A RBF meshless approach for modeling a fractal mobile/immobile transport model

Liu, Qingxia, Liu, Fawang, Turner, Ian, Anh, Vo, & Gu, YuanTong (2014) A RBF meshless approach for modeling a fractal mobile/immobile transport model. Applied Mathematics and Computation, 226, pp. 336-347.

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Abstract

A 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 (RBFs) to discretize the space variable. In 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 which is presented to describe a 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 fractional differential equations, and it has good potential in the development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Impact and interest:

13 citations in Scopus
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12 citations in Web of Science®

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ID Code: 65162
Item Type: Journal Article
Refereed: Yes
Keywords: Fractal mobile/immobile transport model, Finite difference method, Meshless method
DOI: 10.1016/j.amc.2013.10.008
ISSN: 0096-3003
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > MECHANICAL ENGINEERING (091300) > Numerical Modelling and Mechanical Characterisation (091307)
Divisions: Current > Schools > School of Chemistry, Physics & Mechanical Engineering
Past > QUT Faculties & Divisions > Faculty of Science and Technology
Current > Schools > School of Mathematical Sciences
Deposited On: 05 Dec 2013 22:20
Last Modified: 14 May 2014 03:49

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