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  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.
- heat conduction
- method of fundamental solutions (MFS)
- inverse Stefan problem
Johansson, B. T., Lesnic, D., & Reeve, T. (2011). A method of fundamental solutions for the one-dimensional inverse Stefan problem. Applied Mathematical Modelling, 35(9), 4367–4378. https://doi.org/10.1016/j.apm.2011.03.005