A new conservative high-order accurate difference scheme for the Rosenau equation

Abstract

This article is devoted to the study of high-order conservative difference scheme for the Rosenau equation. The difference scheme is two-layered and a seven-point stencil is used for spatial variable. Existence of solutions is shown using a variant of Brouwer fixed point theorem. The unconditional stability as well as uniqueness of the scheme are also derived. The convergence of the difference scheme is proved by utilizing the energy method to be of fourth-order in space and second-order in time in the discrete -norm. Some numerical examples are given in order to validate the theoretical results.

Keywords:

• Rosenau equation
• conservative difference scheme
• stability
• high-order convergence

AMS Subject Classifications:

• 65M06
• 65N30

Acknowledgements

The authors would like to thank the editor and the reviewers for their valuable comments.