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This paper concerns the numerical study for the generalizedRosenau-Kawahara-RLW equation obtained by coupling the generalized Rosenau-RLWequation and the generalized Rosenau-Kawahara equation. We first derive theenergy conservation law of the equation, and then develop a three-levellinearly implicit difference scheme for solving the equation. We prove that theproposed scheme is energy-conserved, unconditionally stable and second-orderaccurate both in time and space variables. Finally, numerical experiments arecarried out to confirm the energy conservation, the convergence rates of thescheme and effectiveness for long-time simulation.

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