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

Seung Hyun Kim

Journal of Applied Mathematics, 2014, vol. 2014, issue 1

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.

Date: 2014
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https://doi.org/10.1155/2014/764532

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2014:y:2014:i:1:n:764532

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