A Legendre spectral element method for the family of regularized long wave equations

Abstract

Regularized Long Wave (RLW) equation is one of the most important nonlinear PDEs. It is related to the famous KdV equation and acts as an alternative for scrutinizing soliton phenomena. In this paper, we use the Legendre Spectral Element Method (LSEM) for the numerical study of the family of the RLW equations containing RLW, modified RLW, and generalized RLW. We perform the space discretization by the LSEM, and the Crank–Nicolson method is applied to discretize the time. To confirm the accuracy and efficiency of the proposed method, the conservation properties of the equations are checked, and various types of errors are reported.