An advanced implicit meshless approach for fractional partial differential equation in computational mechanics

Gu, YuanTong (2010) An advanced implicit meshless approach for fractional partial differential equation in computational mechanics. In Howard, Ian, Teh, Kian, & Davies, Ian (Eds.) Proceedings from the 6th Australasian Congress on Applied Mechanics, Engineers Australia, Perth Convention Exhibition Centre, Perth, WA, pp. 1-8.

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Recently, the numerical modelling and simulation for fractional partial differential equations (FPDE), which have been found with widely applications in modern engineering and sciences, are attracting increased attentions. The current dominant numerical method for modelling of FPDE is the explicit Finite Difference Method (FDM), which is based on a pre-defined grid leading to inherited issues or shortcomings. This paper aims to develop an implicit meshless approach based on the radial basis functions (RBF) for numerical simulation of time fractional diffusion equations. The discrete system of equations is obtained by using the RBF meshless shape functions and the strong-forms. The stability and convergence of this meshless approach are then discussed and theoretically proven. Several numerical examples with different problem domains are used to validate and investigate accuracy and efficiency of the newly developed meshless formulation. The results obtained by the meshless formations are also compared with those obtained by FDM in terms of their accuracy and efficiency. It is concluded that the present meshless formulation is very effective for the modelling and simulation for FPDE.

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ID Code: 40084
Item Type: Conference Paper
Refereed: Yes
Keywords: Fractional Partial Differential Equation, FDM, FEM, Meshless, RBF
ISBN: 9780858259416
ISSN: 1448-4846
Subjects: 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 2010 Engineers Australia
Deposited On: 06 Mar 2011 22:24
Last Modified: 29 Feb 2012 14:30

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