TO THE SOLUTION OF NONLINEAR INVERSE BOUNDARY VALUE HEAT CONDUCTION PROBLEMS

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J. of Mech. Eng., 2016, vol. 19, no. 1, pp. 28-36

DOI:  https://doi.org/10.15407/pmach2016.01.028

Journal Journal of Mechanical Engineering
Publisher A. Podgorny Institute for Mechanical Engineering Problems
National Academy of Science of Ukraine
ISSN 0131-2928 (Print), 2411-0779 (Online)
Issue Vol. 19, no. 1, 2016 (March)
Pages 28–36

 

Authors

Yu. M. Matsevityy, A. Podgorny Institute of Mechanical Engineering Problems of NASU (2/10, Pozharsky Str., Kharkiv, 61046, Ukraine), V. N. Karazin Kharkiv National University, (4 Svobody Sq., Kharkiv, 61022, Ukraine),
e-mail: matsevit@ipmach.kharkov.ua

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

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

 

Abstract

To obtain a stable solution to the nonlinear inverse boundary value heat conduction problem, we use the A. N. Tikhonov regularization method with an effective algorithm for finding a regularizing parameter. The desired heat flux at the boundary is approximated in time coordinate by the first-degree Schoenberg splines. To apply the method of influence functions to a nonlinear heat conduction problem, we reduce it to a sequence of linear inverse boundary value problems. Numerous computational experiments have been carried out using stabilizing zero and first order functionals, as well as an analysis of the effect of the random measurement error variance on the error in the resulting solution. As a result of the computational experiment, it became clear that for this class of problems, first-order regularization turns out to be more efficient than zero-order regularization.

 

Keywords: inverse boundary value heat conduction problem, Galerkin weighted residual method, heat flow, superposition principle, Tikhonov regularization method, functional, stabilizer, regularization parameter, identification, approximation, first-degree Schoenberg spline

 

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Received 12 January 2016