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

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.