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.
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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|Item Type:||Journal Article|
|Keywords:||two-sided time-space fractional advection-dispersion, fractional Fick’s law, finite volume, finite difference, shifted Grünwald|
|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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