A meshless method for an inverse two-phase one-dimensional nonlinear Stefan problem

We extend a meshless method of fundamental solutions recently proposed by the authors for the one-dimensional two-phase nverse linear Stefan problem, to the nonlinear case. In this latter situation the free surface is also considered unknown which is ore realistic from the practical point of view. Building on the earlier work, the solution is approximated in each phase by a linear ombination of fundamental solutions to the heat equation. The implementation and analysis are more complicated in the present ituation since one needs to deal with a nonlinear minimization problem to identify the free surface. Furthermore, the inverse problem s ill-posed since small errors in the input measured data can cause large deviations in the desired solution. Therefore, regularization eeds to be incorporated in the objective function which is minimized in order to obtain a stable solution. Numerical results are resented and discussed. 2014 IMACS. Published by Elsevier B.V. All rights reserved.