The article investigates optimal quadrature formulas designed for the approximate evaluation of highly oscillatory integrals, which frequently arise in many applied problems of mathematical physics, signal theory, and computational mathematics. The work is based on the formulation and solution of Sard’s problem in a Sobolev space, where quadrature formulas are constructed taking into account not only the values of the integrand but also its derivatives at the nodal points. This approach makes it possible to significantly improve the accuracy of approximation. To determine the optimal coefficients of the quadrature formula, the Sobolev method is applied, which allows one to derive an analytical expression for the norm of the error functional. Based on the use of the extremal function and the Riesz representation theorem, a boundary value problem is constructed, the solution of which yields the explicit form of the optimal coefficients and an exact estimate of the error. The presented results have a solid theoretical foundation and confirm the effectiveness of the proposed method. The obtained optimal quadrature formulas provide high accuracy in computing integrals with highly oscillatory kernels, opening up prospects for their application in numerical methods for solving differential equations, modeling physical processes, and other areas of computational mathematics.
| Mualliflar | Shadimetov, X.M., Nuraliyev, F.A., Mirkomilov, D.M., Шадиметов, Х.М., Нуралиев, Ф.А., Миркомилов, Д.М. |
|---|---|
| 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 | 2025-09-20 |
| Son | 4 |
| Betlar | 110-121 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.71310/pcam.4_68.2025.08 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.4_68.2025.08 · Maqolaning asl sahifasi
Sobolev space, optimal coefficients, error functional, extremal function, пространство Соболева, оптимальные коэффициенты, функционал погрешности, экстремальная функция
| APA | Shadimetov, X.M., Nuraliyev, F.A., Mirkomilov, D.M., Шадиметов, Х.М., Нуралиев, Ф.А., & Миркомилов, Д.М. (2025). Optimal Quadrature Formulas for Approximate Calculation of Fast Oscillating Integral. Ҳисоблаш ва амалий математика муаммолари, (4), 110-121. https://doi.org/10.71310/pcam.4_68.2025.08 |
|---|---|
| GOST (OAK) | Shadimetov, X.M. va b. Optimal Quadrature Formulas for Approximate Calculation of Fast Oscillating Integral // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 4. – P. 110-121. – DOI: 10.71310/pcam.4_68.2025.08. |
| MLA | Shadimetov, X.M., Nuraliyev, F.A., Mirkomilov, D.M., Шадиметов, Х.М., Нуралиев, Ф.А., and Миркомилов, Д.М. “Optimal Quadrature Formulas for Approximate Calculation of Fast Oscillating Integral.” Ҳисоблаш ва амалий математика муаммолари, (4), 110-121, 2025. https://doi.org/10.71310/pcam.4_68.2025.08 |
| Chicago | Shadimetov, X.M., Nuraliyev, F.A., Mirkomilov, D.M., Шадиметов, Х.М., Нуралиев, Ф.А., and Миркомилов, Д.М. “Optimal Quadrature Formulas for Approximate Calculation of Fast Oscillating Integral.” Ҳисоблаш ва амалий математика муаммолари, (4), 110-121 (2025). https://doi.org/10.71310/pcam.4_68.2025.08 |
| Harvard | Shadimetov, X.M., Nuraliyev, F.A., Mirkomilov, D.M., Шадиметов, Х.М., Нуралиев, Ф.А., and Миркомилов, Д.М (2025) ‘Optimal Quadrature Formulas for Approximate Calculation of Fast Oscillating Integral’, Ҳисоблаш ва амалий математика муаммолари, (4), 110-121. https://doi.org/10.71310/pcam.4_68.2025.08 |
| BibTeX | @article{shadimetovxm2025,
title = {Optimal Quadrature Formulas for Approximate Calculation of Fast Oscillating Integral},
author = {Shadimetov, X.M. and Nuraliyev, F.A. and Mirkomilov, D.M. and Шадиметов, Х.М. and Нуралиев, Ф.А. and Миркомилов, Д.М.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {4},
pages = {110-121},
doi = {10.71310/pcam.4_68.2025.08},
url = {https://doi.org/10.71310/pcam.4_68.2025.08}
} |
Boshqa maqola uchun iqtibos tayyorlash
The article considers the problem of constructing self-similar solutions of a system of nonlinear differential equations modeling mutual diffusion processes in multicomponent media. An analysis of a mathematical model…
This paper addresses the problem of constructing optimal quadrature formulas for the numerical evaluation of Hadamard-type hypersingular integrals with hihg oscillation. Such integrals frequently arise in the analysis…
In this work, the problem of stabilizing the equilibrium state for a hyperbolic equation with negative nonlocal characteristic velocity and measurement error is investigated. The formulation of the mixed control problem…
In the world, special attention is given to developing various optimal computational methods for the approximate calculation of definite integrals. This article focuses on constructing composite optimal quadrature…
The article studies the dynamics of derivatives up to the highest derivative of an ordinary differential equation of the fourth order with a small parameter at the highest derivative. The solution of the differential…
The relationship between class objects is considered for analyzing the cluster structure of the training dataset. The uniqueness of the solution to the problem of minimal coverage of the training set by prototypes is…
Many practical problems, such as a solar panel, a microplate inside an electronic device, a thin layer of metal exposed to a laser, or the bending of a reinforced concrete slab, are described by various boundary value…
The paper presents a mathematical model of pollutant dispersion in turbulent airflows within the atmospheric boundary layer. The model is based on the advection–diffusion equation and the system of Navier–Stokes…
This paper presents a detailed comparative analysis of the numerical results of the 2D Backward Facing Step (2DBFS) problem. using modern software packages OpenFOAM, COMSOL Multiphysics and Ansys Fluent. The study…
A mathematical and numerical model is presented for the process of liquid solution filtration in a cylindrical porous filter. The model is based on the Brinkman-Darcy equations, describing fluid motion in a porous…
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…
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…
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…
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.