Error estimate on the tanh meshes for the time fractional diffusion equation | |
Zhang, Jiali3; Huang, Jizu1,4; Wang, Kun3; Wang, Xin2 | |
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. |
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