A Fast Algorithm for the Caputo Fractional Derivative

doi:10.4208/eajam.080418.200618

	A Fast Algorithm for the Caputo Fractional Derivative
	Wang, Kun 1; Huang, Jizu2,3
	2018-11-01
发表期刊	EAST ASIAN JOURNAL ON APPLIED MATHEMATICS
ISSN	2079-7362
卷号	8 期号:4 页码:656-677
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.
关键词	Caputo derivative fast algorithm polynomial approximation error graded mesh
DOI	10.4208/eajam.080418.200618
语种	英语
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
WOS类目	Mathematics, Applied
WOS记录号	WOS:000456113500004
出版者	GLOBAL SCIENCE PRESS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/32209
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.