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Numerical difference solution of moving boundary random Stefan problems

Author

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  • Casabán, M.-C.
  • Company, R.
  • Jódar, L.

Abstract

This paper deals with the construction of numerical solutions of moving boundary random problems where the uncertainty is limited to a finite degree of randomness in the mean square framework. Using a front fixing approach the problem is firstly transformed into a fixed boundary one. Then a random finite difference scheme for both the partial differential equation and the Stefan condition, allows the discretization. Since statistical moments of the approximate stochastic process solution are required, we combine the sample approach of the difference schemes together with Monte Carlo technique to perform manageable approximations of the expectation and variance of both the approximating stochastic process solution and the stochastic moving boundary solution. Qualitative and reliability properties such as positivity, monotonicity and stability in the mean square sense are treated. Feasibility of the proposed method is checked with illustrative examples of a melting problem and a binary metallic alloys problems.

Suggested Citation

  • Casabán, M.-C. & Company, R. & Jódar, L., 2023. "Numerical difference solution of moving boundary random Stefan problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 878-901.
    • Handle: RePEc:eee:matcom:v:205:y:2023:i:c:p:878-901
    DOI: 10.1016/j.matcom.2022.10.026
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    References listed on IDEAS

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    1. María Consuelo Casabán & Rafael Company & Lucas Jódar, 2021. "Reliable Efficient Difference Methods for Random Heterogeneous Diffusion Reaction Models with a Finite Degree of Randomness," Mathematics, MDPI, vol. 9(3), pages 1-15, January.
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    Cited by:

    1. Casabán, M.-C. & Company, R. & Egorova, V.N. & Jódar, L., 2024. "A random free-boundary diffusive logistic differential model: Numerical analysis, computing and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 55-78.

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    1. Casabán, M.-C. & Company, R. & Egorova, V.N. & Jódar, L., 2024. "A random free-boundary diffusive logistic differential model: Numerical analysis, computing and simulation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 221(C), pages 55-78.
    2. Lucas Jódar & Rafael Company, 2022. "Preface to “Mathematical Methods, Modelling and Applications”," Mathematics, MDPI, vol. 10(9), pages 1-2, May.

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