Fast Finite Difference Schemes for Time-Fractional Diffusion Equations with a Weak Singularity at Initial Time

被引：54

作者：

Shen, Jin-ye ^{[1
]}

Sun, Zhi-zhong ^{[1
]}

Du, Rui ^{[1
]}

机构：

[1] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China

来源：

EAST ASIAN JOURNAL ON APPLIED MATHEMATICS | 2018年 / 8卷 / 04期

基金：

中国国家自然科学基金;

关键词：

Fractional differential equation; difference scheme; fast algorithm; singularity; NONUNIFORM TIMESTEPS; STEPPING METHOD; DYNAMICS; MESHES;

D O I：

10.4208/eajam.010418.020718

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A sharp estimate for the L1 formula on graded meshes, which approximates the Caputo derivatives of functions with a weak singularity at t = 0 is obtained. Combining such approximations with the sum-of-exponential approximations of the kernel, we develop fast difference schemes for one- and two-dimensional fractional diffusion equations, the solutions of which have a weak singularity at the starting time. The proof of the stability and convergence is based on the maximum principle. Numerical examples confirm theoretical estimates.

引用

页码：834 / 858

页数：25

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