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Application of the Homotopy Method for Fractional Inverse Stefan Problem

Author

Listed:
  • 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)

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.

Suggested Citation

  • Damian Słota & Agata Chmielowska & Rafał Brociek & Marcin Szczygieł, 2020. "Application of the Homotopy Method for Fractional Inverse Stefan Problem," Energies, MDPI, vol. 13(20), pages 1-14, October.
  • Handle: RePEc:gam:jeners:v:13:y:2020:i:20:p:5474-:d:431569
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    Citations

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    Cited by:

    1. Tao Liu & Zijian Ding & Jiayuan Yu & Wenwen Zhang, 2023. "Parameter Estimation for Nonlinear Diffusion Problems by the Constrained Homotopy Method," Mathematics, MDPI, vol. 11(12), pages 1-12, June.
    2. Naeem Saleem & Salman Furqan & Kinda Abuasbeh & Muath Awadalla, 2023. "Fuzzy Triple Controlled Metric like Spaces with Applications," Mathematics, MDPI, vol. 11(6), pages 1-30, March.

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