A computationally effective alternating direction method for the space and time fractional Bloch-Torrey equation in 3-D
A computationally effective alternating direction method for the space and time fractional Bloch-Torrey equation in 3-D
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DOI：
10.1016/j.amc.2012.10.056
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发表时间：
2012-12
期刊：
影响因子：
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通讯作者：
Q. Yu;Fawang Liu;I. Turner;K. Burrage
中科院分区：
文献类型：
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作者：
Q. Yu;Fawang Liu;I. Turner;K. Burrage
利用时空分数阶Bloch-Torrey方程（ST-FBTE）研究了人脑中的反常弥散。在三维空间中求解ST-FBTE的数值方法在计算上要求很高。在本文中，我们提出了一个计算有效的分数交替方向法（FADM），以克服这个问题。我们考虑有限域上的ST-FBTE，其中时间和空间导数分别用Caputo-Djrbashian和序列Riesz分数导数代替。讨论了FADM的稳定性和收敛性。最后，给出了ST-FBTE的数值结果，以证实我们的理论研究结果。
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.