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Finite difference approximations for fractional advection-dispersion flow equations. (English) Zbl 1126.76346

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:

76M20 Finite difference methods applied to problems in fluid mechanics
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
26A33 Fractional derivatives and integrals
35Q35 PDEs in connection with fluid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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