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.
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.
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|Item Type:||Journal Article|
|Keywords:||Fractional Bloch–Torrey equation, Fractional calculus, Implicit numerical method, Alternating direction method, Stability, Convergence|
|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|
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