  In this paper we apply a scaling invariance analysis to reduce a class of
parabolic moving boundary problems to free boundary problems governed by
ordinary differential equations. As well known free boundary problems are
always non-linear and, consequently, their numerical solution is often obtained
iteratively. Among the numerical methods, developed for the numerical solution
of this kind of problems, we focus on the iterative transformation method that
has been defined within scaling invariance theory. Then, as illustrative
examples, we solve two problems of interest in the applications. The obtained
numerical results are found in good agreement with exact or approximate ones.
