Evaluation of shallow water waves modelled by the Rosenau-Kawahara equation using pseudo-compact finite difference approach

Abstract

This paper presents a finite difference method for the Rosenau-Kawahara equation, which is performed under pseudo-compactness; this facilitates accuracy improvement. It is shown that the proposed scheme can generate a unique numerical solution with second-order convergence in both space and time and that the solution is stable with respect to (Formula presented.). Also, it turns out that discrete mass and energy at each time step maintain; hence conservation. To guarantee these theoretical results, some numerical experiments are conducted to show how accurate and efficient the scheme can perform. Furthermore, comparisons between the presented method and some existing ones are provided in order to ensure improvement.