A Fourier method for the fractional diffusion equation describing sub-diffusion

Chen, Chang-Ming, Liu, Fawang, Turner, Ian W., & Anh, Vo V. (2007) A Fourier method for the fractional diffusion equation describing sub-diffusion. Journal of Computational Physics, 227(2), pp. 886-897.

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In this paper, a fractional partial differential equation (FPDE) describing sub-diffusion is considered. An implicit difference approximation scheme (IDAS) for solving a FPDE is presented. We propose a Fourier method for analyzing the stability and convergence of the IDAS, derive the global accuracy of the IDAS, and discuss the solvability. Finally, numerical examples are given to compare with the exact solution for the order of convergence, and simulate the fractional dynamical systems.

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186 citations in Scopus
168 citations in Web of Science®
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ID Code: 14739
Item Type: Journal Article
Refereed: Yes
Keywords: Fractional diffusion equation, Sub, diffusion, Implicit difference approximation, Fourier method, Stability, Convergence
DOI: 10.1016/j.jcp.2007.05.012
ISSN: 0021-9991
Subjects: Australian and New Zealand Standard Research Classification > PHYSICAL SCIENCES (020000) > OTHER PHYSICAL SCIENCES (029900) > Physical Sciences not elsewhere classified (029999)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > PURE MATHEMATICS (010100) > Ordinary Differential Equations Difference Equations and Dynamical Systems (010109)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 2007 Elsevier
Copyright Statement: Reproduced in accordance with the copyright policy of the publisher.
Deposited On: 05 Sep 2008 00:00
Last Modified: 29 Feb 2012 13:37

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