An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations

doi:10.1088/1674-1056/22/10/100204

中国物理B ›› 2013, Vol. 22 ›› Issue (10): 100204-100204.doi: 10.1088/1674-1056/22/10/100204

An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations

刘永庆^a, 程荣军^b, 葛红霞^c

a Faculty of Science, Ningbo University, Ningbo 315211, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
c Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China

收稿日期:2012-10-19 修回日期:2013-04-07 出版日期:2013-08-30 发布日期:2013-08-30
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11072117 and 61074142), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110007), Scientific Research Fund of Zhejiang Provincial Education Department, China (Grant No. Z201119278), the Natural Science Foundation of Ningbo City (Grant Nos. 2012A610152 and 2012A610038), the Disciplinary Project of Ningbo City, China (Grant No. SZXL1067), and K. C. Wong Magna Fund in Ningbo University.

An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations

Liu Yong-Qing (刘永庆)^a, Cheng Rong-Jun (程荣军)^b, Ge Hong-Xia (葛红霞)^c

a Faculty of Science, Ningbo University, Ningbo 315211, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China;
c Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China

Received:2012-10-19 Revised:2013-04-07 Online:2013-08-30 Published:2013-08-30
Contact: Ge Hong-Xia E-mail:gehongxia@nbu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 11072117 and 61074142), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110007), Scientific Research Fund of Zhejiang Provincial Education Department, China (Grant No. Z201119278), the Natural Science Foundation of Ningbo City (Grant Nos. 2012A610152 and 2012A610038), the Disciplinary Project of Ningbo City, China (Grant No. SZXL1067), and K. C. Wong Magna Fund in Ningbo University.

摘要/Abstract

摘要： The present paper deals with the numerical solution of the coupled Schrödinger-KdV equations using the element-free Galerkin (EFG) method which is based on the moving least-square approximation. Instead of traditional mesh oriented methods such as the finite difference method (FDM) and the finite element method (FEM), this method needs only scattered nodes in the domain. For this scheme, a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method. In numerical experiments, the results are presented and compared with the findings of the finite element method, the radial basis functions method, and an analytical solution to confirm the good accuracy of the presented scheme.

关键词: element-free Galerkin (EFG) method, meshless method, the coupled Schrö, dinger-KdV equations

Abstract: The present paper deals with the numerical solution of the coupled Schrödinger-KdV equations using the element-free Galerkin (EFG) method which is based on the moving least-square approximation. Instead of traditional mesh oriented methods such as the finite difference method (FDM) and the finite element method (FEM), this method needs only scattered nodes in the domain. For this scheme, a variational method is used to obtain discrete equations and the essential boundary conditions are enforced by the penalty method. In numerical experiments, the results are presented and compared with the findings of the finite element method, the radial basis functions method, and an analytical solution to confirm the good accuracy of the presented scheme.

Key words: element-free Galerkin (EFG) method, meshless method, the coupled Schrö, dinger-KdV equations

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)

刘永庆, 程荣军, 葛红霞. An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations[J]. 中国物理B, 2013, 22(10): 100204-100204.

Liu Yong-Qing (刘永庆), Cheng Rong-Jun (程荣军), Ge Hong-Xia (葛红霞). An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations[J]. Chin. Phys. B, 2013, 22(10): 100204-100204.

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An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations

An element-free Galerkin (EFG) method for numerical solution of the coupled Schrödinger-KdV equations

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