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A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions
Joint Authors
Source
Advances in Mathematical Physics
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-09-24
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
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(KlogK).
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.
American Psychological Association (APA)
Liu, Taohua& Hou, Muzhou. 2017. A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions. Advances in Mathematical Physics،Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1123323
Modern Language Association (MLA)
Liu, Taohua& Hou, Muzhou. A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions. Advances in Mathematical Physics No. 2017 (2017), pp.1-8.
https://search.emarefa.net/detail/BIM-1123323
American Medical Association (AMA)
Liu, Taohua& Hou, Muzhou. A Fast Implicit Finite Difference Method for Fractional Advection-Dispersion Equations with Fractional Derivative Boundary Conditions. Advances in Mathematical Physics. 2017. Vol. 2017, no. 2017, pp.1-8.
https://search.emarefa.net/detail/BIM-1123323
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1123323