An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation

Gu, YuanTong, Zhuang, Pinghui, & Liu, Fawang (2010) An advanced implicit meshless approach for the non-linear anomalous subdiffusion equation. Computer Modeling in Engineering & Sciences, 56(3), pp. 303-334.

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Recently, the numerical modelling and simulation for anomalous subdiffusion equation (ASDE), which is a type of fractional partial differential equation( FPDE) and has been found with widely applications in modern engineering and sciences, are attracting more and more attentions. The current dominant numerical method for modelling ASDE is 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 the non-linear ASDE. The discrete system of equations is obtained by using the 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 formulations 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 modeling and simulation of the ASDE. Therefore, the meshless technique should have good potential in development of a robust simulation tool for problems in engineering and science which are governed by the various types of fractional differential equations.

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47 citations in Scopus
46 citations in Web of Science®
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ID Code: 34155
Item Type: Journal Article
Refereed: Yes
Keywords: anomalous subdiffusion equation, fractional differential equation, numerical simulation, meshless method, radial basis functions
ISSN: 1526-1492
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: Past > QUT Faculties & Divisions > Faculty of Built Environment and Engineering
Past > QUT Faculties & Divisions > Faculty of Science and Technology
Deposited On: 18 Aug 2010 01:18
Last Modified: 12 Jul 2017 12:02

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