A finite volume method for solving the two-sided time-space fractional advection-dispersion equation

Hejazi, Hala, Moroney, Timothy, & Liu, Fawang (2013) A finite volume method for solving the two-sided time-space fractional advection-dispersion equation. Central European Journal of Physics, 11(10), pp. 1275-1283.

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Abstract

We present a finite volume method to solve the time-space two-sided fractional advection-dispersion equation on a one-dimensional domain. The spatial discretisation employs fractionally-shifted Grünwald formulas to discretise the Riemann-Liouville fractional derivatives at control volume faces in terms of function values at the nodes. We demonstrate how the finite volume formulation provides a natural, convenient and accurate means of discretising this equation in conservative form, compared to using a conventional finite difference approach. Results of numerical experiments are presented to demonstrate the effectiveness of the approach.

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ID Code: 69053
Item Type: Journal Article
Refereed: Yes
Keywords: two-sided time-space fractional advection-dispersion, fractional Fick’s law, finite volume, finite difference, shifted Grünwald
DOI: 10.2478/s11534-013-0317-y
ISSN: 1895-1082
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Solution of Differential and Integral Equations (010302)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2013 Versita sp. z o.o.
Copyright Statement: The final publication is available at Springer via http://dx.doi.org/10.2478/s11534-013-0317-y
Deposited On: 23 Mar 2014 22:51
Last Modified: 03 Nov 2014 17:58

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