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  1. 1 Hejazi H.

  2. 1 Liu F.

  3. 1 Moroney T.

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

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Hejazi H., Moroney T., Liu F.
Open Physics
|
2013
|
vol. 11
|
issue 10
1275-1283
EN
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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