Open Access

ARTICLE

Solving the BBMB Equation in Shallow Water Waves via Space-Time MQ-RBF Collocation

Hongwei Ma¹, Yingqian Tian^2,*, Fuzhang Wang^3,*, Quanfu Lou⁴, Lijuan Yu⁴

1 College of Civil Science and Engineering, Yangzhou University, Yangzhou, 225127, China
2 School of Mathematics and Statistics, Huaibei Normal University, Huaibei, 235000, China
3 Institute of Data Science and Engineering, Xuzhou University of Technology, Xuzhou, 221018, China
4 Department of Mathematics, Nanchang Normal College of Applied Technology, Nanchang, 330108, China

* Corresponding Authors: Yingqian Tian. Email: ; Fuzhang Wang. Email:

(This article belongs to the Special Issue: Meshless Methods and Its Applications in Porous Media Problems)

Computer Modeling in Engineering & Sciences 2025, 144(3), 3419-3432. https://doi.org/10.32604/cmes.2025.070791

Received 24 July 2025; Accepted 26 August 2025; Issue published 30 September 2025

Abstract

This study introduces a novel single-layer meshless method, the space-time collocation method based on multiquadric-radial basis functions (MQ-RBF), for solving the Benjamin-Bona-Mahony-Burgers (BBMB) equation. By reconstructing the time variable as a space variable, this method establishes a combined space-time structure that can eliminate the two-step computational process required in traditional grid methods. By introducing shape parameter-optimized MQ-RBF, high-precision discretization of the nonlinear, dispersive, and dissipative terms in the BBMB equation is achieved. The numerical experiment section validates the effectiveness of the proposed method through three benchmark examples. This method shows significant advantages in computational efficiency, providing a new numerical tool for engineering applications in fields such as shallow water wave dynamics.

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Keywords

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