Maqola

Optimization of the Approximate Integration Formula Using the Discrete Analogue of a High-Order Differential Operator

Kholmat ShadimetovDepartment of Informatics and Computer Graphics, Tashkent State Transport University, 1 Odilkhodjayev Str., Tashkent 100167, UzbekistanA.K. BoltaevDepartment of Computational Mathematics and Information Systems, National University of Uzbekistan Named after M. Ulugbek, 4 University Str., Tashkent 100174, UzbekistanRoman ParovikInternational Integrative Research Laboratory of Extreme Phenomena of Kamchatka, Vitus Bering Kamchatka State University, 4 Pogranichnaya St., Petropavlovsk-Kamchatskiy 683032, Russia

Mathematicsjournal2023en

Ochiq kirishOltin

Litsenziya: cc-by

ABI

Annotatsiya

It is known that discrete analogs of differential operators play an important role in constructing optimal quadrature, cubature, and difference formulas. Using discrete analogs of differential operators, optimal interpolation, quadrature, and difference formulas exact for algebraic polynomials, trigonometric and exponential functions can be constructed. In this paper, we construct a discrete analogue Dm(hβ) of the differential operator d2mdx2m+2dmdxm+1 in the Hilbert space W2(m,0). We develop an algorithm for constructing optimal quadrature formulas exact on exponential-trigonometric functions using a discrete operator. Based on this algorithm, in m=2, we give an optimal quadrature formula exact for trigonometric functions. Finally, we present the rate of convergence of the optimal quadrature formula in the Hilbert space W2(2,0) for the case m=2.

Hali tarjima qilinmagan

Mavzular

Iterative Methods for Nonlinear Equations Mathematical functions and polynomials Numerical methods for differential equations

Identifikatorlar

DOI: 10.3390/math11143114

Iqtiboslar va manbalar

7 ta iqtibos 31 ta foydalanilgan manba