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

Numerical modelling of convection-diffusion-reaction problems with free boundary in 1D