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Reconstruction of the boundary condition for the heat conduction equation of fractional order

Brociek Rafal (Silesian University of Technology, Institute of Mathematics, Gliwice, Poland)
Slota Damian (Silesian University of Technology, Institute of Mathematics, Gliwice, Poland)

This paper describes reconstruction of the heat transfer coefficient occurring in the boundary condition of the third kind for the time fractional heat conduction equation. Fractional derivative with respect to time, occurring in considered equation, is defined as the Caputo derivative. Additional information for the considered inverse problem is given by the temperature measurements at selected points of the domain. The direct problem is solved by using the implicit finite difference method. To minimize functional defining the error of approximate solution the Nelder-Mead algorithm is used. The paper presents results of computational examples to illustrate the accuracy and stability of the presented algorithm.

Keywords: inverse problem, identification, heat conduction equation, time fractional heat transfer coefficient