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, cilt.18, sa.6, ss.965-980, 2020 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 18 Sayı: 6
  • Basım Tarihi: 2020
  • Doi Numarası: 10.28924/2291-8639-18-2020-965
  • Dergi Adı: International Journal of Analysis and Applications
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.965-980
  • Anahtar Kelimeler: highly oscillatory kernel, Gauss quadrature, hypersingular integrals, Chebyshev and modified Chebyshev algorithms, algebraic and logarithm singular integrals
  • Manisa Celal Bayar Üniversitesi Adresli: Hayır

Özet

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.