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

doi:10.1002/num.22656

CSpace

	Error estimate on the tanh meshes for the time fractional diffusion equation
	Zhang, Jiali 1; Huang, Jizu 2,3; Wang, Kun 1; Wang, Xin 4
	2020-11-24
发表期刊	NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
ISSN	0749-159X
页码	21
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.
关键词	Caputo fractional derivative error estimate the tanh meshes unconditionally stable weak singularity
DOI	10.1002/num.22656
收录类别	SCI
语种	英语
资助项目	Strategic Priority Research Program of the Chinese Academy of Sciences[XDB22020100] ; Natural Science Foundation of Chongqing[cstc2020jcyj-msxmX0551] ; Fundamental Research Funds for the Central Universities[2019CDXYST0016] ; NSFC[11871069]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000591776600001
出版者	WILEY
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/52489
专题	中国科学院数学与系统科学研究院
通讯作者	Huang, Jizu
作者单位	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
推荐引用方式 GB/T 7714	Zhang, Jiali,Huang, Jizu,Wang, Kun,et al. Error estimate on the tanh meshes for the time fractional diffusion equation[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,2020:21.
APA	Zhang, Jiali,Huang, Jizu,Wang, Kun,&Wang, Xin.(2020).Error estimate on the tanh meshes for the time fractional diffusion equation.NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS,21.
MLA	Zhang, Jiali,et al."Error estimate on the tanh meshes for the time fractional diffusion equation".NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS (2020):21.