now clearly the absolute value of the Frst is 1. The absolute value of the other two is the same and it is
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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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