A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D

Yu, Q., Liu, F., Turner, I., & Burrage, K. (2012) A computationally effective alternating direction method for the space and time fractional Bloch–Torrey equation in 3-D. Applied Mathematics and Computation, 219(8), pp. 4082-4095.

View at publisher


The space and time fractional Bloch–Torrey equation (ST-FBTE) has been used to study anomalous diffusion in the human brain. Numerical methods for solving ST-FBTE in three-dimensions are computationally demanding. In this paper, we propose a computationally effective fractional alternating direction method (FADM) to overcome this problem. We consider ST-FBTE on a finite domain where the time and space derivatives are replaced by the Caputo–Djrbashian and the sequential Riesz fractional derivatives, respectively. The stability and convergence properties of the FADM are discussed. Finally, some numerical results for ST-FBTE are given to confirm our theoretical findings.

Impact and interest:

16 citations in Scopus
Search Google Scholar™
13 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:

86 since deposited on 16 May 2013
11 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: 60023
Item Type: Journal Article
Refereed: Yes
Keywords: Fractional Bloch–Torrey equation, Fractional calculus, Implicit numerical method, Alternating direction method, Stability, Convergence
DOI: 10.1016/j.amc.2012.10.056
ISSN: 00963003
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > NUMERICAL AND COMPUTATIONAL MATHEMATICS (010300) > Numerical Analysis (010301)
Divisions: Current > Schools > School of Mathematical Sciences
Current > QUT Faculties and Divisions > Science & Engineering Faculty
Copyright Owner: Copyright 2012 Elsevier.
Deposited On: 16 May 2013 06:56
Last Modified: 16 May 2013 06:56

Export: EndNote | Dublin Core | BibTeX

Repository Staff Only: item control page