Fast and efficient finite difference/finite element method for the two-dimensional multi-term time-space fractional Bloch-Torrey equation

作者：

Highlights：

• Presenting a novel numerical scheme with faster calculation speed and lower storage.

• Establishing numerical scheme based on the non-uniform meshes, which enables the low regularity of exact solution in time to be handled and some time adaptive algorithms to be developed in future work.

• Overcoming low temporal convergence rate of classical numerical schemes for fractional Bloch-Torrey equation by decoupling.

• Skillfully, obtaining higher precision in time based on a coupled equation.

摘要

•Presenting a novel numerical scheme with faster calculation speed and lower storage.•Establishing numerical scheme based on the non-uniform meshes, which enables the low regularity of exact solution in time to be handled and some time adaptive algorithms to be developed in future work.•Overcoming low temporal convergence rate of classical numerical schemes for fractional Bloch-Torrey equation by decoupling.•Skillfully, obtaining higher precision in time based on a coupled equation.

论文关键词：Fractional Bloch-Torrey equation,Non-uniform mesh,Fast finite difference method,Finite element method,Stability and convergence

论文评审过程：Received 25 July 2020, Revised 2 January 2021, Accepted 4 January 2021, Available online 20 January 2021, Version of Record 20 January 2021.

论文官网地址：https://doi.org/10.1016/j.amc.2021.125985