## Numerical solutions of the space-time fractional advection-dispersion equation.(English)Zbl 1148.76044

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:

 76M25 Other numerical methods (fluid mechanics) (MSC2010) 76M30 Variational methods applied to problems in fluid mechanics 76R99 Diffusion and convection 76S05 Flows in porous media; filtration; seepage 86A05 Hydrology, hydrography, oceanography
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