New Algorithms to Compute Hypersingular Integrals with Rapidly Oscillating Kernels

Maria Rosaria Capobianco and Giuliana Criscuolo
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Maria Rosaria Capobianco: CNR Institute for Applied Mathematics “Mauro Picone” (IAC), Italy
Giuliana Criscuolo: University of Naples Federico II, Italy

European Journal of Mathematics and Statistics, 2025, vol. 6, issue 2, 11-18

Abstract: The paper is dedicated to the study of two new algorithms for approximating hypersingular integrals with rapidly oscillating kernels. The methods use an interpolatory procedure at zeros of orthogonal polynomials. Estimates of the error are given, as well as of the amplification factors. Some numerical examples show the coherence of the theoretical results with the numerical ones.

Keywords: Error bound; finite-part integral; oscillatory integral; stability (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:epw:ejmath:v:6:y:2025:i:2:id:14393

DOI: 10.24018/ejmath.2025.6.2.393

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