Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

Zhuang, P., Liu, F., Anh, V., & Turner, I. W. (2009) Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process. IMA Journal of Applied Mathematics, 74(5), pp. 645-667.

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In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP):

Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

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28 citations in Web of Science®
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ID Code: 29759
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: fractional reaction–subdiffusion equation, implicit numerical method, convergence and stability, energy method
DOI: 10.1093/imamat/hxp015
ISSN: 0272-4960
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > APPLIED MATHEMATICS (010200)
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Past > Schools > Mathematical Sciences
Deposited On: 18 Jan 2010 21:33
Last Modified: 01 Mar 2012 00:04

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