OPTIMAL QUADRATURE FORMULA OF THE HERMITE TYPE
Keywords:
Error functional, extremal function, Sobolev space, optimal coefficients, optimal quadrature formula.Abstract
In this work, we discuss the construction of derivative optimal quadrature formulas in the Sobolev space. We derive an analytical expression for an error functional norm and obtain a system of linear equations Winner-Hopf type by the coefficients using the method of Lagrange multipliers. Further, we apply the Sobolev method to get the analytical representation of the optimal coefficients. Using these coefficients, we calculate the norm of the error functional of the optimal quadrature formula in cases and in Sobolev space. We verify our theoretical conclusions with the help of numerical experiments.
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Sobolev S.L. Introduction to the theory of cubature formulas. - M.: Nauka, 1974. - 808 p.
Sobolev S.L., Vaskevich V.L. Cubature formulas. - Novosibirsk: Publishing House IM SB RAS, 1996. - 484 p.
Nikolsky S.M. Quadrature formulas. - M.: Nauka, 1988. - 256 p.
Ramazanov M.D. Theory of lattice cubature formulas with a limited boundary layer. Ufa. 2009. 178 p.
Muhammad Mujtaba Shaikh, Muhammad Saleem Chandio and Abdul Wasim Shaikh. Some new time and cost efficient quadrature formulas to compute integrals using derivatives with error analysis. Symmetry 2022, 14(12), 2611; https://doi.org/10.3390/sym14122611.
Irina P., Tam P., Petr F . Quadrature rules for the -transform polynomial components. Axioms 2022 , 11(10 ), 501 ; https://doi.org/10.3390/axioms11100501.
Sanda M,. Iterative Numerical Methods for a Fredholm–Hammerstein Integral Equation with Modified Argument. Symmetry 2023 , 15(1), 66; https://doi.org/10.3390/sym15010066.
Ayman H., Rania S., Raed H., Mohammad W., Ahmad Q. A Perturbed Milne's quadrature rule for n -times differentiable functions with -error estimates.Axioms 2023, 12 (9), 803; https://doi.org/10.3390/axioms12090803.
S Qo’ziyev, Methods, tools and forms of distance learning, Конференции.
Shadimetov Kh., Nuraliev F., Kuziev Sh., Coefficients and errors of the optimal quadrature formula of the Hermite type, AIP Conference Proceedings 3147 (1), 2024, pp. 1-12.
S.S. Qo’ziyev, B.S. Tillaboyev, Talabalarda ijodkorlikni rivojlantirishda axborot kommunikatsion texnologiyalarning o‘rni, Oriental renaissance: Innovative, educational, natural and social sciences, 2021, pp. 344-352.
F.A.Nuraliev, Sh.S.Kuziev, Optimal Quadrature Formulas with Derivative in the Space: Optimal Quadrature Formulas with Derivative in the Space, Modern problems and prospects of applied mathematics, 2024, 6(7), pp. 1-10.
F.A.Nuraliev, Sh.S.Kuziev, The coefficients of an optimal quadrature formula in the space of differentiable functions, Uzbek Mathematical Journal, 2023 4(1), pp. 127-138.
Shadimetov Kh., Nuraliev F., Kuziev Sh., Optimal Quadrature Formula of Hermite Type in the Space of Differentiable Functions, International Journal of Analysis and Applications, 2024, №25, pp. 1-19.
Shadimetov Kh, Hayotov A., Nuraliev F. Construction of Optimal Interpolation Formulas in the Sobolev Space. Journal of Mathematical Sciences (United States), 2022, 264(6), pp 782-793.
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