Numerical Solution of the Generalized Rosenau-Burgers Equation by Using Method of Lines

This paper presents a robust numerical scheme for solving the generalized Rosenau-Burgers equationusing a meshless Method of Lines (MOL) approach based on Radial Basis Functions (RBFs). To evaluatethe accuracy and stability of the proposed scheme, two distinct numerical examples are investigated, including the propagation of single solitary waves and their dynamic behavior under varying parameters. The numerical results demonstrate that the proposed method achieves exceptional accuracy and, significantly outperforming existing results in the literature. The study concludes that the RBF-based MOL is a highly effective and reliable tool for simulating high-order nonlinear evolution equations.