Solitary wave solutions of the MRLW equation using a spatial five-point stencil of finite difference approximation

Abstract

This paper proposes a finite difference scheme with a three-level time and a five-point stencil in space to solve an initial boundary value problem for the MRLW equation. The scheme is shown to be marginally stable and convergent with a fourth-order convergence in the space direction and a second-order convergence in the time variable direction with regard to the maximum norm. The conservation properties of the proposed scheme are assessed using the three motion invariants for mass, momentum, and energy. To validate the theoretical results, numerical experiments are given for both single and interaction of two and three solitary waves.