Quadrature rule for Abel's equations: Uniformly approximating fractional derivatives

被引：24

作者：

Sugiura, Hiroshi ^{[2
]}

Hasegawa, Takemitsu ^{[1
]}

机构：

[1] Univ Fukui, Dept Informat Sci, Fukui 9108507, Japan

[2] Nanzan Univ, Dept Informat Syst & Math Sci, Aichi 4890863, Japan

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2009年 / 223卷 / 01期

关键词：

Abel integral equation; Fractional derivative; Chebyshev interpolation; Quadrature rule; Automatic quadrature; Error analysis; Uniform approximation; GENERALIZED CHEBYSHEV INTERPOLATION; CLENSHAW-CURTIS QUADRATURE; INTEGRAL-EQUATIONS; DIFFUSION; CALCULUS; FFT;

D O I：

10.1016/j.cam.2008.01.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An automatic quadrature method is presented for approximating fractional derivative D-q f(x), which is defined by an indefinite integral involving f(x). The present method interpolates f(x) in terms of the Chebyshev polynomials in the range [0, 1] to approximate the fractional derivative D-q f(x) uniformly for 0 <= x <= 1, namely the error is bounded independently of x. Some numerical examples demonstrate the performance of the present automatic method. (C) 2008 Elsevier B.V. All rights reserved.

引用

页码：459 / 468

页数：10

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