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QUADRATURE FORMULAS FOR SINGULAR INTEGRALS CONTAINING THE VALUES OF A FUNCTION AND ITS DERIVATIVES
- Authors: Khubezhty S.S.1,2,3, Plieva L.Y.1,2,3
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Affiliations:
- K. L. Khetagurov North Ossetian State University
- Southern Mathematical Institute, branch of Vladikavkaz Scientific Center, RAS
- Financial University under the Government of the Russian Federation
- Issue: Vol 64, No 12 (2024)
- Pages: 2303–2311
- Section: General numerical methods
- URL: https://journals.rcsi.science/0044-4669/article/view/279980
- DOI: https://doi.org/10.31857/S0044466924120064
- EDN: https://elibrary.ru/KCAUSX
- ID: 279980
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Abstract
Quadrature formulas for singular integrals on the integration interval [−1, 1] with certain weight functions 𝑝(𝑡) are constructed. The values of the function and its derivatives in zeros of the Chebyshev polynomial are used in the construction. The resulting formulas are quadrature formulas of the interpolation type and have an algebraic degree of accuracy of 2𝑚 − 1. The error estimate is given.
About the authors
Sh. S. Khubezhty
K. L. Khetagurov North Ossetian State University; Southern Mathematical Institute, branch of Vladikavkaz Scientific Center, RAS; Financial University under the Government of the Russian Federation
Email: shalva57@rambler.ru
Vladikavkaz branch, Republic of North Ossetia – Alania; Vladikavkaz branch, Republic of North Ossetia – Alania; Vladikavkaz branch, Republic of North Ossetia – Alania
L. Yu. Plieva
K. L. Khetagurov North Ossetian State University; Southern Mathematical Institute, branch of Vladikavkaz Scientific Center, RAS; Financial University under the Government of the Russian Federation
Email: plieva-21@mail.ru
Vladikavkaz branch, Republic of North Ossetia – Alania; Vladikavkaz branch, Republic of North Ossetia – Alania; Vladikavkaz branch, Republic of North Ossetia – Alania
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