Middle European Scientific Bulletin

Volume 18, November 2021, Pages 233-241

Full Lenght Article
Optimal Quadrature Formulas with Derivatives in the Space

Under a Creative Commons license
Open Access

Abstract

In the paper we consider an extension problem of the Euler-Maclaurin quadrature formula in the space   by constructing an optimal quadrature formula.

Abstract

In the paper we consider an extension problem of the Euler-Maclaurin quadrature formula in the space   by constructing an optimal quadrature formula.

Keywords

Optimal quadrature formula
Hilbert space
the error functional
Sobolev method
discrete argument function

Declarations

Conflict of Interest Statement

The author (s) declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Downloads

Download data is not yet available.

References

1. J.H. Ahlberg, E.N. Nilson, J.L. Walsh, The Theory of Splines and Their Applications, Academic Press, New York – London, 1967.
2. Kh.M. Shadimetov, A.R. Hayotov, Construction of the discrete analogue of the differential operator , Uzbek mathematical journal, 2004, no.2, pp. 85-95.
3. Kh.M. Shadimetov, A.R. Hayotov, Optimal quadrature formulas with positive coefficients in space, J. Comput. Appl. Math. 235 (2011) 1114–1128.
4. Kh.M. Shadimetov, A.R. Hayotov, Optimal quadrature formulas in the sense of Sard in space, Calcolo 51 (2014) 211–243.
5. Kh.M. Shadimetov, A.R. Hayotov, F.A. Nuraliev, On an optimal quadrature formula in Sobolev space , J. Comput. Appl. Math. 243 (2013) 91–112.
6. Kh.M. Shadimetov, A.R. Hayotov, F.A. Nuraliev, Optimal quadrature formulas of Euler-Maclaurin type, Applied Mathematics and Computation 276 (2016) 340–355.
7. S.L. Sobolev, Introduction to the Theory of Cubature Formulas (Russian), Nauka, Moscow, 1974.
8. S.L. Sobolev, V.L. Vaskevich, The Theory of Cubature Formulas, Kluwer Academic Publishers Group, Dordrecht, 1997.
9. Hayotov A. R., Rasulov R. G. The order of convergence of an optimal quadrature formula with derivative in the space $ W_2^{(2, 1)} $ //arXiv preprint arXiv:1908.00450. – 2019.
10. Hayotov A., Rasulov R. Improvement of the accuracy for the Euler-Maclaurin quadrature formulas //AIP Conference Proceedings. – AIP Publishing LLC, 2021. – Т. 2365. – №. 1. – С. 020035.
11. Хаётов А. Р., Расулов Р. Г., Сайфуллаева Н. Б. Extension of the Euler-Maclaurin quadrature formula in a Hilbert space //Проблемы вычислительной и прикладной математики. – 2020. – №. 2 (26). – С. 12-23.
12. Хаетов А. Р., Расулов Р. Г. Расширение квадратурной формулы Эйлера-Маклорена в пространстве W //Matematika Instituti Byulleteni Bulletin of the Institute of Mathematics Бюллетень Института. – 2020. – №. 3. – С. 167-176.
13. ABDULKHAEV Z. E. Protection of Fergana City from Groundwater //Euro Afro Studies International Journal. – 2021. – №. 6. – С. 70-81.
14. Abdulkhaev, Zokhidjon E., et al. "Calculation of the Transition Processes in the Pressurized Water Pipes at the Start of the Pump Unit." JournalNX, vol. 7, no. 05, 2021, pp. 285-291, doi:10.17605/OSF.IO/9USPT.
15. Zokhidjon Erkinjonovich Abdulkhaev, Mamadali Mamadaliyevich Madraximov, Salimjon Azamdjanovich Rahmankulov, & Abdusalom Mutalipovich Sattorov. (2021). Increasing the efficiency of solar collectors installed in the building. "ONLINE - CONFERENCES&Quot; PLATFORM, 174–177. Retrieved from http://papers.online-conferences.com/index.php/titfl/article/view/167
16. Sattorov A. M., Xujaxonov Z. Z. APPROACH CALCULATION OF CERTAIN SPECIFIC INTEGRALS BY INTERPOLATING POLYNOMIALS //Scientific Bulletin of Namangan State University. – 2019. – Т. 1. – №. 3. – С. 10-12.
17. Bozarov B. I. An optimal quadrature formula with sinx weight function in the Sobolev space //UZBEKISTAN ACADEMY OF SCIENCES VI ROMANOVSKIY INSTITUTE OF MATHEMATICS. – 2019. – С. 47.
18. Hayotov A., Bozarov B. Optimal quadrature formulas with the trigonometric weight in the Sobolev space //AIP Conference Proceedings. – AIP Publishing LLC, 2021. – Т. 2365. – №. 1.

Bibliographic Information

Verify authenticity via CrossMark

Cite this article as:

Rashidjon, R., & Sattorov, A. (2021). Optimal Quadrature Formulas with Derivatives in the Space. Middle European Scientific Bulletin, 18, 233-241. Retrieved from https://cejsr.academicjournal.io/index.php/journal/article/view/876
  • Submitted
    17 November 2021
  • Revised
    17 November 2021
  • Published
    17 November 2021