Solving Whitham-Broer-Kaup-Like Equations Numerically by using Hybrid Differential Transform Method and Finite Differences Method

Abstract

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.

Keywords

• Differential Transform Method, Finite Differences Method, Hybrid Differential Transform - Finite Differences Method, Whitham-Broer-Kaup-Like Equations