KMS Of Academy of mathematics and systems sciences, CAS
| Error estimate on the tanh meshes for the time fractional diffusion equation | |
| Zhang, Jiali1; Huang, Jizu2,3; Wang, Kun1; Wang, Xin4 | |
| 2020-11-24 | |
| Source Publication | NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
 |
| ISSN | 0749-159X |
| Pages | 21 |
| Abstract | 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. |
| Keyword | Caputo fractional derivative error estimate the tanh meshes unconditionally stable weak singularity |
| DOI | 10.1002/num.22656 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | 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 Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000591776600001 |
| Publisher | WILEY |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/52489 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Huang, Jizu |
| Affiliation | 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 |
| Recommended Citation 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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