Optimization of the Approximate Integration Formula Using the Discrete Analogue of a High-Order Differential Operator-Reference-Cited by-同舟云学术

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

Published:2023-07-14 Issue:14 Volume:11 Page:3114
ISSN:2227-7390
Container-title:Mathematics
language:en
Short-container-title:Mathematics

Author:

Shadimetov Kholmat¹²^ORCID,Boltaev Aziz¹²³^ORCID,Parovik Roman⁴⁵^ORCID

Affiliation:

1. Department of Informatics and Computer Graphics, Tashkent State Transport University, 1 Odilkhodjayev Str., Tashkent 100167, Uzbekistan

2. Computational Mathematics Laboratory, V.I. Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences, 4b University Str., Tashkent 100174, Uzbekistan

3. Department of Computational Mathematics and Information Systems, National University of Uzbekistan Named after M. Ulugbek, 4 University Str., Tashkent 100174, Uzbekistan

4. International Integrative Research Laboratory of Extreme Phenomena of Kamchatka, Vitus Bering Kamchatka State University, 4 Pogranichnaya St., Petropavlovsk-Kamchatskiy 683032, Russia

5. Laboratory for Simulation of Physical Processes, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 7 Mirnaya St., Kamchatka Krai, Yelizovsky District, Paratunka 684034, Russia

Abstract

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.

Funder

President of the Russian Federation

Physical processes in the system of near space and geospheres under solar and lithospheric influences

Publisher

MDPI AG

Subject

General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)

Link

https://www.mdpi.com/2227-7390/11/14/3114/pdf

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