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 solving integral equations. This work is devoted to comparing various approximate methods for solving linear Fredholm equations of the second kind. The main goal of the work is to determine the most effective method. Our method is the use of optimal quadrature formulas with derivatives to solve linear Fredholm integral equations of the second kind. The effectiveness of the method depends on the accuracy of the results. In this case, the exact solution was used to compare the results. The effectiveness of this method is proven.
| 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 | 118-133 |
| Til | Rus |
linear integral equation, optimal quadrature formula, quadrature formula with derivatives, system of algebraic equations, maximum absolute error, линейное интегральное уравнение, оптимальная квадратурная формула, квадратурная формула с производными, система алгебраических уравнений, максимальная абсолютная погрешность
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…
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…
A multidimensional mathematical model of simultaneous heat and moisture transfer processes in inhomogeneous porous bodies is proposed, considering internal heat and moisture release, heat and moisture exchange with the…
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…
A numerical study of the non-stationary technological process of filtering lowconcentration solutions through a porous medium, proceeding in accordance with Darcy’s law taking into account the phenomena of colmatation…
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 this work, a mathematical model of the thermo-electro-magnetic-elastic deformation process of thin plates with a complex shape was developed and calculation experiments were carried out using the…
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…
Using the Duhamel-Neumann relationship and the equations of motion, the Saint-Venant compatibility conditions, are written as a system of six dynamic equations with respect to strains. It is shown that, unlike the…
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…