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

Yu, Q., Liu, F., Turner, I. and 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: 4082-4095. doi:10.1016/j.amc.2012.10.056


Author Yu, Q.
Liu, F.
Turner, I.
Burrage, K.
Title A computationally effective alternating direction method for the space and time fractional Bloch-Torrey equation in 3-D
Journal name Applied Mathematics and Computation   Check publisher's open access policy
ISSN 0096-3003
1873-5649
Publication date 2012-12-15
Sub-type Article (original research)
DOI 10.1016/j.amc.2012.10.056
Open Access Status Not Open Access
Volume 219
Issue 8
Start page 4082
End page 4095
Total pages 14
Place of publication Philadelphia, PA, United States
Publisher Elsevier
Language eng
Abstract 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.
Keyword Alternating direction method
Convergence
Fractional Bloch-Torrey equation
Fractional calculus
Implicit numerical method
Stability
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: Centre for Advanced Imaging Publications
 
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Citation counts: TR Web of Science Citation Count  Cited 14 times in Thomson Reuters Web of Science Article | Citations
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