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Bulletin of Abai KazNPU. Series of Physical and mathematical sciences

ON LIMIT ERROR OF THE OPTIMAL DISCRETIZATION OPERATOR FOR SOLUTION OF POISSON EQUATION

Published September 2024

53

14

G.+
Aktobe regional university named after K. Zhubanov, Aktobe
A. Utessov+
Aktobe regional university named after K. Zhubanov, Aktobe
R. Shanauov+
Aktobe regional university named after K. Zhubanov, Aktobe
N. Amanov+
Aktobe regional university named after K. Zhubanov, Aktobe
Aktobe regional university named after K. Zhubanov, Aktobe
Aktobe regional university named after K. Zhubanov, Aktobe
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A. Utessov

Associate professor

Aktobe regional university named after K. Zhubanov, Aktobe
Aktobe regional university named after K. Zhubanov, Aktobe
Abstract

The purpose of this study is to construct an optimal discretization operator for the solution of the Poisson equation and find its limit error. The research methodology is based on considering the problem of discretizing the solution of the Poisson equation as one of the concretizations of the general problem of optimal recovery of the operator and using well-known statements of approximation theory. In this study, within the framework of this general optimal recovery problem, firstly, in the uniform metric, the exact order of the smallest discretization error of the solution of the Poisson equation with the right-hand side  from the multidimensional periodic Sobolev class is established; secondly, based on a finite set of Fourier coefficients of the function , a discretization operator  is constructed that implements the established exact order; thirdly, the limit error of the optimal discretization operator  was found. Poisson's equation describes many physical phenomena such as the electrostatic field, stationary temperature field, pressure field and velocity potential field in hydrodynamics. Therefore, the relevance of the research conducted here is beyond doubt.

pdf (Русский)
Language

Русский

How to Cite

[1]
Г., Utessov А., Shanauov Р. and Amanov Н. 2024. ON LIMIT ERROR OF THE OPTIMAL DISCRETIZATION OPERATOR FOR SOLUTION OF POISSON EQUATION. Bulletin of Abai KazNPU. Series of Physical and mathematical sciences. 87, 3 (Sep. 2024), 57–69. DOI:https://doi.org/10.51889/2959-5894.2024.87.3.005.