A linearly implicit conservative difference scheme for the generalized Rosenau-Kawahara-RLW equation
This work provides a numerical method for solving a specific nonlinear wave equation, but it is an incremental contribution within the domain of numerical analysis.
The paper develops a three-level linearly implicit difference scheme for the generalized Rosenau-Kawahara-RLW equation, proving it is energy-conserved, unconditionally stable, and second-order accurate in time and space, with numerical experiments confirming these properties.
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.