A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions

Taohua Liu and Muzhou Hou

Advances in Mathematical Physics, 2017, vol. 2017, 1-8

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 and computational cost of . Traditionally, the Gaussian elimination method requires storage of and computational cost of . Finally, the accuracy and efficiency of the method are checked with a numerical example.

Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlamp:8716752

DOI: 10.1155/2017/8716752

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