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

• Authors: Qiang Yu , Fawang Liu , Ian Turner , Kevin Burrage
• Languages of publication: EN

Abstracts

EN

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.

Keywords

EN

fractional Bloch-Torrey equation; fractional centered difference; implicit numerical method; matrix transfer technique; bounded domains

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 6
• Pages: 646-665

Dates

published

1 - 6 - 2013

online

9 - 10 - 2013

Contributors

author

Qiang Yu

• School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia

author

Fawang Liu

• School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia

author

Ian Turner

• School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane, Qld., 4001, Australia

author

Kevin Burrage

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Identifiers

DOI

10.2478/s11534-013-0220-6