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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation


Authors: Chang-Ming Chen, F. Liu, V. Anh and I. Turner
Journal: Math. Comp. 81 (2012), 345-366
MSC (2010): Primary 65M20, 65L06, 65R10, 26A33
Published electronically: June 9, 2011
MathSciNet review: 2833498
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Abstract: Anomalous subdiffusion equations have in recent years received much attention. In this paper, we consider a two-dimensional variable-order anomalous subdiffusion equation. Two numerical methods (the implicit and explicit methods) are developed to solve the equation. Their stability, convergence and solvability are investigated by the Fourier method. Moreover, the effectiveness of our theoretical analysis is demonstrated by some numerical examples.


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Additional Information

Chang-Ming Chen
Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen 361005, China
Email: cmchen@xmu.edu.cn

F. Liu
Affiliation: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia
Email: f.liu@qut.edu.au

V. Anh
Affiliation: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia
Email: v.anh@qut.edu.au

I. Turner
Affiliation: School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, QLD 4001, Australia
Email: i.turner@qut.edu.au

DOI: http://dx.doi.org/10.1090/S0025-5718-2011-02447-6
PII: S 0025-5718(2011)02447-6
Keywords: Fractional derivative of variable order, anomalous subdiffusion equation, explicit numerical method
Received by editor(s): November 8, 2009
Received by editor(s) in revised form: April 29, 2010
Published electronically: June 9, 2011
Additional Notes: This research was supported by the Australian Research Council grants DP0559807 and DP0986766, the National Natural Science Foundation of China grant 10271098 and the Natural Science Foundation of Fujian province grant 2009J01014. The authors wish to thank the referee for many useful suggestions to improve this paper.
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.