A meshless method for the nonlinear generalized regularized long wave equation

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

中国物理B ›› 2011, Vol. 20 ›› Issue (3): 30206-030206.doi: 10.1088/1674-1056/20/3/030206

A meshless method for the nonlinear generalized regularized long wave equation

白福浓¹, 程玉民¹, 王聚丰²

(1)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; (2)Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

收稿日期:2010-06-18 修回日期:2010-10-10 出版日期:2011-03-15 发布日期:2011-03-15
基金资助:
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).

A meshless method for the nonlinear generalized regularized long wave equation

Wang Ju-Feng(王聚丰)^a)b), Bai Fu-Nong(白福浓)^a), and Cheng Yu-Min(程玉民)^a)†

^a Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China; ^b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

Received:2010-06-18 Revised:2010-10-10 Online:2011-03-15 Published:2011-03-15
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: generalized regularized long wave equation, meshless method, moving least-squares approximation, convergence

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.

Key words: generalized regularized long wave equation, meshless method, moving least-squares approximation, convergence

中图分类号: (Ordinary and partial differential equations; boundary value problems)

02.60.Lj

03.65.Ge (Solutions of wave equations: bound states)

王聚丰, 白福浓, 程玉民. A meshless method for the nonlinear generalized regularized long wave equation[J]. 中国物理B, 2011, 20(3): 30206-030206.

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[J]. Chin. Phys. B, 2011, 20(3): 30206-030206.

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A meshless method for the nonlinear generalized regularized long wave equation

A meshless method for the nonlinear generalized regularized long wave equation

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