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Abstract
The main contribution of this paper is the application of the iterative transformation method to the numerical solution of the sequence of free boundary problems obtained from one-dimensional parabolic moving boundary problems via the implicit Euler's method. The combination of the two methods represents a numerical approach to the solution of those problems. Three parabolic moving boundary problems, two with explicit and one with implicit moving boundary conditions, are solved in order to test the validity of the proposed approach. As far as the moving boundary position is concerned the obtained numerical results are found to be in agreement with those available in literature.