Numerical computations for natural systems and acquiring travelling wave solutions of nonlinear wave equations in relation to sciences such as optics, fluid mechanics, solid state physics, plasma physics, kinetics, and geology have become very important in the field of mathematical modeling recently. For this, many methods have been suggested. The strategy applied for this article is to obtain more perfect numerical solutions of Modified Equal Width equation (MEW), which is one of the equations used to model the nonlinear phenomena mentioned. For this purpose, the Lie-Trotter splitting technique is applied to the MEW equation. Firstly, the problem is split into two sub-problems, one linear and the other nonlinear, containing derivative with respect to time. Secondly, each subproblem is reduced to the algebraic equation system by using collocation finite element method (FEM) based on the quintic B-spline approximate functions for spatial discretization and the convenient classical finite difference approaches for temporal discretization. Then, the obtained systems are solved with the Lie Trotter splitting algorithm. Explanatory test problems are considered, showing that the newly proposed algorithm has superior accuracy than previous methods, and the numerical results produced by the proposed algorithm are shown in tables and graphs. In addition, the stability analysis of the new approach is examined. Therefore, it is appropriate to state that this new technique can be easily applied to partial differential equations used in other disciplines in terms of the results obtained and the cost of Matlab calculation software.

In this paper, a numerical scheme based on quintic B-spline collocation method using the Strang splitting technique is presented for the solution of the generalized Rosenau-RLW equation given by appropriate initial-boundary values. For our purpose, firstly the problem is split into two subproblems such that each one includes the derivative in the direction of time. Secondly, each subproblem using collocation finite element method with quintic B-splines for spatial integration is reduced to a system of ordinary differential equations (ODEs). Then, the resulting ODEs for time integration are solved using the Strang time-splitting technique with the second order via the usual Runge-Kutta (RK-4) algorithm with the fourth order. To measure the accuracy and efficiency of the present scheme, a model problem with an exact solution is taken into consideration and investigated for various values of the parameter p. The L₂ and L_{∞} errors with the invariants of discrete mass Q and discrete energy E have been computed and given a comparison with other ones found in the literature. The convergence order of the present numerical scheme has also been computed. Furthermore, the stability analysis of the scheme is numerically examined.