An implicit RBF meshless approach for time fractional diffusion equations

Liu, QingXia, Gu, YuanTong, Zhuang, Pinghui, Liu, Fawang, & Nie, Yufeng (2011) An implicit RBF meshless approach for time fractional diffusion equations. Computational Mechanics, 48(1), pp. 1-12.

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This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

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64 citations in Scopus
58 citations in Web of Science®
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ID Code: 45681
Item Type: Journal Article
Refereed: Yes
Keywords: Fractional differential equation, Meshless method, RBF, Time fractional diffusion equation
DOI: 10.1007/s00466-011-0573-x
ISSN: 1432-0924
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Numerical Modelling and Mechanical Characterisation (091307)
Divisions: Current > Schools > School of Teacher Education & Leadership
Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering
Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > School of Engineering Systems
Copyright Owner: Copyright 2011 Springer
Copyright Statement: The original publication is available at SpringerLink
Deposited On: 04 Sep 2011 23:53
Last Modified: 27 Mar 2013 20:06

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