A Fast Algorithm for the Caputo Fractional Derivative
文献类型：期刊论文
| 作者 | Wang, Kun1; Huang, Jizu2,3
|
| 刊名 | EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
 |
| 出版日期 | 2018-11-01 |
| 卷号 | 8期号:4页码:656-677 |
| 关键词 | Caputo derivative fast algorithm polynomial approximation error graded mesh |
| ISSN号 | 2079-7362 |
| DOI | 10.4208/eajam.080418.200618 |
| 英文摘要 | A fast algorithm with almost optimal memory for the computation of Caputo's fractional derivative is developed. It is based on a nonuniform splitting of the time interval [0, t(n)] and a polynomial approximation of the kernel function (1 - tau )(-alpha). Both the storage requirements and the computational cost are reduced from O(n) to (K +1)O(log n) with K being the degree of the approximated polynomial. The algorithm is applied to linear and nonlinear fractional diffusion equations. Numerical results show that this scheme and the corresponding direct methods have the same order of convergence but the method proposed performs better in terms of computational time. |
| 资助项目 | National Natural Science Foundation of China[11501554] ; National Natural Science Foundation of China[91630205] ; Fundamental Research Funds for the Central Universities[106112017CDJXY100006] ; Chongqing Research Program of Basic Research and Frontier Technology[CSTC2017JCYJAX0231] ; Strategic Priority Research Program of the Chinese Academy of Science[XDB22020100] |
| WOS研究方向 | Mathematics |
| 语种 | 英语 |
| WOS记录号 | WOS:000456113500004 |
| 出版者 | GLOBAL SCIENCE PRESS |
| 源URL | [http://ir.amss.ac.cn/handle/2S8OKBNM/32208]  |
| 专题 | 计算数学与科学工程计算研究所 |
| 通讯作者 | Huang, Jizu |
| 作者单位 | 1.Chongqing Univ, Coll Math & Stat, Chongqing 401331, Peoples R China 2.Chinese Acad Sci, Acad Math & Syst Sci, ICMSEC, LSEC, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China |
| 推荐引用方式 GB/T 7714 | Wang, Kun,Huang, Jizu. A Fast Algorithm for the Caputo Fractional Derivative[J]. EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,2018,8(4):656-677. |
| APA | Wang, Kun,&Huang, Jizu.(2018).A Fast Algorithm for the Caputo Fractional Derivative.EAST ASIAN JOURNAL ON APPLIED MATHEMATICS,8(4),656-677. |
| MLA | Wang, Kun,et al."A Fast Algorithm for the Caputo Fractional Derivative".EAST ASIAN JOURNAL ON APPLIED MATHEMATICS 8.4(2018):656-677. |
入库方式： OAI收割
来源：数学与系统科学研究院
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