Abstract:
I will describe a technique for constructing hyperbolic PDE approximations of higher order dispersive wave equations like the KdV, BBM, and NLS equations. These hyperbolic systems take the form of a relaxation system that formally approximates the original problem in the limit as the relaxation parameter vanishes. Then I will show how IMEX Runge-Kutta methods can be used to efficiently integrate these systems in a way that also ensures they numerically approximate the original problem when the relaxation parameter is small.