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

作者：Yu Q; Liu F^*; Turner I; Burrage K

来源：Applied Mathematics and Computation, 2012, 219(8): 4082-4095.

DOI：10.1016/j.amc.2012.10.056

• Fractional Bloch-Torrey equation
• Fractional calculus
• Implicit numerical method
• Alternating direction method
• Stability
• Convergence

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.

• 出版日期2012-12-15