Solitons and shock waves solutions for the rosenau-kdv-RLW equation

Abstract

In this article, a space time numerical scheme has been proposed to approximate solutions of the nonlinear Rosenau-Korteweg-de Vries-Regularized Long Wave (Rosenau-KdV-RLW) equation which represents the dynamics of shallow water waves. The scheme is based on a septic B-spline finite element method for the spatial approximation followed by a method of lines for the temporal integration. The proposed scheme has been illustarated with two test problems involving single solitary and shock waves. To demonstrate the competency of the present numerical algorithm the error norms L2 , L and two lowest invariants MI and E I have been calculated. Linear stability analysis of the scheme has been studied using von-Neumann theory. The illustrated results confirm that the method is efficient and preserves desired accuracy.