Improved solution to nonlinear generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation by a meshless RBFs method
محورهای موضوعی : Numerical Analysis
Mehran Nemati
1
,
Seyedeh Fayezeh Teimoori
2
1 - Department of Mathematics, Roudbar Branch, Islamic Azad University, Roudbar, Iran
2 - Department of Mathematics, Roudbar Branch, Islamic Azad University, Roudbar, Iran
کلید واژه: Crank-Nicolson Scheme, Radial basis functions (RBFs), Finite differences, Nonlinear Generalized Benjamin–Bona–Mahony–Burgers (GBBMB) equation,
چکیده مقاله :
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.
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.
