A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions. (24th September 2017)

• Record Type: Journal Article
• Authors: Liu, Taohua; Hou, Muzhou
• Other Names: Torrisi Mariano Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2017(2017)
• Publication Date: 2017-09-24
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2017/8716752
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : Fractional advection-dispersion equations, as generalizations of classical integer-order advection-dispersion equations, are used to model the transport of passive tracers carried by fluid flow in a porous medium. In this paper, we develop an implicit finite difference method for fractional advection-dispersion equations with fractional derivative boundary conditions. First-order consistency, solvability, unconditional stability, and first-order convergence of the method are proven. Then, we present a fast iterative method for the implicit finite difference scheme, which only requires storage of O ( K ) and computational cost of O ( K log ⁡ K ) . Traditionally, the Gaussian elimination method requires storage of O ( K 2 ) and computational cost of O ( K 3 ) . Finally, the accuracy and efficiency of the method are checked with a numerical example.