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

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

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.

Keywords: element-free Galerkin (EFG) method meshless method time fractional partial differential equations

Received: 21 July 2011
Revised: 06 September 2011
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 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.

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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 2012 Chin. Phys. B 21 010206

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

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