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arXiv:0912.2027 [math.NA]AbstractReferencesReviewsResources

Convergence of numerical schemes for short wave long wave interaction equations

Paulo Amorim, Mário Figueira

Published 2009-12-10, updated 2010-12-22Version 2

We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schr\"odinger equation coupled with a hyperbolic conservation law. This system arises in models for the interaction of short and long waves. Using the compensated compactness method, we prove convergence of approximate solutions generated by semi-discrete finite volume type methods towards the unique entropy solution of the Cauchy problem. Some numerical examples are presented.

Comments: 31 pages, 7 figures
Categories: math.NA, math.AP
Subjects: 65M12, 35M31
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