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

In this study, two efficient numerical schemes based on B-spline finite element and time-splittings methods for solving Rosenau-KdV-RLW equation are going to be presented. As the first method, the equation is going to be solved by cubic B-spline Galerkin finite element method. For the second method, after splitting Rosenau-KdV-RLW equation in time, it is going to be solved by the second order Strang time-splitting technique using cubic B-spline Galerkin finite element method. The differential equation system encountered in the second method has been solved by the fourth order Runge-Kutta method. The stability analysis of the presented methods have been performed. Both methods have been applied to an example of which analytical solution is known. The numerical results obtained by the presented methods are compared with some those of the methods available in the literature by calculating the error norms L₂ and L_{∞}, convergence rates, mass and energy conservation constants. The obtained results have been found to be consistent with the compared ones.