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

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Central European Journal of Physics

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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Authors and Affiliations

  1. School of Mathematical Sciences, Queensland University of Technology, GPO BOX 2434, Brisbane, QLD., 4001, Australia

    Hala Hejazi, Timothy Moroney & Fawang Liu

Authors
  1. Hala Hejazi
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  2. Timothy Moroney
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  3. Fawang Liu
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Correspondence to Hala Hejazi.

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Hejazi, H., Moroney, T. & Liu, F. A finite volume method for solving the two-sided time-space fractional advection-dispersion equation. centr.eur.j.phys. 11, 1275–1283 (2013). https://doi.org/10.2478/s11534-013-0317-y

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  • DOI: https://doi.org/10.2478/s11534-013-0317-y

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