Numerical methods and analysis for a class of fractional advection-dispersion models

Liu, F., Zhuang, P., & Burrage, K. (2012) Numerical methods and analysis for a class of fractional advection-dispersion models. Computers and Mathematics with Applications, 64(10), pp. 2990-3007.

View at publisher


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.

Impact and interest:

50 citations in Scopus
Search Google Scholar™
48 citations in Web of Science®

Citation counts are sourced monthly from Scopus and Web of Science® citation databases.

These databases contain citations from different subsets of available publications and different time periods and thus the citation count from each is usually different. Some works are not in either database and no count is displayed. Scopus includes citations from articles published in 1996 onwards, and Web of Science® generally from 1980 onwards.

Citations counts from the Google Scholar™ indexing service can be viewed at the linked Google Scholar™ search.

Full-text downloads:

114 since deposited on 10 Jul 2012
14 in the past twelve months

Full-text downloads displays the total number of times this work’s files (e.g., a PDF) have been downloaded from QUT ePrints as well as the number of downloads in the previous 365 days. The count includes downloads for all files if a work has more than one.

ID Code: 51515
Item Type: Journal Article
Refereed: Yes
Keywords: Fractional advection–dispersion models, Implicit numerical methods, Stability, Convergence, Fractional calculus
DOI: 10.1016/j.camwa.2012.01.020
ISSN: 0898-1221
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

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page