Numerical solution of the Whitham-Broer-Kaup shallow water equation by quartic B-spline collocation method

Author:

Sabawi Younis AORCID,Hamad Hoshman Q

Abstract

Abstract This paper introduces a novel quartic B-spline collocation method to address the coupled Whitham–Broer–Kaup (WBK) problem. The WBK problem is a topic of interest in the study of nonlinear wave phenomena and has applications in various fields, including fluid dynamics, plasma physics, and nonlinear optics. The method combines spatial quartic B-spline scheme discretization, and Crank–Nicolson temporal discretization. It is unconditionally stable as proven by the Von-Neumann technique. Numerical examples demonstrate the method’s superior accuracy compared to existing solutions. Error analysis employs l 2 and l norms, while the method exhibits high computational efficiency. The nonlinearity is managed through Rubin-Graves linearization. Comparisons with prior approaches highlight its efficiency, stability, adaptability to complex problems. The quartic B-spline method is well-suited for simulating fluid flow phenomena in shallow water scenarios, offering high accuracy and low computational cost.

Publisher

IOP Publishing

Subject

Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics

Reference56 articles.

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4. Mathematics of dispersive water waves;Kupershmidt;Commun. Math. Phys.,1985

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