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

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...

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Bibliographic Details
Published inChinese physics B Vol. 22; no. 6; pp. 150 - 155
Main Author 程荣军 魏麒
Format Journal Article
LanguageEnglish
Published 01.06.2013
Subjects
Approximation
Boundary conditions
Computation
Galerkin methods
Least squares method
Mathematical analysis
Mathematical models
Variational methods
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ISSN1674-1056
2058-3834
1741-4199
DOI10.1088/1674-1056/22/6/060209

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Summary: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 fewer coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, fewer 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.
Bibliography:11-5639/O4
meshless method, improved moving least-square （IMLS） approximation, improved element-freeGalerkin （IEFG） method, generalized Camassa and Holm （CH） equation
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 fewer coefficients in the IMLS approximation than in the MLS approximation, and in the IEFG method, fewer 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.
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ISSN:1674-1056
2058-3834
1741-4199
DOI:10.1088/1674-1056/22/6/060209