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.
Highlights
In various scientific fields, the vast majority of the arising phenomena are known to be described by partial differential equations (PDEs)
Our investigations restricted to solve nonlinear PDEs according to the initial conditions of the adopted variable (IVP)
The associated WBKL equations studied by Whitham[3], Broer 4 and Caup 5 are given as follows:
Summary
The vast majority of the arising phenomena are known to be described by partial differential equations (PDEs). Wave propagation, heat flow and other physical phenomena. It is important to be aware of all the traditional techniques recently developed to solve PDEs and to implement these techniques. The double-equation (WBKL) is considered to describe the propagating shallow-water waves which have different dispersion relationships 2. Many researchers have discussed various numerical and analytical methods to solve the shallow wave equation since its emergence. The Whitham-Broer-Kaup equations and their variances were solved by using the homotopy perturbation method 7,the bifurcation method 2,the Adomian decomposition method 8, and the power series method 9. For instance Chu and Ghen have utilized it to solve the nonlinear heat construction problem. Che has studied the nonlinear heat combustion problem via the hybrid method. Couettenanofluid flow and heat transfer by using the hybrid method. The finite difference method is one of the most important methods in the field of numerical analysis because of its accurate and detailed results
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