A numerical algorithm for solitary wave solutions of the GEW equation

Abstract

The present article attempts to obtain numerical solutions for the GEW equation with the Lie–Trotter splitting algorithm. For this reason, in accordance with the rules of the algorithm, the main problem is split into two sub-equations, linear and non-linear. By applying Galerkin finite element method with cubic B-spline to each sub-equation, two numerical schemes are obtained and two problems for them are discussed. Error norms \(L_{2}\) and \(L_{\infty }\) and three conservation properties \(I_{1},I_{2}\) and \(I_{3}\) are calculated to measure the reliability and performance of the proposed technique and find new approximate solutions. The results generated as a result of the calculation are compared with those produced by other methods in the literature. Stability analysis is examined using the Fourier method to indicate that the numerical approach is unconditionally stable. Based on the results obtained, it can be seen that this technique may be preferred to be applied to other partial differential equations such as the equation discussed in the current study.