Similarity and numerical analysis for free boundary value problems ^∗

^∗The present work was supported by the C.N.R. through the G.N.F.M.

Abstract

We consider the similarity properties of nonlinear ordinary free boundary value problems, i.e.,

u″ = f(x,u,u′) x∊(0,s) s>0

u(0) = α; u(s) = u′(s) = 0; α≠0.

By making use of group properties we show that for the two classes of problems

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.

Keywords:

• Free boundary value problem
• similarity properties

^∗The present work was supported by the C.N.R. through the G.N.F.M.

^∗The present work was supported by the C.N.R. through the G.N.F.M.

Notes

^∗The present work was supported by the C.N.R. through the G.N.F.M.