An effective algorithm of the numerical solution to the Stefan problem

The method of the frontal interval of the numerical solution to Stefan problems is proposed. The method allows the calculation of the position of the phase transition boundary with high accuracy at any of time. Using the example of a plane two-phase Stefan problem, which has an exact analytical solution, the advantages of the proposed method in comparison with a variable time stepping method are demonstrated with respect to the calculation of the position of the phase transition boundary. An example of the solution to the one-phase Stefan problem using the frontal interval method is also given.