Numerical algorithms for the time‐Caputo and space‐Riesz fractional Bloch‐Torrey equations
Numerical algorithms for the time‐Caputo and space‐Riesz fractional Bloch‐Torrey equations
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DOI：
10.1002/num.22451
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发表时间：
2019-12
影响因子：
3.9
通讯作者：
Heng-fei Ding;Changpin Li
中科院分区：
文献类型：
--
作者：
Heng-fei Ding;Changpin Li
In this paper, high‐order numerical methods for time‐Caputo and space‐Riesz fractional Bloch‐Torrey equations in one‐ and two‐dimensional space are constructed, where the second‐order backward fractional difference operator and the sixth‐order fractional‐compact difference operator are applied to approximate the time and space fractional derivatives, respectively. The stability and convergence of the methods are analyzed and it is shown that the convergence orders are higher than the earlier work. Finally, some numerical experiments are presented to demonstrate the effectiveness of the methods and confirm our theoretical results.
