A linearly implicit conservative difference scheme for the generalized Rosenau-Kawahara-RLW equation

TL;DR

This paper introduces a new linearly implicit difference scheme for the generalized Rosenau-Kawahara-RLW equation that conserves energy, is unconditionally stable, and achieves second-order accuracy, validated through numerical experiments.

Contribution

A novel energy-conserving, unconditionally stable, second-order accurate difference scheme for the generalized Rosenau-Kawahara-RLW equation is developed and analyzed.

Findings

The scheme conserves energy exactly.

The scheme is unconditionally stable.

Numerical experiments confirm second-order accuracy.

Abstract

This paper concerns the numerical study for the generalized Rosenau-Kawahara-RLW equation obtained by coupling the generalized Rosenau-RLW equation and the generalized Rosenau-Kawahara equation. We first derive the energy conservation law of the equation, and then develop a three-level linearly implicit difference scheme for solving the equation. We prove that the proposed scheme is energy-conserved, unconditionally stable and second-order accurate both in time and space variables. Finally, numerical experiments are carried out to confirm the energy conservation, the convergence rates of the scheme and effectiveness for long-time simulation.