Discontinuous Galerkin method for numerical solution of the regularized long wave equation

In this paper we are concerned with the development of sufficiently robust, accurate and efficient numerical method for the solution of the regularized long wave (RLW) equation, an important nonlinear equation describing a large class of physical phenomena. The main idea is based on the discretization of the RLW equation with the aid of a combination of the discontinuous Galerkin method for the space semi-discretization and the backward difference formula for the time discretization. This proposed scheme seems to be a promising technique due to the high-order piecewise polynomial discontinuous approximation and avoiding the time step restriction. The appended numerical experiments investigate the conservative properties of the RLW equation related to mass, momentum and energy, and illustrate the potency of the scheme, consequently.