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

被引：7

作者：

Fu, Hongfei ^{[1
]}

Zhu, Chen ^{[2
]}

Liang, Xueting ^{[2
]}

Zhang, Bingyin ^{[2
]}

机构：

[1] Ocean Univ China, Sch Math Sci, Qingdao 266100, Shandong, Peoples R China

[2] China Univ Petr East China, Coll Sci, Qingdao 266580, Shandong, Peoples R China

来源：

ADVANCES IN COMPUTATIONAL MATHEMATICS | 2021年 / 47卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Variable-order time-fractional diffusion equations; Finite difference method; ADI method; Compact ADI method; Stability and convergence; SUB-DIFFUSION; COLLOCATION METHOD; CONSTANT-ORDER; ELEMENT-METHOD; SCHEMES; SPACE; DISCRETIZATION; ACCURACY; CALCULUS; MODEL;

D O I：

10.1007/s10444-021-09881-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页数：33

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