Efficient spatial second-/fourth-order finite difference ADI methods for multi-dimensional variable-order time-fractional diffusion equations
Efficient spatial second-/fourth-order finite difference ADI methods for multi-dimensional variable-order time-fractional diffusion equations
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DOI：
10.1007/s10444-021-09881-8
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发表时间：
2021-08
影响因子：
1.7
通讯作者：
Hongfei Fu;Che Zhu;Xueting Liang;Bingyin Zhang
中科院分区：
文献类型：
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作者：
Hongfei Fu;Che Zhu;Xueting Liang;Bingyin Zhang
考虑了可用于模拟非均匀多孔介质中溶质运移的变阶时间分数阶扩散方程。关于适定性和正则性理论(参看，郑王，分析。应用，2020)，针对二维VO-TFDE分别提出了两种有限差分ADI格式和紧致ADI格式。我们证明了这两个格式是无条件稳定的，并且在空间中关于相应的离散范数以二阶和四阶收敛。此外，还讨论了ADI格式的效率和实际计算量。在此基础上，将ADI方法和紧致ADI方法推广到三维VO-TFDE模型，并证明了无条件稳定性和收敛性质。最后，给出了几个数值算例，验证了理论分析，并说明了ADI方法的有效性。
Variable-order time-fractional diffusion equations (VO-tFDEs), which can be used to model solute transport in heterogeneous porous media are considered. Concerning the well-posedness and regularity theory (cf., Zheng & Wang, Anal. Appl., 2020), two finite difference ADI and compact ADI schemes are respectively proposed for the two-dimensional VO-tFDE. We show that the two schemes are unconditionally stable and convergent with second and fourth orders in space with respect to corresponding discrete norms. Besides, efficiency and practical computation of the ADI schemes are also discussed. Furthermore, the ADI and compact ADI methods are extended to model three-dimensional VO-tFDE, and unconditional stability and convergence are also proved. Finally, several numerical examples are given to validate the theoretical analysis and show efficiency of the ADI methods.