Convergence of numerical schemes for short wave long wave interaction equations
Provides rigorous convergence guarantees for numerical schemes in a specific PDE system, but is incremental as it applies known techniques to a particular coupled equation set.
The paper proves convergence of semi-discrete finite volume methods for the short wave long wave interaction equations using compensated compactness, with numerical examples confirming the theoretical results.
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.