A new application for numerical computations of the modified equal width equation (MEW) based on Lumped Galerkin method with the cubic B-spline

In this paper, numerical computation of the modified equal width equation (MEW), which is one of the equations used to model nonlinear events, will be carried out. For this equation, numerical computations have been obtained by many researchers using different methods. The goal of the new approach is to check how well it performs with respect to the numerical calculations the researchers found. For this, the proposed study presents a Lie-Trotter splitting algorithm in accordance with the time-splitting technical rules combined with Lumped Galerkin FEM based on the basis function of the cubic B-spline. Two valid test examples are given to determine the validity and effectiveness of the current technique. The results obtained in a new way with the Matlab computational software are compared with the studies of other authors in the literature and are shown graphically. Based on these new results, it can clearly be stated that the benefit of the proposed approach is to demonstrate that reliability is achieved in obtaining approximate computations.