Geodesic
Analysis of biharmonic and harmonic models by the methods of iterative extensions
Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 15 (2022) no. 3, pp. 51-66

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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. 
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     author = {A. L. Ushakov and E. A. Meltsaykin},
     title = {Analysis of biharmonic and harmonic models by the methods of iterative extensions},
     journal = {Vestnik \^U\v{z}no-Uralʹskogo gosudarstvennogo universiteta. Seri\^a, Matemati\v{c}eskoe modelirovanie i programmirovanie},
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     publisher = {mathdoc},
     volume = {15},
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     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VYURU_2022_15_3_a3/}
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A. L. Ushakov; E. A. Meltsaykin. Analysis of biharmonic and harmonic models by the methods of iterative extensions. Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 15 (2022) no. 3, pp. 51-66. http://geodesic.mathdoc.fr/item/VYURU_2022_15_3_a3/