In this work, using the method of periodization of functions, optimal quadrature formulas of Hermite type will be constructed in spaces where the second derivatives are summable with squares. For this purpose, optimal quadrature formulas are used in spaces of periodic functions. In addition, exact upper bounds will be obtained for the constructed optimal quadrature formulas for the approximate calculation of integrals of rapidly oscillating functions.
| Mualliflar | Shadimetov, Kh.M., Gulomov, O.Kh., Шадиметов, Х.М., Гуломов, О.Х. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashriyot | Тошкент ахборот технологиялари университети қошидаги, Ахборот-коммуникация технологиялари илмий-инновацион, маркази |
| ISSN | 2181-8460, 2181-046X |
| Nashr sanasi | 2025-01-03 |
| Son | 4/2 |
| Betlar | 56-65 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-08-27 |
Sobolev space, extremal function, error functional, пространство Соболева, экстремальная функция, функционал погрешность
| APA | Shadimetov, Kh.M., Gulomov, O.Kh., Шадиметов, Х.М., & Гуломов, О.Х. (2025). Optimal Quadrature Formulas for Calculating Integrals of Rapidly Oscillating Functions. Ҳисоблаш ва амалий математика муаммолари, (4/2), 56-65. https://journals.airi.uz/index.php/pvpm/article/view/63 |
|---|---|
| GOST (OAK) | Shadimetov, Kh.M. va b. Optimal Quadrature Formulas for Calculating Integrals of Rapidly Oscillating Functions // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 4/2. – P. 56-65. |
| MLA | Shadimetov, Kh.M., Gulomov, O.Kh., Шадиметов, Х.М., and Гуломов, О.Х. “Optimal Quadrature Formulas for Calculating Integrals of Rapidly Oscillating Functions.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 56-65, 2025. https://journals.airi.uz/index.php/pvpm/article/view/63 |
| Chicago | Shadimetov, Kh.M., Gulomov, O.Kh., Шадиметов, Х.М., and Гуломов, О.Х. “Optimal Quadrature Formulas for Calculating Integrals of Rapidly Oscillating Functions.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 56-65 (2025). https://journals.airi.uz/index.php/pvpm/article/view/63 |
| Harvard | Shadimetov, Kh.M., Gulomov, O.Kh., Шадиметов, Х.М., and Гуломов, О.Х (2025) ‘Optimal Quadrature Formulas for Calculating Integrals of Rapidly Oscillating Functions’, Ҳисоблаш ва амалий математика муаммолари, (4/2), 56-65. https://journals.airi.uz/index.php/pvpm/article/view/63 |
| BibTeX | @article{shadimetovkhm2025,
title = {Optimal Quadrature Formulas for Calculating Integrals of Rapidly Oscillating Functions},
author = {Shadimetov, Kh.M. and Gulomov, O.Kh. and Шадиметов, Х.М. and Гуломов, О.Х.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {4/2},
pages = {56-65},
url = {https://journals.airi.uz/index.php/pvpm/article/view/63}
} |
Boshqa maqola uchun iqtibos tayyorlash
Many mathematical models in science and technology have been reduced to the approximate calculation of singular integrals with Cauchy and Hilbert kernels and the approximate solution of integral equations. In this…
A number of books by I.P. Mysovkikh, A.H. Stroud, V.I. Krylov and H.T. Shulgina are devoted to the approximate calculation of integrals, where the theory of constructing quadrature and cubature formulas is presented and…
The solution of the Cauchy problem for partial differential equations of hyperbolic type J. Hadamard led to singular integrals of a special form. Later they were called integrals in the sense of Hadamard, or Hadamard…
In spline theory, there are algebraic and variational approaches. In the algebraic approach, splines are considered as some smooth piecewise polynomial functions. In the variational approach, splines are understood as…
One of the main problems of computational mathematics is the optimization of computational methods in function spaces. Optimization of computational methods has proven itself well in problems of the theory of quadrature…
In the world, special attention is paid to the creation of various optimal calculation methods. This article is devoted to the construction of derivative optimal quadrature formulas in the space of differentiable…
This paper presents the construction of an optimal quadrature formula in Sobolev space for integrals with power-logarithmic kernels. Formulas are derived for calculating the coefficients of the optimal quadrature…
One of the classical problems in computational mathematics is to construct an interpolation formulas from a countable set of data. This paper demonstrates the problem of construction of optimal interpolation formulas…
In the present article, the problem of constructing the optimal quadrature formula in the sense of Sard is discussed for numerical integration of the weighted integrals in the Hilbert space of real-valued functions…
This paper investigates the construction of an optimal quadrature formula for Fourier integrals of ????(????) function using the method of ????-functions. The function ????(????) belongs to the Hilbert space, which…
Ҳисоблаш ва амалий математика муаммолари — barcha maqolalar · 2025-yil arxivi
This paper presents the construction of an optimal quadrature formula in Sobolev space for integrals with power-logarithmic kernels. Formulas are derived for calculating the coefficients of the optimal quadrature…
The paper considers the application of the optimal quadrature formula in the space to numerical solution of linear Fredholm integral equations of the second kind. The results of specific examples are analyzed. The exact…
Many mathematical models in science and technology have been reduced to the approximate calculation of singular integrals with Cauchy and Hilbert kernels and the approximate solution of integral equations. In this…
The approximate solution of linear Fredholm integral equations of the second kind is one of the pressing problems in the field of computational mathematics today. Most researchers offer various approximate methods for…
There are algebraic and variational approaches of construction in the spline theory. In algebraic approach splines are considered as some smooth piecewise polynomial functions. In the variational approach splines are…
The optimization of computational methods in function spaces is one of the main problems in computational mathematics. In this work, using the variational method optimization of difference formulas for an approximate…
This article presents the results of 2018-2023, such as biological diversity, inter-landscape distribution characteristics, density,and number of straggly insects identified from natural and anthropogenic areas of…
This article observational data on the species composition, distribution, population, density, and seasonal damage caused causedby herbivorus bugs. Observationes were carried out in April and September 2021. When…
In the article, the research fields of some species belonging to Paeonia, their significance in human life, adaptation features tovarious ecological conditions are highlighted, and the ecologist groups and other…
This article studies the number of species, population density of terrestrial mollusks of the Topalangdarya basin, located in theSurkhandarya region of Uzbekistan, in various altitudinal regions and biotopes and…
This article sheds light on changes in biomass formation and antimicrobial activity against test pathogenic strains under theinfluence of epigenetic modifiers and elicitors of the endophytic fungus Penicillium…
Shahimardonsoy covered issues such as the soil in the river basin and measures to increase its condition, salinity and fertility, theflora and fauna present in the basin landscape and their conservation.