A method of fundamental solutions for the one-dimensional inverse Stefan problem

We investigate an application of the method of fundamental solutions (MFS) to the one-dimensional inverse Stefan problem for the heat equation by extending the MFS proposed in [5] for the one-dimensional direct Stefan problem. The sources are placed outside the space domain of interest and in the time interval (−T, T). Theoretical properties of the method, as well as numerical investigations, are included, showing that accurate and stable results can be obtained efficiently with small computational cost.