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One-Dimensional Inverse Stefan Problem Numerical Approximation Utilizing a Meshless Method

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Applied Mathematics and Modelling in Finance, Marketing and Economics

Part of the book series: Studies in Computational Intelligence ((SCI,volume 1114))

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Abstract

We extend a meshless method of fundamental solutions to the one-dimensional inverse Stefan problem for the heat equation, where the boundary data is to be reconstructed on the fixed boundary. The inverse problem is ill-posed for small errors in the input measured data can cause high deviations in solution. Therefore, we incorporate Tikhonov regularization to obtain a stable solution. Numerical results are presented.

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References

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Authors and Affiliations

  1. Laboratory MISI, Faculty of Science and Technology of Settat, University Hassan 1 er, Settat, Morocco

    Mohammed Baati & Mohamed Louzar

Authors
  1. Mohammed Baati
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  2. Mohamed Louzar
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Correspondence to Mohammed Baati .

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Editors and Affiliations

  1. Department of Mathematics, Sultan Moulay Slimane University, Beni-Mellal, Morocco

    Said Melliani

  2. Div of Graduate Studies and Research, Tijuana Institute of Technology, Tijuana, BC, CP, Baja California, Mexico

    Oscar Castillo

  3. National School of Trade and Management, Chouaib Doukkali University, El Jadida, Morocco

    Abdelmajid El Hajaji

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Baati, M., Louzar, M. (2024). One-Dimensional Inverse Stefan Problem Numerical Approximation Utilizing a Meshless Method. In: Melliani, S., Castillo, O., El Hajaji, A. (eds) Applied Mathematics and Modelling in Finance, Marketing and Economics. Studies in Computational Intelligence, vol 1114. Springer, Cham. https://doi.org/10.1007/978-3-031-42847-0_12

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  • DOI: https://doi.org/10.1007/978-3-031-42847-0_12

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-42846-3

  • Online ISBN: 978-3-031-42847-0

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