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

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.