Improved solution to nonlinear generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation by a meshless RBFs method

Subject Areas : Numerical Analysis

Mehran Nemati ¹ , Seyedeh Fayezeh Teimoori ²

1 - گروه ریاضی ، واحد رودبار، دانشگاه آزاد اسلامی، رودبار، ایران
2 - گروه کامپیوتر، واحد رودبار، دانشگاه آزاد اسلامی، رودبار، ایران

Received: 2023-05-03 Accepted : 2023-06-24 Published : 2023-03-01

Keywords: Crank-Nicolson Scheme, Radial basis functions (RBFs), Finite differences, Nonlinear Generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation,

Abstract :

In this paper, based on the RBF collocation method and finite differences, a numerical method is proposed to solve nonlinear generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation. First order finite differences and Crank-Nicolson method are applied to discretize the temporal parts. The spatial parts are approximated by MQ-RBF interpolation which results in a linear system of algebraic equations. Approximate solutions are determined by solving such a system. The proposed scheme is verified by solving some test problems and computing error norms and . Results show the efficiency of the suggested method and the error has been improved.