Discrete comparison principle of a finite difference method for the multi-term time fractional diffusion equation

被引：6

作者：

Wang, Yue ^{[1
]}

Zhao, Youxing ^{[2
]}

Chen, Hu ^{[1
]}

机构：

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

[2] Ocean Univ China, Network & Informat Ctr, Qingdao 266100, Peoples R China

来源：

NUMERICAL ALGORITHMS | 2023年 / 93卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Discrete comparison principle; Multi-term time fractional; Finite difference method; Error analysis; alpha-robust; ELEMENT-METHOD;

D O I：

10.1007/s11075-022-01480-y

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A discrete comparison principle is given for the multi-term time fractional diffusion equation, where the discrete scheme is based on L1 approximation of the multi-term temporal Caputo derivative and the standard finite difference approximation of the spatial derivative. Then we use the discrete comparison principle to give an error analysis of the discrete scheme by constructing a barrier function. The final numerical results verify our theoretical analysis under the realistic assumption that the solution of the time fractional diffusion equation has a weak singularity near the initial time t = 0.

引用

页码：1581 / 1593

页数：13

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