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A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation

Shen, S., Liu, F., Anh, V., Turner, I., & Chen, J. (2012) A second-order accurate numerical approximation for the Riesz space fractional advection-dispersion equation. In Chen, Wen, Sun, HongGuang, & Baleanu, Dumitru (Eds.) The Proceedings of the Fifth Symposium on Fractional Differentiation and Its Applications, Hohai University, Hohai University, Nanjing.

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Abstract

In this paper, we consider a space Riesz fractional advection-dispersion equation. The equation is obtained from the standard advection-diffusion equation by replacing the ¯rst-order and second-order space derivatives by the Riesz fractional derivatives of order β 1 Є (0; 1) and β2 Є(1; 2], respectively. Riesz fractional advection and dispersion terms are approximated by using two fractional centered difference schemes, respectively. A new weighted Riesz fractional ¯nite difference approximation scheme is proposed. When the weighting factor Ѳ = 1/2, a second- order accurate numerical approximation scheme for the Riesz fractional advection-dispersion equation is obtained. 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: 51460
Item Type: Conference Paper
Keywords: Riesz fractional advection-dispersion equation, weighted finite difference approximation scheme, Crank-Nicolson scheme, second-order accurate, stability, consistency
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
Copyright Owner: Copyright 2012 [please consult the author]
Deposited On: 06 Jul 2012 09:35
Last Modified: 13 Jun 2013 00:54

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