Numerical simulation of wave flow: Integrating the BBM-KdV equation using compact difference schemes

Apipoom Polwang, Kanyuta Poochinapan and Ben Wongsaijai

Mathematics and Computers in Simulation (MATCOM), 2025, vol. 236, issue C, 70-89

Abstract: The nonlinear convection term uux plays a critical role in scientific and engineering contexts, capturing the complex interaction between a function and its spatial derivative. In numerical analysis, this term significantly impacts the stability of computational methods and requires careful treatment for accurate solutions. This study presents efficient, high-order linear numerical schemes for solving the Benjamin–Bona–Mahony-KdV equation, incorporating three strategies to approximate the nonlinear term while preserving mass and/or energy. The effectiveness and precision of the proposed methods are demonstrated through rigorous testing in comprehensive numerical experiments, providing clear insight into their performance. Our observations show that these schemes preserve conservative properties while offering improved accuracy and stability compared to the standard second-order scheme. These findings underscore the potential to advance numerical methods for differential equations and provide strong evidence for the effectiveness of the proposed high-order approach in accurately modeling complex wave behavior.

Keywords: Finite difference method; Compact difference operator; Mass-preserving property; Benjamin–Bona–Mahony-KdV equation (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0378475425000874
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:236:y:2025:i:c:p:70-89

DOI: 10.1016/j.matcom.2025.03.012

Access Statistics for this article

Mathematics and Computers in Simulation (MATCOM) is currently edited by Robert Beauwens

More articles in Mathematics and Computers in Simulation (MATCOM) from Elsevier
Bibliographic data for series maintained by Catherine Liu ().