2016/04/15 by Zhenhua Xu, Xu, Zhenhua
Mathematics · Physics and Astronomy · #Electromagnetic Scattering and Analysis #FOS: Mathematics #Mathematical Approximation and Integration #Mathematical functions and polynomials #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.1604.04483
openalex publication_date 2016/04/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we present a Clenshaw-Curtis-Filon-type method for the weakly singular oscillatory integral with Fourier and Hankel kernels. By interpolating the non-oscillatory and nonsingular part of the integrand at (N+1) Clenshaw-Curtis points, the method can be implemented in O(Nlog N) operations. The method requires the accurate computation of modified moments. We first give a method for the derivation of the recurrence relation for the modified moments, which can be applied to the derivation of the recurrence relation for the modified moments corresponding to other type oscillatory integrals. By using recurrence relation, special functions and classic quadrature methods, the modified moments can be computed accurately and efficiently. Then, we present the corresponding error bound in inverse powers of frequencies k and ω for the proposed method. Numerical examples are provided to support the theoretical results and show the efficiency and accuracy of the method.