Abu-Saman, Awni M. Stability and convergence of Crank-Nicolson method for fractional advection dispersion equation. (English) Zbl 1178.65145 Adv. Appl. Math. Anal. 2, No. 2, 117-125 (2007). 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. Cited in 7 Documents 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 Keywords:fractional order differential equation; advection-dispersion equation; Crank-Nicolson method; stability; convergence; algorithm; radial flow problem PDFBibTeX XMLCite \textit{A. M. Abu-Saman}, Adv. Appl. Math. Anal. 2, No. 2, 117--125 (2007; Zbl 1178.65145) Full Text: Link