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An implicit RBF meshless method for a fractal mobile/immobile transport model

Liu, Fawang, Turner, Ian, Anh, Vo, & Gu, YuanTong (2012) An implicit RBF meshless method for a fractal mobile/immobile transport model. In Chen, Wen, Sun, HongGuang, & Baleanu, Dumitru (Eds.) The Proceedings of the 5th Symposium on Fractional Differentiation and Its Applications, Hohai University, Hohai University, Nanjing.

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Abstract

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

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ID Code: 51458
Item Type: Conference Paper
Keywords: fractal mobile/immobile transport model, finite difference method, meshless method
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000)
Divisions: Current > Schools > School of Chemistry, Physics & Mechanical Engineering
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 [please consult the author]
Deposited On: 06 Jul 2012 09:31
Last Modified: 13 Jun 2013 00:54

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