FAST APPROXIMATION OF ALGEBRAIC AND LOGARITHMIC HYPERSINGULAR TYPE SINGULAR INTEGRALS WITH HIGHLY OSCILLATORY KERNEL

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Kayijuka I., Ege S. M., Konuralp A., Topal F. S.

International Journal of Analysis and Applications, vol.18, no.6, pp.965-980, 2020 (ESCI, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 18 Issue: 6
  • Publication Date: 2020
  • Doi Number: 10.28924/2291-8639-18-2020-965
  • Journal Name: International Journal of Analysis and Applications
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus
  • Page Numbers: pp.965-980
  • Keywords: highly oscillatory kernel, Gauss quadrature, hypersingular integrals, Chebyshev and modified Chebyshev algorithms, algebraic and logarithm singular integrals
  • Open Archive Collection: AVESIS Open Access Collection
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

Herein, highly oscillatory integrals with hypersingular type singularities are studied. After transforming the original integral into a sum of line integrals over a positive semi-infinite interval, a Gauss-related quadrature rule is constructed. The vehicle utilized is the moment's information. The comparison of two algorithms (Chebyshev and its modified one) to produce the recursion coefficients that satisfy orthogonal polynomial with respect to Gautschi logarithmic weight function, is investigated. Lastly, numerical examples are given to substantiate the effectiveness of the proposed method.