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

文献类型：期刊论文

作者Zhang, Jiali2; Huang, Jizu3,4; Wang, Kun2; Wang, Xin1
刊名NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
出版日期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
DOI10.1002/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
WOS记录号WOS:000591776600001
出版者WILEY
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.Shanghai Univ, Dept Math, Shanghai, Peoples R China
2.Chongqing Univ, Coll Math & Stat, Chongqing, Peoples R China
3.Chinese Acad Sci, Acad Math & Syst Sci, Inst Computat Math & Sci Engn Comp, LSEC,ICMSEC, Beijing, 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.

入库方式： OAI收割

来源：数学与系统科学研究院

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