An advanced meshless method for time fractional diffusion equation

Gu, YuanTong, Zhuang, Pinghui, & Liu, QingXia (2011) An advanced meshless method for time fractional diffusion equation. International Journal of Computational Methods, 8(4), pp. 653-665.

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Recently, because of the new developments in sustainable engineering and renewable energy, which are usually governed by a series of fractional partial differential equations (FPDEs), the numerical modelling and simulation for fractional calculus are attracting more and more attention from researchers. The current dominant numerical method for modeling FPDE is Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings including difficulty in simulation of problems with the complex problem domain and in using irregularly distributed nodes. Because of its distinguished advantages, the meshless method has good potential in simulation of FPDEs. This paper aims to develop an implicit meshless collocation technique for FPDE. The discrete system of FPDEs is obtained by using the meshless shape functions and the meshless collocation formulation. The stability and convergence of this meshless approach are investigated theoretically and numerically. The numerical examples with regular and irregular nodal distributions are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. It is concluded that the present meshless formulation is very effective for the modeling and simulation of fractional partial differential equations.

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ID Code: 46863
Item Type: Journal Article
Refereed: Yes
Keywords: Fractional Differential Equation, Meshless Method, Moving Least Squares, RBF, Collocation Formulation
DOI: 10.1142/S0219876211002745
ISSN: 0219-8762
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical and Computational Mathematics not elsewhere classified (010399)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Numerical Modelling and Mechanical Characterisation (091307)
Divisions: Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering
Past > Schools > School of Engineering Systems
Copyright Owner: Copyright 2011 World Scientific Publishing.
Deposited On: 06 Nov 2011 21:59
Last Modified: 24 Jan 2012 02:39

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