The problem of constructing optimal quadrature formulas for approximate calculation of definite integrals and approximation of functions is one of the important problems of computational mathematics. These problems have been studied by many mathematicians and there are several methods for constructing optimal quadrature formulas. One of these methods is the method proposed by S.L. Sobolev with the concept of an extremal function of the error functional. This article is devoted to finding the main elements necessary for the process of constructing an optimal quadrature formula for real-valued periodic functions in a Hilbert space. The quadrature formula under consideration is a form of the norm of the error functional for obtaining the upper bound of the error. In turn, to find the form of the norm of the error functional, we need an extremal function corresponding to the error functional. This work is aimed at finding the extremal function of the error functional.
| Mualliflar | Azamov, S.S., Bekmurodova, D.B., Азамов, С.С., Бекмуродова, Д.Б. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2026-03-07 |
| Son | 1 |
| Betlar | 94-102 |
| Til | Rus |
| DOI | 10.71310/pcam.1_71.2026.08 |
DOI: 10.71310/pcam.1_71.2026.08 · Maqolaning asl sahifasi
space, extremal function, generalized function, operator, optimal quadrature formula, error functional, пространство, экстремальная функция, обобщенная функция, оптимальная квадратурная формула, функционал погрешности
The method of displaced nodes is applied when solving the Dirichlet problem for the Poisson equation in a rectangular domain. By approximating the Laplace operator using moving nodes, we obtain an approximate analytical…
In the early 1960s, seminal results in differential game theory, where the game is described by an ordinary differential equation in a finite-dimensional space, were obtained by academicians L.S. Pontryagin and N.N…
The solutions of boundary value problems associated with two-parameter singularly perturbed differential equations are well known to exhibit the formation of two distinct boundary layers, typically occurring near the…
In this article, within the framework of the Saint-Venant compatibility conditions, plane problems of plasticity theory formulated in terms of strains are presented, aimed at investigating the stress-strain state of a…
The discovery of new chemical compounds with specified properties is a challenging problem in drug development. Many studies encode molecules as string representations derived from molecular graphs; however, this…
This article examines the theoretical foundations and practical application of a mathematical model for forecasting groundwater movement and levels based on the analysis of modern literature. The mathematical model for…
This paper examines the dynamic modes of the fractional Zeeman oscillator. The fractional Zeeman oscillator is a system of two ordinary differential equations with fractional derivatives, understood in the…
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…
This paper examines a boundary value problem for a degenerate elliptic equation in a planar domain bounded by a line segment and an analytic curve. The primary objective is to construct an explicit analytical solution…
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…