On the calculation of the moment functions of a stochastic heat conduction process by using the projection method

E. V. Seregina ; M. A. Stepovich ; V. V. Kalmanovich

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.

Résumé

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.

Détail

Keywords: heat equation, projection method of least squares, mathematical expectation, autocorrelation function, modulus of continuity.
Mots-clés : Laguerre functions

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