Integrals of rapidly oscillating functions arise mainly in the theory of special functions and Fourier analysis, but also in other applied and computational sciences and engineering, for example, in theoretical physics, acoustic scattering, quantum chemistry, transport theory, electromagnetism, telecommunications, mechanics, and so on.The computation of integrals of rapidly oscillating functions is often carried out using the Filon method. The Filon method resembles Simpson’s quadrature formula. However, whereas in Simpson’s method the entire integrand is approximated by a parabola, in the Filon method only the function f(x) is approximated by a parabola. In this way, Filon derived a quadrature formula with coefficients that depend onw. In this work, optimal quadrature formulas in the Sobolev space of complex-valued periodic functions will be constructed for the approximate computation of rapidly oscillating integrals.
| Mualliflar | Shadimetov, Kh.M., Elmuratov, G.Ch., Шадиметов, Х.М., Элмуратов, Г.Ч. |
|---|---|
| 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 | 2026-01-11 |
| Son | 6 |
| Betlar | 132-142 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| DOI | 10.71310/pcam.6_70.2025.11 |
| Indeksga qo‘shilgan | 2026-08-27 |
DOI: 10.71310/pcam.6_70.2025.11 · Maqolaning asl sahifasi
complex-valued functions, error functional, optimal quadrature formulas, discrete analogues of differential operators, комплекснозначные функции, функционал погрешности, оптимальные квадратурные формулы, дискретных аналогов дифференциальных операторов
| APA | Shadimetov, Kh.M., Elmuratov, G.Ch., Шадиметов, Х.М., & Элмуратов, Г.Ч. (2026). Optimization of Approximate Computation of Integrals of Rapidly Oscillating Functions in the Sobolev SPACE OF Complex-Valued Functions. Ҳисоблаш ва амалий математика муаммолари, (6), 132-142. https://doi.org/10.71310/pcam.6_70.2025.11 |
|---|---|
| GOST (OAK) | Shadimetov, Kh.M. va b. Optimization of Approximate Computation of Integrals of Rapidly Oscillating Functions in the Sobolev SPACE OF Complex-Valued Functions // Ҳисоблаш ва амалий математика муаммолари. – 2026. – № 6. – P. 132-142. – DOI: 10.71310/pcam.6_70.2025.11. |
| MLA | Shadimetov, Kh.M., Elmuratov, G.Ch., Шадиметов, Х.М., and Элмуратов, Г.Ч. “Optimization of Approximate Computation of Integrals of Rapidly Oscillating Functions in the Sobolev SPACE OF Complex-Valued Functions.” Ҳисоблаш ва амалий математика муаммолари, (6), 132-142, 2026. https://doi.org/10.71310/pcam.6_70.2025.11 |
| Chicago | Shadimetov, Kh.M., Elmuratov, G.Ch., Шадиметов, Х.М., and Элмуратов, Г.Ч. “Optimization of Approximate Computation of Integrals of Rapidly Oscillating Functions in the Sobolev SPACE OF Complex-Valued Functions.” Ҳисоблаш ва амалий математика муаммолари, (6), 132-142 (2026). https://doi.org/10.71310/pcam.6_70.2025.11 |
| Harvard | Shadimetov, Kh.M., Elmuratov, G.Ch., Шадиметов, Х.М., and Элмуратов, Г.Ч (2026) ‘Optimization of Approximate Computation of Integrals of Rapidly Oscillating Functions in the Sobolev SPACE OF Complex-Valued Functions’, Ҳисоблаш ва амалий математика муаммолари, (6), 132-142. https://doi.org/10.71310/pcam.6_70.2025.11 |
| BibTeX | @article{shadimetovkhm2026,
title = {Optimization of Approximate Computation of Integrals of Rapidly Oscillating Functions in the Sobolev SPACE OF Complex-Valued Functions},
author = {Shadimetov, Kh.M. and Elmuratov, G.Ch. and Шадиметов, Х.М. and Элмуратов, Г.Ч.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2026},
number = {6},
pages = {132-142},
doi = {10.71310/pcam.6_70.2025.11},
url = {https://doi.org/10.71310/pcam.6_70.2025.11}
} |
Boshqa maqola uchun iqtibos tayyorlash
In this paper, the Cauchy problem with boundary conditions for an inhomogeneous parabolic equation with changing time direction is investigated. To construct the solution, the method of separation of variables (Fourier…
This paper proposes a Context-adaptive Audio-Visual Neural Network (CAVN) model for anomaly detection in public safety systems. Existing approaches primarily rely on visual data and employ simple fusion strategies for…
For the first time, a fractal solar collector operating in the cogeneration mode is proposed. In this context, we are talking about a modern innovative system that uses fractal structures to optimize the processes of…
The paper addresses a numerical solution of a plane–radial boundary inverse problem for the relaxation filtration equation describing fluid flow in an elastically deformable porous medium. The study is motivated by the…
Hypersingular integral equations are encountered in a number of fields, such as the dynamics of air and fluid flow, elasticity, and wave propagation theory. Analytical solutions for these integral equations exist, but…
For the numerical solution of the Dirichlet problem for the Poisson equation, both direct and iterative methods have been developed. However, the required number of arithmetic operations for direct methods, as well as…
This study addresses the mathematical modeling of the dispersion process of harmful substances released into the atmosphere in complex urban environments. A mathematical model has been developed to determine the…
This article examines unsteady flows of rheologically complex fluids in a flat channel using the Oldroyd-B model after the actuator is switched off. It is assumed that until the actuator is switched off, the fluid flow…
This paper explores the numerical modeling of flow during filtration and transport of dissolved components in a cylindrical porous medium. The mathematical formulation is based on the axisymmetric Brinkman-Darcy…
This article is devoted to the study of the properties of solutions of systems of heat conduction equations associated with nonlinear boundary conditions, to the construction of self-similar solutions and finding their…
Ҳисоблаш ва амалий математика муаммолари — barcha maqolalar · 2026-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.