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
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
Collection year 2014
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 5 times in Thomson Reuters Web of Science Article | Citations
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