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A Fast Algorithm for the Caputo Fractional Derivative
Wang, Kun1; Huang, Jizu2,3
AbstractA 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.
KeywordCaputo derivative fast algorithm polynomial approximation error graded mesh
Funding ProjectNational 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 Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000456113500004
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Document Type期刊论文
Corresponding AuthorHuang, Jizu
Affiliation1.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
Recommended Citation
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.
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