Application of the Homotopy Method for Fractional Inverse Stefan Problem

Damian Słota, Agata Chmielowska, Rafał Brociek and Marcin Szczygieł
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Damian Słota: Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
Agata Chmielowska: Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
Rafał Brociek: Department of Mathematics Applications and Methods for Artificial Intelligence, Faculty of Applied Mathematics, Silesian University of Technology, 44-100 Gliwice, Poland
Marcin Szczygieł: Department of Mechatronics, Faculty of Electrical Engineering, Silesian University of Technology, 44-100 Gliwice, Poland

Energies, 2020, vol. 13, issue 20, 1-14

Abstract: The paper presents an application of the homotopy analysis method for solving the one-phase fractional inverse Stefan design problem. The problem was to determine the temperature distribution in the domain and functions describing the temperature and the heat flux on one of the considered area boundaries. It was demonstrated that if the series constructed for the method is convergent then its sum is a solution of the considered equation. The sufficient condition of this convergence was also presented as well as the error of the approximate solution estimation. The paper also includes the example presenting the application of the described method. The obtained results show the usefulness of the proposed method. The method is stable for the input data disturbances and converges quickly. The big advantage of this method is the fact that it does not require discretization of the area and the solution is a continuous function.

Keywords: inverse Stefan problem; heat transfer; solidification; inverse problem; fractional derivative (search for similar items in EconPapers)
JEL-codes: Q Q0 Q4 Q40 Q41 Q42 Q43 Q47 Q48 Q49 (search for similar items in EconPapers)
Date: 2020
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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