Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method

doi:10.1088/1674-1056/22/6/060209

中国物理B ›› 2013, Vol. 22 ›› Issue (6): 60209-060209.doi: 10.1088/1674-1056/22/6/060209

Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method

Cheng Rong-Jun, Wei Qi

Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

收稿日期:2012-10-04 修回日期:2012-10-29 出版日期:2013-05-01 发布日期:2013-05-01
基金资助:
Project supported by the Natural Science Foundation of Ningbo City, Zhejiang Province, China (Grant Nos. 2012A610038 and 2012A610023) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110007).

Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method

Cheng Rong-Jun, Wei Qi

Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

Received:2012-10-04 Revised:2012-10-29 Online:2013-05-01 Published:2013-05-01
Contact: Wei Qi E-mail:weiqi@nit.zju.edu.cn
Supported by:
Project supported by the Natural Science Foundation of Ningbo City, Zhejiang Province, China (Grant Nos. 2012A610038 and 2012A610023) and the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6110007).

摘要/Abstract

摘要： In this paper, we analyze the generalized Camassa and Holm (CH) equation by the improved element-free Galerkin (IEFG) method. By employing the improved moving least-square (IMLS) approximation, we derive the formulas for the generalized CH equation with the IEFG method. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Because there are less coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, less nodes are selected in the entire domain than in the conventional EFG method, the IEFG method should result in a higher computing speed. The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper.

关键词: meshless method, improved moving least-square (IMLS) approximation, improved element-free Galerkin (IEFG) method, generalized Camassa and Holm (CH) equation

Abstract: In this paper, we analyze the generalized Camassa and Holm (CH) equation by the improved element-free Galerkin (IEFG) method. By employing the improved moving least-square (IMLS) approximation, we derive the formulas for the generalized CH equation with the IEFG method. A variational method is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Because there are less coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, less nodes are selected in the entire domain than in the conventional EFG method, the IEFG method should result in a higher computing speed. The effectiveness of the IEFG method for the generalized CH equation is investigated by numerical examples in this paper.

Key words: meshless method, improved moving least-square (IMLS) approximation, improved element-free Galerkin (IEFG) method, generalized Camassa and Holm (CH) equation

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)

Cheng Rong-Jun, Wei Qi. Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method[J]. 中国物理B, 2013, 22(6): 60209-060209.

Cheng Rong-Jun, Wei Qi. Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method[J]. Chin. Phys. B, 2013, 22(6): 60209-060209.

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Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method

Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method

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