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Numerical solutions of the space‐time fractional advection‐dispersion equation
Author(s) -
Momani Shaher,
Odibat Zaid
Publication year - 2008
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.20324
Subject(s) - mathematics , advection , adomian decomposition method , dispersion (optics) , fractional calculus , partial differential equation , series (stratigraphy) , mathematical analysis , decomposition method (queueing theory) , convergent series , flow (mathematics) , geometry , physics , paleontology , discrete mathematics , biology , optics , thermodynamics , power series
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. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008