A meshless method for the nonlinear generalized regularized long wave equation

doi:10.1088/1674-1056/20/3/030206

Abstract This paper presents a meshless method for the nonlinear generalized regularized long wave (GRLW) equation based on the moving least-squares approximation. The nonlinear discrete scheme of the GRLW equation is obtained and is solved using the iteration method. A theorem on the convergence of the iterative process is presented and proved using theorems of the infinity norm. Compared with numerical methods based on mesh, the meshless method for the GRLW equation only requires the scattered nodes instead of meshing the domain of the problem. Some examples, such as the propagation of single soliton and the interaction of two solitary waves, are given to show the effectiveness of the meshless method.

Keywords: generalized regularized long wave equation meshless method moving least-squares approximation convergence

Received: 18 June 2010
Revised: 10 October 2010
Accepted manuscript online:

PACS:	02.60.Lj	(Ordinary and partial differential equations; boundary value problems)
	03.65.Ge	(Solutions of wave equations: bound states)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 10871124) and the Innovation Program of the Shanghai Municipal Education Commission, China (Grant No. 09ZZ99).

Cite this article:

Wang Ju-Feng(王聚丰), Bai Fu-Nong(白福浓), and Cheng Yu-Min(程玉民) A meshless method for the nonlinear generalized regularized long wave equation 2011 Chin. Phys. B 20 030206

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