Geodesic
On the calculation of the moment functions of a stochastic heat conduction process by using the projection method
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 192 (2021), pp. 102-110

Voir la notice de l'article provenant de la source Math-Net.Ru

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, mathematical expectation, autocorrelation function, modulus of continuity.
Mots-clés : Laguerre functions 
@article{INTO_2021_192_a10,
     author = {E. V. Seregina and M. A. Stepovich and V. V. Kalmanovich},
     title = {On the calculation of the moment functions of a stochastic heat conduction process by using the projection method},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {102--110},
     publisher = {mathdoc},
     volume = {192},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2021_192_a10/}
}
TY  - JOUR
AU  - E. V. Seregina
AU  - M. A. Stepovich
AU  - V. V. Kalmanovich
TI  - On the calculation of the moment functions of a stochastic heat conduction process by using the projection method
JO  - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
PY  - 2021
SP  - 102
EP  - 110
VL  - 192
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/INTO_2021_192_a10/
LA  - ru
ID  - INTO_2021_192_a10
ER  - 
%0 Journal Article
%A E. V. Seregina
%A M. A. Stepovich
%A V. V. Kalmanovich
%T On the calculation of the moment functions of a stochastic heat conduction process by using the projection method
%J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory
%D 2021
%P 102-110
%V 192
%I mathdoc
%U http://geodesic.mathdoc.fr/item/INTO_2021_192_a10/
%G ru
%F INTO_2021_192_a10
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. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, 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, Tome 192 (2021), pp. 102-110. http://geodesic.mathdoc.fr/item/INTO_2021_192_a10/