Element-free Galerkin method for a kind of KdV equation

doi:10.1088/1674-1056/19/6/060201

中国物理B ›› 2010, Vol. 19 ›› Issue (6): 60201-060201.doi: 10.1088/1674-1056/19/6/060201

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Element-free Galerkin method for a kind of KdV equation

王聚丰¹, 程荣军¹, 孙凤欣²

(1)Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China; (2)Ningbo University of Technology, Ningbo 315016, China

收稿日期:2009-05-26 修回日期:2009-12-28 出版日期:2010-06-15 发布日期:2010-06-15
基金资助:
Project supported by the Natural Science Foundation of Ningbo City (Grant No.~2009A610014), the Natural Science Foundation of Zhejiang Province (Grant No.~Y6090131), and the Research Foundation of Ningbo University of Technology (Grant No.~2008004).

Element-free Galerkin method for a kind of KdV equation

Wang Ju-Feng(王聚丰)^a)†, Sun Feng-Xin(孙凤欣)^b), and Cheng Rong-Jun(程荣军)^a)

^a Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China; ^b Ningbo University of Technology, Ningbo 315016, China

Received:2009-05-26 Revised:2009-12-28 Online:2010-06-15 Published:2010-06-15
Supported by:
Project supported by the Natural Science Foundation of Ningbo City (Grant No.~2009A610014), the Natural Science Foundation of Zhejiang Province (Grant No.~Y6090131), and the Research Foundation of Ningbo University of Technology (Grant No.~2008004).

摘要/Abstract

摘要： The present paper deals with the numerical solution of the third-order nonlinear KdV equation using the element-free Galerkin (EFG) method which is based on the moving least-squares approximation. A variational method is used to obtain discrete equations, and the essential boundary conditions are enforced by the penalty method. Compared with numerical methods based on mesh, the EFG method for KdV equations needs only scattered nodes instead of meshing the domain of the problem. It does not require any element connectivity and does not suffer much degradation in accuracy when nodal arrangements are very irregular. The effectiveness of the EFG method for the KdV equation is investigated by two numerical examples in this paper.

Abstract: The present paper deals with the numerical solution of the third-order nonlinear KdV equation using the element-free Galerkin (EFG) method which is based on the moving least-squares approximation. A variational method is used to obtain discrete equations, and the essential boundary conditions are enforced by the penalty method. Compared with numerical methods based on mesh, the EFG method for KdV equations needs only scattered nodes instead of meshing the domain of the problem. It does not require any element connectivity and does not suffer much degradation in accuracy when nodal arrangements are very irregular. The effectiveness of the EFG method for the KdV equation is investigated by two numerical examples in this paper.

Key words: element-free Galerkin method, meshless method, KdV equation

中图分类号: (Finite-element and Galerkin methods)

02.70.Dh

02.30.Xx (Calculus of variations) 02.70.Rr (General statistical methods)

王聚丰, 孙凤欣, 程荣军. Element-free Galerkin method for a kind of KdV equation[J]. 中国物理B, 2010, 19(6): 60201-060201.

Wang Ju-Feng(王聚丰), Sun Feng-Xin(孙凤欣), and Cheng Rong-Jun(程荣军). Element-free Galerkin method for a kind of KdV equation[J]. Chin. Phys. B, 2010, 19(6): 60201-060201.

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Element-free Galerkin method for a kind of KdV equation

Element-free Galerkin method for a kind of KdV equation

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