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Two simple numerical methods for the free boundary in one-phase Stefan problem. (English) Zbl 1442.80004

Summary: 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.

MSC:

80A22 Stefan problems, phase changes, etc.
35R35 Free boundary problems for PDEs
80M50 Optimization problems in thermodynamics and heat transfer
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