A new application of Heʹs variational iteration method for the solution of the one-phase Stefan problem

In this paper, we will use the variational iteration method to find an approximate solution of a one-phase Stefan problem. This problem consists in finding the distribution of temperature in the domain and the position of a moving interface. The problem under consideration is at first approximated with a system of differential equations in a domain with known boundary, and next, the system constructed in this way is solved by the variational iteration method. The validity of the approach is verified by comparing the results obtained with an analytical solution.