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Zbl 1126.76346
Meerschaert, Mark M.; Tadjeran, Charles
Finite difference approximations for fractional advection-dispersion flow equations. (English)
[J] J. Comput. Appl. Math. 172, No. 1, 65-77 (2004). ISSN 0377-0427

Summary: Fractional advection-dispersion equations are used in groundwater hydrology to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper we develop practical numerical methods to solve one dimensional fractional advection-dispersion equations with variable coefficients on a finite domain. The practical application of these results is illustrated by modeling a radial flow problem. Use of the fractional derivative allows the model equations to capture the early arrival of tracer observed at a field site.

MSC 2000:: *76M20 Finite difference methods
65M06 Finite difference methods (IVP of PDE)
26A33 Fractional derivatives and integrals (real functions)
35Q35 Other equations arising in fluid mechanics
65M12 Stability and convergence of numerical methods (IVP of PDE)

Keywords: Finite difference approximation; Stability; Backward Euler method; Implicit Euler method; Radial dispersion; Radial advection; Fractional diffusion; Fractional derivative; Fractional advection--dispersion; Numerical fractional ADE

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Zentralblatt MATH Berlin [Germany]