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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:
76M20Finite difference methods (fluid mechanics)
65M06Finite difference methods (IVP of PDE)
26A33Fractional derivatives and integrals (real functions)
35Q35PDEs in connection with fluid mechanics
65M12Stability and convergence of numerical methods (IVP of PDE)