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 differential equations can be transformed to initial value problems. The interest in the numerical solution of free boundary problems arises because these are always nonlinear problems. Furthermore we show that free boundary problems arise also via a similarity analysis of moving boundary 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 unifies results already available in literature. As far as applications of the proposed approach are concerned, three problems of interest are considered and numerical results for each of them are reported.