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

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.