TY  - EJOU
AU  - Ma, Hongwei 
AU  - Tian, Yingqian 
AU  - Wang, Fuzhang 
AU  - Lou, Quanfu 
AU  - Yu, Lijuan 

TI  - Solving the BBMB Equation in Shallow Water Waves via Space-Time MQ-RBF Collocation
T2  - Computer Modeling in Engineering \& Sciences

PY  - 2025
VL  - 144
IS  - 3
SN  - 1526-1506

AB  - 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.
KW  - Numerical method; BBMB equation; meshless method; radial basis function; nonlinear partial differential equation

DO  - 10.32604/cmes.2025.070791