Numerical Solution of Nonlinear Whitham-Broer-Kaup Shallow Water Model Using Finite Difference Methods

Abstract

In this paper, we presented finite difference methods for solving nonlinear Whitham-Broer-Kaup (WBK) shallow water model numerically. We first subdivided the domain of the model by a net with a finite number of mesh points, and the derivative at each point replaced by explicit, Crank-Nicolson, and exponential finite difference approximations. The result is the system of algebraic equations which when solved, provide an approximation to the solutions of WBK model at the selected grid points. Also, a comparison has been made between the approximate solutions obtained by the proposed methods and the exact solutions. Numerical results represented in tables and figures with the help of MATLAB R2015a.