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 formula for the case. In addition, an upper bound for the error of the optimal quadrature formula is given. A conclusion is given on the applicability of this optimal quadrature formula.
| Mualliflar | Shadimetov, Kh.M., Usmanov, Kh.I., Шадиметов, Х.М., Усманов, Х.И. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2025-01-03 |
| Son | 4/2 |
| Betlar | 74-89 |
| Til | Rus |
optimal quadrature formula, coefficients of the quadrature formula, errors of the quadrature formula, with power-logarithmic kernels, absolute error, оптимальная квадратурная формула, коэффициенты квадратурной формулы, погрешности квадратурной формулы, со степенно – логарифмическими ядрами, абсолютная погрешность
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 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…
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…
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 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…
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…
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…
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…
The nonlinear viscoelastic vibration protection system is considered, which consists of a vibration protection object installed on a platform, which, in turn, is installed on another platform, the lower platform is…
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…