Results 1 to 10 of about 1,516 (157)

On an Optimal Quadrature Formula in a Hilbert Space of Periodic Functions

Algorithms, 2022
The present work is devoted to the construction of optimal quadrature formulas for the approximate calculation of the integrals ∫02πeiωxφ(x)dx in the Sobolev space H˜2m.
Kholmat Shadimetov, Abdullo Hayotov, Botir Abdikayimov   +2 more
doaj   +4 more sources

The numerical solution of a Fredholm integral equations of the second kind by the weighted optimal quadrature formula

Results in Applied Mathematics
This work considers the optimal quadrature formula in a Hilbert space for the numerical approximation of the integral equations. It discusses the sequence of solving integral equations with quadrature formulas.
Abdullo Hayotov, Samandar Babaev
doaj   +3 more sources

Weighted Optimal Quadrature Formulas in Sobolev Space and Their Applications

Algorithms
The optimization of computational algorithms is one of the main problems of computational mathematics. This optimization is well demonstrated by the example of the theory of quadrature and cubature formulas.
Kholmat Shadimetov, Khojiakbar Usmanov
doaj   +2 more sources

Optimal quadrature formulas in the space W2​​(m,m−1) of periodic functions

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2022
This paper is devoted to the process of finding the upper bound for the absolute error of the optimal quadrature formula in the space W2​​(m,m−1) of real-valued, periodic functions. For this the extremal function of the quadrature formula is used.
Hayotov, A.R., Khayriev, U.N.
doaj   +1 more source

Optimization of the Approximate Integration Formula Using the Discrete Analogue of a High-Order Differential Operator

Mathematics, 2023
It is known that discrete analogs of differential operators play an important role in constructing optimal quadrature, cubature, and difference formulas.
Kholmat Shadimetov, Aziz Boltaev, Roman Parovik   +2 more
doaj   +1 more source

Optimal formulas for the approximate-analytical solution of the general Abel integral equation in the Sobolev space

Results in Applied Mathematics, 2022
This article discusses the development of a new algorithm, which is based on optimal quadrature formulas for obtaining solutions to the generalized Abel integral equations.
Kholmat M. Shadimetov, Bakhtiyor S. Daliev   +1 more
doaj   +1 more source

Some Generalized Error Inequalities and Applications

Journal of Inequalities and Applications, 2008
We present a family of four-point quadrature rule, a generalization of Gauss-two point, Simpson's , and Lobatto four-point quadrature rule for twice-differentiable mapping. Moreover, it is shown that the corresponding optimal quadrature formula presents
Mir NazirAhmad, Zafar Fiza
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Euler-Maclaurin type optimal formulas for numerical integration in Sobolev space

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2020
In the present paper the problem of construction of optimal quadrature formulas in the sense of Sard in the space  L2(m)(0,1) is considered. Here the quadrature sum consists of values of the integrand at nodes and values of the first and the third ...
Hayotov, A.R., Nuraliev, F.A., Parovik, R.I., Shadimetov, Kh.M.   +3 more
doaj   +1 more source

Optimal quadrature formulas in Sobolev space for solving the generalized Abel integral equation [PDF]

E3S Web of Conferences
In this article, a composite optimal quadrature formula is constructed for an approximate analytical solution of the generalized integral Abel equation in the Sobolev functional space.
Daliyev Bakhtiyor, Tukxtasinov Dadakhon, Bozarov Bakhromjon, Sabirov Salim, Abdullayev Jamoliddin, Ruzimatova Makhfuza   +5 more
doaj   +1 more source

A New First Order Expansion Formula with a Reduced Remainder

Axioms, 2022
This paper is devoted to a new first order Taylor-like formula, where the corresponding remainder is strongly reduced in comparison with the usual one, which appears in the classical Taylor’s formula.
Joel Chaskalovic, Hessam Jamshidipour
doaj   +1 more source