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

doi:10.1002/num.22656

	Error estimate on the tanh meshes for the time fractional diffusion equation
	Zhang, Jiali 3; Huang, Jizu 1,4; Wang, Kun 3; Wang, Xin 2
刊名	NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
	2020-11-24
页码	21
关键词	Caputo fractional derivative error estimate the tanh meshes unconditionally stable weak singularity
ISSN号	0749-159X
DOI	10.1002/num.22656
英文摘要	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.
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
语种	英语
出版者	WILEY
WOS记录号	WOS:000591776600001
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/52488]
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.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC,ICMSEC, Beijing, Peoples R China 2.Shanghai Univ, Dept Math, Shanghai, Peoples R China 3.Chongqing Univ, Coll Math & Stat, Chongqing, Peoples R China 4.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, 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.