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.
ON LIMIT ERROR OF THE OPTIMAL DISCRETIZATION OPERATOR FOR SOLUTION OF POISSON EQUATION
Published September 2024
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Abstract
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.