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

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  • Maria Rosaria Capobianco
  • Giuliana Criscuolo

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.

Suggested Citation

  • Maria Rosaria Capobianco & Giuliana Criscuolo, 2023. "Approximate Method to Compute Hypersingular Finite-Part Integrals with Rapidly Oscillating Kernels," European Journal of Mathematics and Statistics, European Open Science, vol. 4(5), pages 1-4, September.
    • Handle: RePEc:epw:ejmath:v:4:y:2023:i:5:id:14283
    DOI: 10.24018/ejmath.2023.4.5.283
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