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

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.