ERKN integrators solving multi-frequency highly oscillatory systems with applications

摘要

This paper presents an introduction to ERKN integrators for multi-frequency highly oscillatory systems with applications to nonlinear Klein-Gordon equations. The result of error analysis stated in this paper is a nature extension of that for Gautschi-type methods of order two. In particular, the error bound of ERKN integrators, when applied to nonlinear Klein-Gordon equations, is shown to be independent of the refinement of spatial discretisation based on the finite energy condition which appeared in the literature.