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Chin. Phys. B, 2013, Vol. 22(6): 060209    DOI: 10.1088/1674-1056/22/6/060209
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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
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.
Keywords:  meshless method      improved moving least-square (IMLS) approximation      improved element-free Galerkin (IEFG) method      generalized Camassa and Holm (CH) equation  
Received:  04 October 2012      Revised:  29 October 2012      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 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).
Corresponding Authors:  Wei Qi     E-mail:  weiqi@nit.zju.edu.cn

Cite this article: 

Cheng Rong-Jun, Wei Qi Analysis of the generalized Camassa and Holm equation with the improved element-free Galerkin method 2013 Chin. Phys. B 22 060209

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