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JOURNALS // Vestnik Yuzhno-Ural'skogo Universiteta. Seriya Matematicheskoe Modelirovanie i Programmirovanie // Archive

Vestnik YuUrGU. Ser. Mat. Model. Progr., 2022 Volume 15, Issue 3, Pages 51–66 (Mi vyuru649)

This article is cited in 1 paper

Survey Articles

Analysis of biharmonic and harmonic models by the methods of iterative extensions

A. L. Ushakov, E. A. Meltsaykin

South Ural State University, Chelyabinsk, Russian Federation

Abstract: The article describes the results of recent years on the analysis of biharmonic and harmonic models by the methods of iterative extensions. In mechanics, hydrodynamics and heat engineering, various stationary physical systems are modeled using boundary value problems for inhomogeneous Sophie Germain and Poisson equations. Deflection of plates, flows during fluid flows are described using the biharmonic model, i.e. boundary value problem for the inhomogeneous Sophie Germain equation. Deflection of membranes, stationary temperature distributions near the plates are described using the harmonic model, i.e. boundary value problem for the inhomogeneous Poisson equation. With the help of the developed methods of iterative extensions, efficient algorithms for solving the problems under consideration are obtained.

Keywords: biharmonic and harmonic models, methods of iterative extensions.

UDC: 519.63

MSC: 65N85

Received: 17.03.2022

Language: English

DOI: 10.14529/mmp220304



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