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New Algorithms to Compute Hypersingular Integrals with Rapidly Oscillating Kernels

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  • Maria Rosaria Capobianco
  • Giuliana Criscuolo

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.

Suggested Citation

  • Maria Rosaria Capobianco & Giuliana Criscuolo, 2025. "New Algorithms to Compute Hypersingular Integrals with Rapidly Oscillating Kernels," European Journal of Mathematics and Statistics, European Open Science, vol. 6(2), pages 11-18, March.
    • Handle: RePEc:epw:ejmath:v:6:y:2025:i:2:id:14393
    DOI: 10.24018/ejmath.2025.6.2.393
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    References listed on IDEAS

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    1. Liu, Guidong & Xiang, Shuhuang, 2019. "Clenshaw–Curtis-type quadrature rule for hypersingular integrals with highly oscillatory kernels," Applied Mathematics and Computation, Elsevier, vol. 340(C), pages 251-267.
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