Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Zh. Vychisl. Mat. Mat. Fiz.:
Year:
Volume:
Issue:
Page:
Find




Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register

Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, 2024, Volume 64, Number 12, Pages 2303–2311
DOI: https://doi.org/10.31857/S0044466924120064 (Mi zvmmf11890) 		 
General numerical methods

Quadrature formulas for singular integrals containing the values of a function and its derivatives

Sh. S. Khubezhtyabc, L. Yu. Plievaabc

a North Ossetian State University after Kosta Levanovich Khetagurov, 362025, Vladikavkaz, North Ossetia–Alania Republic, Russia
b Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, 362025, Vladikavkaz, North Ossetia–Alania Republic, Russia
c Financial University under the Government of the Russian Federation, Vladikavkaz Branch, 362002, Vladikavkaz, North Ossetia–Alania Republic, Russia
English version article
DOI: https://doi.org/10.31857/S0044466924120064
Abstract: Quadrature formulas for singular integrals on the integration interval $[-1,1]$ with certain weight functions $p(t)$ are constructed. The formulas use the values of the function and its derivatives at the zeros of the Chebyshev polynomial. The resulting formulas are quadrature formulas of the interpolation type and have an algebraic degree of accuracy $2m-1$. The error estimate is given.
Key words: singular integrals, quadrature formula, nodes, derivative of a function, weight function, interpolation polynomial, remainder term.
Received: 18.04.2024
Revised: 18.04.2024
Accepted: 23.08.2024
English version:
Computational Mathematics and Mathematical Physics, 2024, Volume 64, Issue 12, Pages 2813–2822
DOI: https://doi.org/10.1134/S0965542524701732
Bibliographic databases:
Document Type: Article
UDC: 517.38
Language: Russian
Citation: Sh. S. Khubezhty, L. Yu. Plieva, “Quadrature formulas for singular integrals containing the values of a function and its derivatives”, Zh. Vychisl. Mat. Mat. Fiz., 64:12 (2024), 2303–2311; Comput. Math. Math. Phys., 64:12 (2024), 2813–2822
Citation in format AMSBIB
\Bibitem{KhuPli24}
\by Sh.~S.~Khubezhty, L.~Yu.~Plieva
\paper Quadrature formulas for singular integrals containing the values of a function and its derivatives
\jour Zh. Vychisl. Mat. Mat. Fiz.
\yr 2024
\vol 64
\issue 12
\pages 2303--2311
\mathnet{http://mi.mathnet.ru/zvmmf11890}
\elib{https://elibrary.ru/item.asp?id=80299822}
\transl
\jour Comput. Math. Math. Phys.
\yr 2024
\vol 64
\issue 12
\pages 2813--2822
\crossref{https://doi.org/10.1134/S0965542524701732}
Linking options:
  • https://www.mathnet.ru/eng/zvmmf11890
  • https://www.mathnet.ru/eng/zvmmf/v64/i12/p2303
    • Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
    Statistics & downloads:
    Abstract page:123
    References:3
     
      Contact us:
    		  Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2026