Convergence of numerical schemes for short wave long wave interaction equations

Paulo Amorim; Mário Figueira

doi:10.1142/s0219891611002573

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arXiv · 0912.2027

Convergence of numerical schemes for short wave long wave interaction equations

Paulo Amorim·Mário Figueira

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Abstract

We consider the numerical approximation of a system of partial differential equations involving a nonlinear Schrödinger 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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Paulo Amorim, Mário Figueira. 2010-12-22. Convergence of numerical schemes for short wave long wave interaction equations. https://doi.org/10.1142/s0219891611002573

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