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On the numerical solution of a class of variable coefficients parabolic moving boundary problems

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Abstract

This study deals with a class of variable coefficients second-order parabolic moving boundary problems. The evolution of the domain is considered to be an unknown function. Based on the front-fixing approach, first, the problem is derived as a nonlinear fixed domain parabolic problem, and the uniqueness of solution of this problem is shown. An iterative approach based on a backward finite difference method is proposed to solve this nonlinear problem. The solvability of the finite difference method is shown, and the stability and convergence of the numerical solution are proved. Two examples are considered to show the efficiency and compatibility of the numerical method.

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Acknowledgements

The author is grateful to the respected referees and the handling editor for their helpful comments, which directly contribute to the readability and reliability of the current paper.

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  1. School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran

    Morteza Garshasbi & Javad Sharafi

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  1. Morteza Garshasbi
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  2. Javad Sharafi
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Correspondence to Morteza Garshasbi.

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Garshasbi, M., Sharafi, J. On the numerical solution of a class of variable coefficients parabolic moving boundary problems. J. Appl. Math. Comput. 69, 2509–2530 (2023). https://doi.org/10.1007/s12190-023-01844-0

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  • DOI: https://doi.org/10.1007/s12190-023-01844-0

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