Approximate Method to Compute Hypersingular Finite-Part Integrals with Rapidly Oscillating Kernels

Maria Rosaria Capobianco and Giuliana Criscuolo
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Maria Rosaria Capobianco: Istituto per le Applicazioni del Calcolo “Mauro Picone” – CNR, Italy
Giuliana Criscuolo: Università degli Studi di Napoli “Federico II”, Italy

European Journal of Mathematics and Statistics, 2023, vol. 4, issue 5, 1-4

Abstract: In this paper, an algorithm for the numerical evaluation of hypersingular finite-part integrals with rapidly oscillating kernels is proposed. The method is based on an interpolatory procedure at zeros of the orthogonal polynomials with respect to the first kind Chebyshev weight. Bounds of the error and of the amplification factor are also provided. Numerically stable procedures are obtained and the corresponding algorithms can be implemented in a fast way.

Keywords: Error bound; Finite-part integral; Oscillatory integral; Stability (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:epw:ejmath:v:4:y:2023:i:5:id:14283

DOI: 10.24018/ejmath.2023.4.5.283

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