  The aim of this work is to point out that the class of free boundary problems
governed by second order autonomous ordinary differential equations can be
transformed to initial value problems. Interest in the numerical solution of
free boundary problems arises because these are always nonlinear problems. The
theoretical content of this paper is original: results already available in
literature are related to the invariance properties of scaling or spiral groups
of point transformations but here we show how it is also possible to use e
invariance properties of a translation group. We test the proposed algorithm by
solving three problems: a problem describing a rope configuration against an
obstacle, a dynamical problem with a nonlinear force, and a problem related to
the optimal length estimate for tubular flow reactors.
