Paper Info
Title
The Lie-group method based on radial basis functions for solving nonlinear high dimensional generalized Benjamin-Bona-Mahony-Burgers equation in arbitrary domains.
Abstract
The aim of this paper is to introduce a new numerical method for solving the nonlinear generalized BenjaminBonaMahonyBurgers (GBBMB) equation. This method is combination of group preserving scheme (GPS) with radial basis functions (RBFs), which takes advantage of two powerful methods, one as geometric numerical integration method and the other meshless method. Thus, we introduce this method as the Lie-group method based on radial basis functions (LGRBFs). In this method, we use Kansas approach to approximate the spatial derivatives and then we apply GPS method to approximate first-order time derivative. One of the important advantages of the developed method is that it can be applied to problems on arbitrary geometry with high dimensions. To demonstrate this point, we solve nonlinear GBBMB equation on various geometric domains in one, two and three dimension spaces. The results of numerical experiments are compared with analytical solutions and the method presented in Dehghan etal. (2014) to confirm the accuracy and efficiency of the presented method.
Year
DOI
Venue
2018
10.1016/j.amc.2017.10.051
Applied Mathematics and Computation
Keywords
Field
DocType
Group preserving scheme (GPS), Kansas approach, Meshless method, Non-regular geometrical domains, Nonlinear generalized BenjaminBonaMahonyBurgers (GBBMB) equation, Radial basis functions (RBFs)
Lie group,Mathematical optimization,Radial basis function,Nonlinear system,Mathematical analysis,Numerical integration,Time derivative,Burgers' equation,Numerical analysis,Mathematics,Regularized meshless method
Journal
Volume
ISSN
Citations 
321
0096-3003
0
PageRank 
References 
Authors
0.34
8
3
Name
Order
Citations
PageRank
M. Hajiketabi100.34
Saeid Abbasbandy218026.64
Fernando Casas37418.30