SIMILARITY AND NUMERICAL-ANALYSIS FOR FREE-BOUNDARY VALUE-PROBLEMS

We consider the similarity properties of nonlinear ordinary free boundary value problems, i.e.,[formula omitted]. By making use of group properties we show that for the two classes of problems [formula omitted], it is possible to define a method that allows us to find the location of the free boundary s through the first numerical integration and the numerical solution by means of a second integration, Moreover, by requiring invariance of some parameter, we give an important extension of the method to solve a problem that does not belong to the two classes in point. Finally we remark that the method is self-validating. © 1990, Taylor & Francis Group, LLC. All rights reserved.