Computational study of coupled Whitham Broer Kaup equations via interpolation technique

Abstract

The main purpose of this study is to investigate the numerical solution of coupled Whitham Broer Kaup (WBK) equation via Quintic B-Spline interpolation technique. This problem is of significant interest in the study of nonlinear wave phenomena because of its applications in various fields, such as fluid dynamics, plasma physics, and nonlinear optics and climate modeling. For the temporal derivative, the forward difference technique and a quadrature rule are utilized to deal the integer and fractional models, respectively, while spatial operators and the solutions are then obtained using Quintic B-spline. Furthermore, the non-linear terms are linearized using Quasi-linearization technique. Absolute error, $L_2$ and $L_{\infty }$ error norms are computed to check the accuracy of the proposed method. The computed results are represented graphically and compared with the exact solution. It is found that our method is efficient due to less computational cost and proffer better accuracy. Stability of the proposed method is discussed using Von-Neumann stability which identifies that the scheme is conditionally stable.