The method of approximate fundamental solutions (MAFS) for Stefan problems for the sphere

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. (C) 2013 Elsevier Inc. All rights reserved.