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

doi:10.1088/1674-1056/21/1/010206

中国物理B ›› 2012, Vol. 21 ›› Issue (1): 10206-010206.doi: 10.1088/1674-1056/21/1/010206

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

葛红霞¹, 刘永庆¹, 程荣军²

(1)Faculty of Science, Ningbo University, Ningbo 315211, China; (2)Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

收稿日期:2011-07-21 修回日期:2011-09-06 出版日期:2012-01-15 发布日期:2012-01-20
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11072117), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. Y6110007 and Y6110502), and the K.C.Wong Magna Fund in Ningbo University, China.

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

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

^a Faculty of Science, Ningbo University, Ningbo 315211, China; ^b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China

Received:2011-07-21 Revised:2011-09-06 Online:2012-01-15 Published:2012-01-20
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11072117), the Natural Science Foundation of Zhejiang Province, China (Grant Nos. Y6110007 and Y6110502), and the K.C.Wong Magna Fund in Ningbo University, China.

摘要/Abstract

摘要： 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.

关键词: element-free Galerkin (EFG) method, meshless method, time fractional partial differential equations

Abstract: 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 $\alpha$ (0<$\alpha$ ≤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.

Key words: element-free Galerkin (EFG) method, meshless method, time fractional partial differential 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)

葛红霞, 刘永庆, 程荣军. Element-free Galerkin (EFG) method for analysis of the time-fractional partial differential equations[J]. 中国物理B, 2012, 21(1): 10206-010206.

Ge Hong-Xia(葛红霞), Liu Yong-Qing(刘永庆), and Cheng Rong-Jun(程荣军) . Element-free Galerkin (EFG) method for analysis of the time-fractional partial differential equations[J]. Chin. Phys. B, 2012, 21(1): 10206-010206.

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

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

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