Uniform approximation to fractional derivatives of functions of algebraic singularity

Material type: 文書・図像類

Author: HASEGAWA, Takemitsuほか

Publisher: Elsevier Science Publishers B. V.

Publication date: 2009-06

Material Format: Digital

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Note (General)：: Fractional derivative D^qf(x) (0 < q < 1, 0 <_ _ - x <_ _ - 1) of a function f(x) is defined in terms of an indefinite integral involving f(x). For fu...

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Material Type: 文書・図像類
Title: Uniform approximation to fractional derivatives of functions of algebraic singularity
Author/Editor: HASEGAWA, Takemitsu
SUGIURA, Hiroshi
Author Heading: HASEGAWA, Takemitsu
SUGIURA, Hiroshi
Publication, Distribution, etc.: Elsevier Science Publishers B. V.
Publication Date: 2009-06
Publication Date (W3CDTF): 2009-06
Periodical title: Journal of Computational and Applied Mathematics
No. or year of volume/issue: 228 1
Volume: 228
Issue: 1
Pages: 247-253
Text Language Code: eng
Subject Heading: fractional derivative
algebraic singularity
uniform approximation
quadrature rule
Chebyshev interpolation
automatic quadrature
error analysis
five-term recurrence relation
Target Audience: 一般
Note (General): Fractional derivative D^qf(x) (0 < q < 1, 0 <_ _ - x <_ _ - 1) of a function f(x) is defined in terms of an indefinite integral involving f(x). For functions of algebraic singularity f(x) = x^αg(x) (α > -1) with g(x) being a well-behaved function, we propose a quadrature method for uniformly approximating D^q{x^αg(x)g}. Present method consists of interpolating g(x) at abscissae in [0,1] by a finite sum of Chebyshev polynomials. It is shown that the use of the lower endpoint x = 0 as an abscissa is essential for the uniform approximation, namely to bound the approximation errors independently of x 2 [0,1]. Numerical examples demonstrate the performance of the present method.
Access Restrictions: 限定公開
Related Material (DOI): 10.1016/j.cam.2008.09.018
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 福井大学 : 福井大学学術機関リポジトリ