Chin. Phys. B, 2014, Vol. 23(4): 040203    DOI: 10.1088/1674-1056/23/4/040203
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# A meshless method based on moving Kriging interpolation for a two-dimensional time-fractional diffusion equation

Ge Hong-Xiaa, Cheng Rong-Junb
a Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China;
b Ningbo Institute of Technology, Zhejiang University, Ningbo 315100, China
Abstract  Fractional diffusion equations have been the focus of modeling problems in hydrology, biology, viscoelasticity, physics, engineering, and other areas of applications. In this paper, a meshfree method based on the moving Kriging interpolation is developed for a two-dimensional time-fractional diffusion equation. The shape function and its derivatives are obtained by the moving Kriging interpolation technique. For possessing the Kronecker delta property, this technique is very efficient in imposing the essential boundary conditions. The governing time-fractional diffusion equations are transformed into a standard weak formulation by the Galerkin method. It is then discretized into a meshfree system of time-dependent equations, which are solved by the standard central difference method. Numerical examples illustrating the applicability and effectiveness of the proposed method are presented and discussed in detail.
Keywords:  meshless method      moving Kriging interpolation      time-fractional diffusion equation
Received:  10 August 2013      Revised:  08 October 2013      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 Ningbo City, China (Grant No. 2013A610103), the Natural Science Foundation of Zhejiang Province, China (Grant No. Y6090131), the DisciplinaryProject of Ningbo City, China (Grant No. SZXL1067), and the K. C. Wong Magna Fund in Ningbo University, China.
Corresponding Authors:  Ge Hong-Xia     E-mail:  gehongxia@nbu.edu.cn