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Two Simple Numerical Methods for the Free Boundary in One-Phase Stefan Problem

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  • Seung Hyun Kim

Abstract

We present two simple numerical methods to find the free boundary in one-phase Stefan problem. The work is motivated by the necessity for better understanding of the solution surface (temperatures) near the free boundary. We formulate a log-transform function with the unfixed and fixed free boundary that has Lipschitz character near free boundary. We solve the quadratic equation in order to locate the free boundary in a time-recursive way. We also present several numerical results which illustrate a comparison to other methods.

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  • Seung Hyun Kim, 2014. "Two Simple Numerical Methods for the Free Boundary in One-Phase Stefan Problem," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-10, June.
    • Handle: RePEc:hin:jnljam:764532
    DOI: 10.1155/2014/764532
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    Cited by:

    1. Chinonso Nwankwo & Weizhong Dai, 2020. "Explicit RKF-Compact Scheme for Pricing Regime Switching American Options with Varying Time Step," Papers 2012.09820, arXiv.org, revised Feb 2022.
    2. Chinonso I. Nwankwo & Weizhong Dai, 2024. "Efficient adaptive strategies with fourth-order compact scheme for a fixed-free boundary regime-switching model," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 47(1), pages 43-82, June.

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