Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D

Yu Q., Liu F., Turner I. and Burrage K. (2013) Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D. Central European Journal of Physics, 11 6: 646-665. doi:10.2478/s11534-013-0220-6

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Author Yu Q.
Liu F.
Turner I.
Burrage K.
Title Numerical investigation of three types of space and time fractional Bloch-Torrey equations in 2D
Journal name Central European Journal of Physics   Check publisher's open access policy
ISSN 1895-1082
1644-3608
Publication date 2013-06-01
Year available 2013
Sub-type Article (original research)
DOI 10.2478/s11534-013-0220-6
Open Access Status File (Author Post-print)
Volume 11
Issue 6
Start page 646
End page 665
Total pages 20
Place of publication Warsaw, Poland
Publisher Versita
Language eng
Subject 3100 Physics and Astronomy
Formatted abstract
Recently, the fractional Bloch-Torrey model has been used to study anomalous diffusion in the human brain. In this paper, we consider three types of space and time fractional Bloch-Torrey equations in two dimensions: Model-1 with the Riesz fractional derivative; Model-2 with the one-dimensional fractional Laplacian operator; and Model-3 with the two-dimensional fractional Laplacian operator. Firstly, we propose a spatially second-order accurate implicit numerical method for Model-1 whereby we discretize the Riesz fractional derivative using a fractional centered difference. We consider a finite domain where the time and space derivatives are replaced by the Caputo and the sequential Riesz fractional derivatives, respectively. Secondly, we utilize the matrix transfer technique for solving Model-2 and Model-3. Finally, some numerical results are given to show the behaviours of these three models especially on varying domain sizes with zero Dirichlet boundary conditions.
Keyword Bounded domains
Fractional Bloch-Torrey equation
Fractional centered difference
Implicit numerical method
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: Non HERDC
Centre for Advanced Imaging Publications
 
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Citation counts: TR Web of Science Citation Count  Cited 11 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 14 times in Scopus Article | Citations
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