Yu.M. Matsevytyi, M.O. Safonov, I.V. Hroza
Èlektron. model. 2021, 43(2):19-28
An approach to solving the internal inverse problem of heat conduction (OCT) is proposed, using the principle of regularization of A. N. Tikhonov and the method of influence functions. In this work, the power of the energy source is presented as a linear combination of the first-order Schoenberg splines, and the temperature is presented as a linear combination of influence functions. The influence function method makes it possible to use the same vector of unknown coefficients in both representations. The unknown coefficients are found as a result of solving the system of equations, which follows from the necessary condition for the minimum of the functional of A.N. Tikhonov with an effective algorithm for finding the regularization parameter, the use of which makes it possible to obtain a stable solution to the GST. For the regularization of the OST solutions, this functional also uses a stabilizing functional with the regularization parameter as a multiplicative factor. The article presents the numerical results of identifying the power of thermal energy by temperature, measured with an error characterized by a random variable distributed according to the normal law.
inverse problem, influence functions, identification, regularization, functional.
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