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Zbl 1148.76044
Momani, Shaher; Odibat, Zaid
Numerical solutions of the space-time fractional advection-dispersion equation. (English)
[J] Numer. Methods Partial Differ. Equations 24, No. 6, 1416-1429 (2008). ISSN 0749-159X; ISSN 1098-2426/e

Summary: Fractional advection-dispersion equations are used in groundwater hydrologhy to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper we present two reliable algorithms, the Adomian decomposition method and variational iteration method, to construct numerical solutions of the space-time fractional advection-dispersion equation in the form of a rabidly convergent series with easily computable components. The fractional derivatives are described in the Caputo sense. Some examples are given. Numerical results show that the two approaches are easy to implement and accurate when applied to space-time fractional advection-dispersion equations.

MSC 2000:: *76M25 Other numerical methods
76M30 Variational methods
76R99 Diffusion and convection
76S05 Flows in porous media
86A05 Hydrology, hydrography, oceanography

Keywords: Caputo fractional derivative; variational iteration method; Adomian decomposition method

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