Quadrature formulae of many highly oscillatory Fourier-type integrals with algebraic or logarithmic singularities and their error analysis

Hongchao Kang and Qi Xu

Applied Mathematics and Computation, 2023, vol. 442, issue C

Abstract: In this article, we propose and analyze the Clenshaw–Curtis–Filon-type method for computing many highly oscillatory Fourier-type integrals with algebraic or logarithmic singularities at the endpoints. First, by using integration by parts and the characteristics of Chebyshev polynomials, four useful recursive relationships of the required modified moments are deduced. We perform the strict error analysis on the presented method and acquire asymptotic error estimations in inverse powers of frequency ω. Our method has the following advantages: when the interpolation node is fixed, the accuracy improves considerably as either the frequency or the interpolated multiplicities at endpoints increase. Numerical experiments verify the efficacy and correctness of the presented method.

Keywords: Fourier transform; Highly oscillatory integrals; Algebraic singularities; Logarithmic singularities; Recurrence relations; Error analysis (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:442:y:2023:i:c:s0096300322008268

DOI: 10.1016/j.amc.2022.127758

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