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

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.