Two efficient numerical methods for solving Rosenau-KdV-RLW equation

Abstract

In this study, two efficient numerical schemes based on B-spline finite element method (FEM) and time-splitting methods for solving Rosenau-KdV-RLW equation are presented. In the first method, the equation is solved by cubic B-spline Galerkin FEM. For the second method, after splitting Rosenau-KdV-RLW equation in time, it is solved by Strang timesplitting technique using cubic B-spline Galerkin FEM. The differential equation system in the methods is solved by the fourth-order Runge-Kutta method. The stability analysis of the methods is performed. Both methods are applied to an example. The obtained numerical results are compared with some methods available in the literature via the error norms and , convergence rates, and mass and energy conservation constants. The present results are found to be consistent with the compared ones.

New approach for solving of Extended KdV Equation

“…There are many forms for KdVequation like Rosenau-KdV [1], extended KdV [2], generalized KdV [3], Rosenau KdV-RLW [4], KdV-Burger [5], the coupled Schrödinger-KdV equation [6], ect.. The KdV equation arises as an approximate equation governing weakly nonlinear long waves when terms up to the second order in the (small) wave amplitude are retained and when the weakly nonlinear and weakly dispersive terms are in balance.…”