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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.

Suggested Citation

  • Seung Hyun Kim, 2014. "Two Simple Numerical Methods for the Free Boundary in One‐Phase Stefan Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnljam:v:2014:y:2014:i:1:n:764532
    DOI: 10.1155/2014/764532
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    References listed on IDEAS

    as
    1. Beom Jin Kim & Yong-Ki Ma & Hi Jun Choe, 2013. "A Simple Numerical Method for Pricing an American Put Option," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    2. Beom Jin Kim & Yong-Ki Ma & Hi Jun Choe, 2013. "A Simple Numerical Method for Pricing an American Put Option," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, February.
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