Search

Abstract: The paper presents a new meshless in space numerical method – the method of approximate fundamental solutions (MAFS) for solving problems with moving boundaries of the Stefan type. This technique first suggested for solving the Stefan problems in plane geometry is now extended onto the cases of inward and outward spherical problems. Computed results for the inward and outward spherical problems are numerically evaluated for comparison with the results obtained by other authors. The comparison shows that the method presented provides a very high precision in determining the position of the moving boundary and the results are in a good agreement with the previous studies. [Copyright &y& Elsevier]

Abstract: 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. [Copyright &y& Elsevier]