A SIMILARITY APPROACH TO THE NUMERICAL-SOLUTION OF FREE-BOUNDARY PROBLEMS

The aim of this work is to point out that within a similarity approach some classes of free boundary value problems governed by ordinary dif ferential equations can be transformed to initial value problems. The interest in the numerical solution of free boundary problems arises be cause these are always nonlinear problems. Furthermore we show that fr ee boundary problems arise also via a similarity analysis of moving bo undary hyperbolic problems and they can be obtained as approximations of boundary value problems defined on infinite intervals. Most of the theoretical content of this survey is original: it generalizes and uni fies results already available in literature. As far as applications o f the proposed approach are concerned, three problems of interest are considered and numerical results for each of them are reported.