Normal variables transformation method applied to free boundary value problems^∗

^∗The present work was supported by the C.N.R. through contract no. 88.01855.01

Abstract

We extend the application of group analysis approach to determining the numerical solution of free boundary value problems.

If the differential problem is invariant under a translation group of transformations we will formulate a non-iterative method of solution. This is done by introducing the concept of normal variables. Application of the method to two problems in the class characterized produces correct numerical results. Moreover, introducing a parameter into the differential problem and requiring invariance under an extended stretching group we give an iterative method applicable to any free boundary value problem.

As further result of the knowledge of the group properties we point out that these methods are self-validating.

Finally we suggest application of numerical transformation methods to boundary value problems.

Keywords:

• Free boundary value problem
• non-iterative and iterative numerical methods
• similarity properties

C.R. Categories:

• G.1.7

^∗The present work was supported by the C.N.R. through contract no. 88.01855.01

^∗The present work was supported by the C.N.R. through contract no. 88.01855.01

Notes

^∗The present work was supported by the C.N.R. through contract no. 88.01855.01