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 functions using the Sobolev method. This quadrature formula consists of a linear combination of the values of the interval [0, 1] up to the second derivative of the function at all nodes. The error of the quadrature formulas is estimated by the norm of the error function. We obtain the optimal quadrature formula by minimizing the norm of the error functional by the coefficients of the derivative quadrature formula. The resulting optimal quadrature formulas are exact for all degree functions. In addition, some methods for the numerical solution of Fredholm integral equations of the second type are given. These methods are derivative optimal quadrature formulas and Simpson’s 1/3 method. Numerical examples are provided to demonstrate the effectiveness and accuracy of the work presented.
| Mualliflar | Nuraliev, F.A., Kuziev, Sh.S., Djuraeva, K.A., Нуралиев, Ф.А., Кузиев, Ш.С., Джураева, К.А. |
|---|---|
| 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 | 66-73 |
| Til | Ingliz |
| Ilmiy soha | Fizika-matematika |
| Indeksga qo‘shilgan | 2026-08-27 |
Sobolev space, Fredholm integral equations, derivative optimal quadrature formula, error functional, Sobolev method, optimal coefficients, пространство Соболева, интегральные уравнения Фредгольма, производная оптимальная квадратурная формула, функционал ошибки, метод Соболева, оптимальные коэффициенты
| APA | Nuraliev, F.A., Kuziev, Sh.S., Djuraeva, K.A., Нуралиев, Ф.А., Кузиев, Ш.С., & Джураева, К.А. (2025). Approximate Solution Fredholm Integral Equation of the Second Kind by the Optimal Quadrature Method. Ҳисоблаш ва амалий математика муаммолари, (4/2), 66-73. https://journals.airi.uz/index.php/pvpm/article/view/64 |
|---|---|
| GOST (OAK) | Nuraliev, F.A. va b. Approximate Solution Fredholm Integral Equation of the Second Kind by the Optimal Quadrature Method // Ҳисоблаш ва амалий математика муаммолари. – 2025. – № 4/2. – P. 66-73. |
| MLA | Nuraliev, F.A., Kuziev, Sh.S., Djuraeva, K.A., Нуралиев, Ф.А., Кузиев, Ш.С., and Джураева, К.А. “Approximate Solution Fredholm Integral Equation of the Second Kind by the Optimal Quadrature Method.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 66-73, 2025. https://journals.airi.uz/index.php/pvpm/article/view/64 |
| Chicago | Nuraliev, F.A., Kuziev, Sh.S., Djuraeva, K.A., Нуралиев, Ф.А., Кузиев, Ш.С., and Джураева, К.А. “Approximate Solution Fredholm Integral Equation of the Second Kind by the Optimal Quadrature Method.” Ҳисоблаш ва амалий математика муаммолари, (4/2), 66-73 (2025). https://journals.airi.uz/index.php/pvpm/article/view/64 |
| Harvard | Nuraliev, F.A., Kuziev, Sh.S., Djuraeva, K.A., Нуралиев, Ф.А., Кузиев, Ш.С., and Джураева, К.А (2025) ‘Approximate Solution Fredholm Integral Equation of the Second Kind by the Optimal Quadrature Method’, Ҳисоблаш ва амалий математика муаммолари, (4/2), 66-73. https://journals.airi.uz/index.php/pvpm/article/view/64 |
| BibTeX | @article{nuralievfa2025,
title = {Approximate Solution Fredholm Integral Equation of the Second Kind by the Optimal Quadrature Method},
author = {Nuraliev, F.A. and Kuziev, Sh.S. and Djuraeva, K.A. and Нуралиев, Ф.А. and Кузиев, Ш.С. and Джураева, К.А.},
journal = {Ҳисоблаш ва амалий математика муаммолари},
year = {2025},
number = {4/2},
pages = {66-73},
url = {https://journals.airi.uz/index.php/pvpm/article/view/64}
} |
Boshqa maqola uchun iqtibos tayyorlash
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 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…
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…
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…
Ҳисоблаш ва амалий математика муаммолари — barcha maqolalar · 2025-yil arxivi
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…
Numerical integration in Sobolev spaces often relies on optimal quadrature formulas in the sense of Sard to minimize the calculation error. While many standard formulas exist, constructing optimal rules that incorporate…
Now splines are being constructed in different spaces and with different methods, and their application is widely studied. In this work, We construct a parametric spline that belongs ????3,???? space. For this , we will…
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…
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.