Optimal Quadrature Formulas with Derivative in the Space
Optimal Quadrature Formulas with Derivative in the Space
Abstract
Abstract. This paper studies the problem of construction of optimal quadrature formulas in the sense of
Sard in the space . In this paper the quadrature sum consists of values of the integrand and its
first derivative at nodes. The coefficients of optimal quadrature formulas are found and the norm of the
optimal error functional is calculated for arbitrary natural number and for any using
S.L. Sobolev method which is based on discrete analogue of the differential operator . In
particular, for optimality of the classical Euler-Maclaurin quadrature formula is obtained. Starting
from new optimal quadrature formulas are obtained.
References
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Shadimetov Kh.M., Hayotov A.R., Nuraliev F.A. On an optimal quadrature formula in the Sobolev space, Journal of Computational and Applied Mathematics., (2013), pp. 91-112.
Shadimetov Kh.M., Hayotov A.R., Nuraliev F.A.,Optimal interpolation formulas with derivative in the space , Filomat, 33(17) (2019).
https://journal.pmf.ni.ac.rs/filomat/index.php/filomat/article/view/10636.
Shadimetov Kh.M., Nuraliev F.A., Kuziev Sh., S., Optimal Quadrature Formula of Hermite Type in the Space of Differentiable Functions, International Journal of Analysis and Applications, 22(25)(2024), https://doi.org/10.28924/2291-8639-22-2024-25
