Error estimate on the tanh meshes for the time fractional diffusion equation

被引：4

作者：

Zhang, Jiali ^{[1
]}

Huang, Jizu ^{[2
,3
]}

Wang, Kun ^{[1
]}

Wang, Xin ^{[4
]}

机构：

[1] Chongqing Univ, Coll Math & Stat, Chongqing, Peoples R China

[2] Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC,ICMSEC, Beijing, Peoples R China

[3] Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China

[4] Shanghai Univ, Dept Math, Shanghai, Peoples R China

来源：

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS | 2021年 / 37卷 / 03期

关键词：

Caputo fractional derivative; error estimate; the tanh meshes; unconditionally stable; weak singularity; FINITE-DIFFERENCE METHOD; SPECTRAL METHOD; WAVE EQUATIONS; APPROXIMATIONS; SCHEME;

D O I：

10.1002/num.22656

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the discrete scheme for the time fractional diffusion equation with order alpha is an element of (0, 1). Since the solution of the given problem usually has a weak singularity near the initial time t = 0, the maximum error of the L1 scheme based on a uniform mesh cannot reach the ideal convergence rate 2 - alpha. As an improvement, a kind of nonuniform meshes (the tanh meshes) is proposed. The L1 scheme based on the tanh meshes is proved to be unconditionally stable and reach the ideal convergence rate by suitably choosing the parameter. Some numerical tests are carried out to confirm the error analysis of the L1 scheme based on the proposed nonuniform meshes.

引用

页码：2046 / 2066

页数：21

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