Convergence of numerical schemes for short wave long wave interaction equations

Details Convergence of numerical schemes for short wave long wave interaction equations Convergence of numerical schemes for short wave long wave interaction equations

2009-12-10

arxiv.org/abs/0912.2027v2

Mathematics

Numerical Analysis

31 pages, 7 figures

Scientific paper

10.1142/S0219891611002573

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.

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