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

Iranian Journal of Optimization

مقاله 2، دوره 15، شماره 1، خرداد 2023

نوع مقاله: Research Paper

نویسندگان

Mehran Nemati^{* 1}؛ Sayedeh Fayezeh Teimoori²

¹Department of Mathematics, Roudbar Branch, Islamic Azad University, Roudbar, Iran.

²Department of Computer, Roudbar Branch, Islamic Azad University, Roudbar, Iran.

چکیده

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.

کلیدواژه‌ها

Radial basis functions (RBFs)؛ Finite differences؛ Crank-Nicolson scheme؛ Nonlinear Generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation