A novel numerical approximation for the space fractional advection-dispersion equation

Shen, S., Liu, F., Anh, V., Turner, I., & Chen, J. (2014) A novel numerical approximation for the space fractional advection-dispersion equation. IMA Journal of Applied Mathematics, 79(3), pp. 431-444.

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In this paper, we consider a space fractional advection–dispersion equation. The equation is obtained from the standard advection–diffusion equation by replacing the first- and second-order space derivatives by the Riesz fractional derivatives of order β1 ∈ (0, 1) and β2 ∈ (1, 2], respectively. The fractional advection and dispersion terms are approximated by using two fractional centred difference schemes. A new weighted Riesz fractional finite-difference approximation scheme is proposed. When the weighting factor θ equals 12, a second-order accuracy scheme is obtained. The stability, consistency and convergence of the numerical approximation scheme are discussed. A numerical example is given to show that the numerical results are in good agreement with our theoretical analysis.

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ID Code: 59969
Item Type: Journal Article
Refereed: Yes
Keywords: Riesz fractional advection–dispersion equation, weighted finite-difference approximation scheme , Crank–Nicolson scheme, second-order accurate scheme, stability; consistency, convergence
DOI: 10.1093/imamat/hxs073
ISSN: 1464-3634
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Deposited On: 14 May 2013 03:27
Last Modified: 26 Aug 2014 01:12

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