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, issue 1

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(Klog⁡K). Traditionally, the Gaussian elimination method requires storage of O(K2) and computational cost of O(K3). Finally, the accuracy and efficiency of the method are checked with a numerical example.

Date: 2017
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2017/8716752

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2017:y:2017:i:1:n:8716752

Access Statistics for this article

More articles in Advances in Mathematical Physics from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().