On the convergence rate of Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:333

Article

Wang, Haiyong^1,2 

[1] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China

[2] Huazhong Univ Sci & Technol, Hubei Key Lab Engn Modeling & Sci Comp, Wuhan 430074, Hubei, Peoples R China

关键词: Clenshaw-Curtis quadrature;    Endpoint singularities;    Chebyshev coefficients;    Convergence rate;   

DOI  :  10.1016/j.cam.2017.10.034

来源: Elsevier

【 摘 要 】

In this paper, we are concerned with Clenshaw-Curtis quadrature for integrals with algebraic endpoint singularities. An asymptotic error expansion and convergence rate are derived by combining a delicate analysis of the Chebyshev coefficients of functions with algebraic endpoint singularities and the aliasing formula of Chebyshev polynomials. Numerical examples are provided to confirm our analysis. (C) 2017 Elsevier B.V. All rights reserved.

【 授权许可】

Free