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

Seung Hyun Kim

Journal of Applied Mathematics, 2014, vol. 2014, 1-10

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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnljam:764532

DOI: 10.1155/2014/764532

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