Stability and convergence of a finite volume method for the space fractional advection-dispersion equation

Hejazi, Hala, Moroney, Timothy J., & Liu, Fawang (2014) Stability and convergence of a finite volume method for the space fractional advection-dispersion equation. Journal of Computational and Applied Mathematics, 255, pp. 684-697.

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Abstract

We consider the space fractional advection–dispersion equation, which is obtained from the classical advection–diffusion equation by replacing the spatial derivatives with a generalised derivative of fractional order. We derive a finite volume method that utilises fractionally-shifted Grünwald formulae for the discretisation of the fractional derivative, to numerically solve the equation on a finite domain with homogeneous Dirichlet boundary conditions. We prove that the method is stable and convergent when coupled with an implicit timestepping strategy. Results of numerical experiments are presented that support the theoretical analysis.

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ID Code: 56974
Item Type: Journal Article
Refereed: Yes
Additional URLs:
Keywords: Fractional advection-dispersion, finite volume method, shifted Grunwald, stability, convergence
DOI: 10.1016/j.cam.2013.06.039
ISSN: 0377-0427
Subjects: 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) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical and Computational Mathematics not elsewhere classified (010399)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Elsevier BV
Copyright Statement: This is the author’s version of a work that was accepted for publication in Journal of Computational and Applied Mathematics. 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 Journal of Computational and Applied Mathematics, [VOL 255, (2014)] DOI: 10.1016/j.cam.2013.06.039
Deposited On: 07 Feb 2013 05:21
Last Modified: 05 Feb 2016 05:53

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