Uniform approximation to fractional derivatives of functions of algebraic singularity

• 資料種別: 文書・図像類
• タイトル: Uniform approximation to fractional derivatives of functions of algebraic singularity
• 著者・編者: HASEGAWA, Takemitsu; SUGIURA, Hiroshi
• 著者標目: HASEGAWA, Takemitsu; SUGIURA, Hiroshi
• 出版事項: Elsevier Science Publishers B. V.
• 出版年月日等: 2009-06
• 出版年（W3CDTF）: 2009-06
• タイトル（掲載誌）: Journal of Computational and Applied Mathematics
• 巻号年月日等（掲載誌）: 228 1
• 掲載巻: 228
• 掲載号: 1
• 掲載ページ: 247-253
• 本文の言語コード: eng
• 件名標目: fractional derivative; algebraic singularity; uniform approximation; quadrature rule; Chebyshev interpolation; automatic quadrature; error analysis; five-term recurrence relation
• 対象利用者: 一般
• 一般注記: 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.
• 一次資料へのリンクURL: https://u-fukui.repo.nii.ac.jp/?action=repository_action_common_download&item_id=22470&item_no=1&attribute_id=22&file_no=1
• オンライン閲覧公開範囲: 限定公開
• 関連情報（DOI）: 10.1016/j.cam.2008.09.018
• 連携機関・データベース: 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
• 提供元機関・データベース: 福井大学 : 福井大学学術機関リポジトリ