Numerical methods and analysis for a class of fractional advection-dispersion models
In this paper, a class of fractional advection–dispersion models (FADMs) is considered. These models include five fractional advection–dispersion models, i.e., the time FADM, the mobile/immobile time FADM with a time Caputo fractional derivative 0 < γ < 1, the space FADM with two sides Riemann–Liouville derivatives, the time–space FADM and the time fractional advection–diffusion-wave model with damping with index 1 < γ < 2. These equations can be used to simulate the regional-scale anomalous dispersion with heavy tails. We propose computationally effective implicit numerical methods for these FADMs. The stability and convergence of the implicit numerical methods are analysed and compared systematically. Finally, some results are given to demonstrate the effectiveness of theoretical analysis.
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|Item Type:||Journal Article|
|Keywords:||Fractional advection–dispersion models, Implicit numerical methods, Stability, Convergence, Fractional calculus|
|Subjects:||Australian and New Zealand Standard Research Classification > INFORMATION AND COMPUTING SCIENCES (080000)|
|Divisions:||Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
|Copyright Owner:||Crown Copyright © 2012 Published by Elsevier Ltd.|
|Copyright Statement:||NOTICE: this is the author’s version of a work that was accepted for publication in Computers & Mathematics with Applications. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Computers & Mathematics with Applications, [Volume 64, Issue 10, (November 2012)]. DOI: 10.1016/j.camwa.2012.01.020|
|Deposited On:||10 Jul 2012 03:21|
|Last Modified:||07 Dec 2013 12:21|
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