A meshless method for one-dimensional Stefan problems

The paper presents a new meshless numerical technique for solving one-dimensional problems with moving boundaries including the Stefan problems. The technique presented is based on the use of the delta-shaped functions and the method of approximate fundamental solutions (MAFS) firstly suggested for solving elliptic problems and for heat equations in domains with fixed boundaries. The numerical examples are presented and the results are compared with analytical solutions. The comparison shows that the method presented provides a very high precision in determining the position of the moving boundary even for a region that initially has zero thickness.