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Stability and convergence of Crank-Nicolson method for fractional advection dispersion equation. (English) Zbl 1178.65145

Summary: This paper is an attempt to study stability and convergence of a practical numerical algorithm used to solve one dimensional fractional advection-dispersion equation. Fractional advection equations are used in groundwater hydrology to model the transport of passive traces carried by fluid flow in a porous medium. Crank-Nicolson algorithm is applied to a one dimensional fractional advection-dispersion equations with variable coefficients on a finite domain. Application of these results is illustrated by modeling a radial flow problem. Use of the space-fractional derivative allows the model equation to capture the early arrival of tracer observed at a field site.

MSC:

65R20 Numerical methods for integral equations
45K05 Integro-partial differential equations
26A33 Fractional derivatives and integrals
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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