TO THE SOLUTION OF NON-STATIONARY NON-LINEAR BOUNDARY-VALUE INVERSE HEAT CONDUCTION PROBLEMS

Authors

Yu. M. Matsevityy, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), e-mail:  matsevit@ipmach.kharkov.ua

A. O. Kostikov, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine), ORCID: 0000-0001-6076-1942

N. A. Safonov, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine)

V. V. Ganchin, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky St., Kharkiv, 61046, Ukraine)

Abstract

In order to solve the non-linear boundary inverse heat conduction problem, A.N. Tikhonov’s regularization method is used, using an effective algorithm for finding a regularization parameter. The desired heat flux at the boundary is approximated by the time coordinate by Schönberg splines. The method of influence functions is used, for which the non-linear problem is reduced to a sequence of linear inverse problems.

Keywords: inverse boundary value heat conduction problem, heat flux, A. N. Tikhonov’s regularization method, functional, stabilizer, regularization parameter, identification, approximation, Schoenberg splines

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Received 18 October 2017

Published 30 December 2017