Element-free Galerkin （EFG） method for analysis of the time-fractional partial differential equations

The present paper deals with the numerical solution of time-fractional partial differential equations using the element-free Galerkin （EFG） method, which is based on the moving least-square approximation. Compared with numerical methods based on meshes, the EFG method for time-fractional partial dif...

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Bibliographic Details
Published in中国物理：英文版 Vol. 21; no. 1; pp. 46 - 51
Main Author 葛红霞 刘永庆 程荣军
Format Journal Article
LanguageEnglish
Published 2012
Subjects
EFG法
Galerkin
伽辽金
偏微分方程
分数阶导数
单元
时间
瑞士
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ISSN1674-1056
2058-3834

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Summary:The present paper deals with the numerical solution of time-fractional partial differential equations using the element-free Galerkin （EFG） method, which is based on the moving least-square approximation. Compared with numerical methods based on meshes, the EFG method for time-fractional partial differential equations needs only scattered nodes instead of meshing the domain of the problem. It neither requires element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. In this method, the first-order time derivative is replaced by the Caputo fractional derivative of order α（0 〈 α≤ 1）. The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Several numerical examples are presented and the results we obtained are in good agreement with the exact solutions.
Bibliography:element-free Galerkin （EFG） method, meshless method, time fractional partial differential equations
Ge Hong-Xia, Liu Yong-Qing, and Cheng Rong-Jun（ a）Faculty of Science, Ningbo University, Ningbo 315211, China b） Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China
11-5639/O4
The present paper deals with the numerical solution of time-fractional partial differential equations using the element-free Galerkin （EFG） method, which is based on the moving least-square approximation. Compared with numerical methods based on meshes, the EFG method for time-fractional partial differential equations needs only scattered nodes instead of meshing the domain of the problem. It neither requires element connectivity nor suffers much degradation in accuracy when nodal arrangements are very irregular. In this method, the first-order time derivative is replaced by the Caputo fractional derivative of order α（0 〈 α≤ 1）. The Galerkin weak form is used to obtain the discrete equations, and the essential boundary conditions are enforced by the penalty method. Several numerical examples are presented and the results we obtained are in good agreement with the exact solutions.
ISSN:1674-1056
2058-3834