Numerical techniques for the variable order time fractional diffusion equation

Shen, S., Liu, F., Chen, J., Turner, I., & Anh, V. (2012) Numerical techniques for the variable order time fractional diffusion equation. Applied Mathematics and Computation, 218(22), pp. 10861-10870.

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Abstract

In this paper we consider the variable order time fractional diffusion equation. We adopt the Coimbra variable order (VO) time fractional operator, which defines a consistent method for VO differentiation of physical variables. The Coimbra variable order fractional operator also can be viewed as a Caputo-type definition. Although this definition is the most appropriate definition having fundamental characteristics that are desirable for physical modeling, numerical methods for fractional partial differential equations using this definition have not yet appeared in the literature. Here an approximate scheme is first proposed. The stability, convergence and solvability of this numerical scheme are discussed via the technique of Fourier analysis. Numerical examples are provided to show that the numerical method is computationally efficient. Crown Copyright © 2012 Published by Elsevier Inc. All rights reserved.

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ID Code: 51509
Item Type: Journal Article
Refereed: Yes
Additional Information: Export Date: 8 July 2012
Source: Scopus
CODEN: AMHCB
Language of Original Document: English
Correspondence Address: Liu, F.; School of Mathematical Sciences, Queensland University of Technology, G.P.O. Box 2434, Brisbane, QLD 4001, Australia; email: f.liu@qut.edu.au
Keywords: Convergence, Fourier analysis, Numerical method, Solvability, Stability, Variable order time fractional diffusion equation
DOI: 10.1016/j.amc.2012.04.047
ISSN: 0096-3003
Divisions: Current > Schools > School of Chemistry, Physics & Mechanical Engineering
Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Crown copyright © 2012 Published by Elsevier Inc.
Copyright Statement: NOTICE: this is the author’s version of a work that was accepted for publication in Applied Mathematics and Computation. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Applied Mathematics and Computation, Volume 218, Issue 22, (15 July 2012). DOI: 10.1016/j.amc.2012.04.047
Deposited On: 10 Jul 2012 01:35
Last Modified: 30 Aug 2013 12:21

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