Solution of the one-phase inverse Stefan problem by using the homotopy analysis method

In this paper we consider the one-phase inverse Stefan problem consisting in determination of the temperature distribution in given domain together with the temperature and the heat flux on one of boundaries of the region. For solving this problem the homotopy analysis method will be used. Concept of this method lies in forming the series, elements of which satisfy some differential equation. It is proven in the paper that if this series is convergent then its sum represents the solution of considered equation. Sufficient condition of this convergence is given in this elaboration, as well as the estimation of error of the solution approximated by taking the partial sum of the above mentioned series. Application of the method is illustrated by examples.