A new conservative fourth‐order accurate difference scheme for solving a model of nonlinear dispersive equations

Abstract

This article is devoted to the study of a nonlinear conservative fourth‐order difference scheme for a model of nonlinear dispersive equations that is governed by the RLW‐KdV equation. The existence of the approximate solution and the convergence of the difference scheme are proved, by using the energy method. In addition, the convergent order in maximum norm is 2 in temporal direction and 4 in spatial direction. The unconditional stability as well as uniqueness of the difference scheme is also derived. An application on the RLW and MRLW equations is discussed numerically in details. Furthermore, interaction of solitary waves with different amplitudes are shown. The 3 invariants of the motion are evaluated to determine the conservation proprieties of the system. The temporal evaluation of a Maxwellian initial pulse is then studied. Some numerical examples are given to validate the theoretical results.