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

A Non-Iterative Transformation Method for a Class of Free Boundary Value Problems Governed by ODEs