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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Numerical methods for solving a two-dimensional variable-order anomalous subdiffusion equation
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by Chang-Ming Chen, F. Liu, V. Anh and I. Turner PDF
Math. Comp. 81 (2012), 345-366 Request permission

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
  • 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.
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Math. Comp. 81 (2012), 345-366
  • MSC (2010): Primary 65M20, 65L06, 65R10, 26A33
  • DOI: https://doi.org/10.1090/S0025-5718-2011-02447-6
  • MathSciNet review: 2833498