A NONLINEAR HYPERBOLIC FREE-BOUNDARY VALUE-PROBLEM

The present paper is concerned with the application of a non-iterative transformation method to the numerical solution of a nonlinear hyperbolic free boundary value problem. Making use of the similarity analysis approach to the hyperbolic model describing time dependent velocity impact to nonlinear inhomogeneous thin rods we recover a free boundary value problem. Since exact solutions are known only in some particular cases, we consider application of numerical methods of integration. Usually iterative numerical methods of solution are known to be applicable to free boundary value problems. However, we can prove that the ordinary differential equation related to the model in point is invariant with respect to a stretching group of transformations. This is the hint to apply group properties and to develop an ad hoc non-iterative transformation method. © 1990 Springer-Verlag.