We discuss a numerical method for convection-diffusion-reaction problems with
a free boundary in 1D. The method is based on the numerical modelling of the
interface evolution, the transformation to a fixed domain problem and the
approximation by an ODE system. The interface evolution is modelled by means of
the local shape of the corresponding travelling wave solution. The method can
be applied to many free boundary problems with a finite speed of the interface.
The presented method can also approximate some problems with an infinite speed
of the interface for damped travelling wave type solutions. In the numerical
experiments we compare our numerical solution with the analytical ones for some
problems.