Solution of the inverse boundary problem of heat exchange for a hollow cylinder
A.I. Sidikova1, A.S. Sushkov2
1South Ural State University, Chelyabinsk, Russia
2Chelyabinsk State University, Chelyabinsk, Russia
Keywords: error estimate, Fourier transform, ill-posed problem
Abstract
The article solves the problem of determining the temperature on the inner wall of a hollow cylinder. Using a time Fourier transform, the problem is reduced to an ordinary differential equation, with the help of which the Fourier transform of an exact solution of the inverse boundary value problem is found. A projection regularization method is considered, which makes it possible to obtain a stable solution to the problem and an accurate in order of magnitude estimate of the error of the approximate solution. Since high accuracy requirements are imposed on solutions of such problems in numerical calculations, an algorithm is developed to improve the accuracy and reliability of processing the results of thermal test data. To check the performance of the algorithm, test calculations are carried out.
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