Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory
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Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory, 2021, Volume 192, Pages 102–110
DOI: https://doi.org/10.36535/0233-6723-2021-192-102-110 (Mi into786) 		 
On the calculation of the moment functions of a stochastic heat conduction process by using the projection method

E. V. Sereginaa, M. A. Stepovichb, V. V. Kalmanovichb

a Kaluga Branch of Bauman Moscow State Technical University
b Tsiolkovsky Kaluga State University
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DOI: https://doi.org/10.36535/0233-6723-2021-192-102-110
Abstract: We present some results of using the projection method of least squares for finding the first- and second-order moment functions for a solution of the heat equation taking into account a random change in the coefficient of heat conductivity. Mathematical modeling was performed for the interaction of a wide beam of pulsed laser radiation with the surface of a single-crystal semiconductor target. An ordinal error estimate for a quadratic functional is obtained. The results of a computational experiment for the parameters characteristic of cadmium telluride are presented.
Keywords: heat equation, projection method of least squares, Laguerre functions, mathematical expectation, autocorrelation function, modulus of continuity.
Funding agency Grant number
Russian Foundation for Basic Research 19-03-00271
18-41-400001
This work was partially supported by the Russian Foundation for Basic Research and the Government of the Kaluga Region (project Nos. 19-03-00271 and 18-41-400001).
Document Type: Article
UDC: 517.584
MSC: 35G16, 33C10, 78A55
Language: Russian
Citation: E. V. Seregina, M. A. Stepovich, V. V. Kalmanovich, “On the calculation of the moment functions of a stochastic heat conduction process by using the projection method”, Proceedings of the Voronezh spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings – XXX”. Voronezh, May 3-9, 2019. Part 3, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 192, VINITI, Moscow, 2021, 102–110
Citation in format AMSBIB
\Bibitem{SerSteKal21}
\by E.~V.~Seregina, M.~A.~Stepovich, V.~V.~Kalmanovich
\paper On the calculation of the moment functions of a stochastic heat conduction process by using the projection method
\inbook Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 3
\serial Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz.
\yr 2021
\vol 192
\pages 102--110
\publ VINITI
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/into786}
\crossref{https://doi.org/10.36535/0233-6723-2021-192-102-110}
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