Efficient spatial second-/fourth-order finite difference ADI methods for multi-dimensional variable-order time-fractional diffusion equations

被引：0
作者：
Hongfei Fu
Chen Zhu
Xueting Liang
Bingyin Zhang
机构：
[1] Ocean University of China,School of Mathematical Sciences
[2] China University of Petroleum (East China),College of Science
来源：
Advances in Computational Mathematics | 2021年 / 47卷
关键词：
Variable-order time-fractional diffusion equations; Finite difference method; ADI method; Compact ADI method; Stability and convergence; 26A33; 65M06; 65M12;
D O I：
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中图分类号：
学科分类号：
摘要：
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.
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