During the last decade many researchers who are dealing with phase change problems start taking into consideration the mushy zone in the mathematical formulation. Most of solved applications are analysed from metallurgical or mechanical points of view, but very few researchers treated these applications from mathematical point of view. In the present paper, a new numerical technique to solve moving boundary problems with mushy zone by using collocation method based RBF. A new algorithm is developed to solve such practical problems specially to track the moving boundaries that appear throughout the process. The results due to the present method give a good agreement with the previous results and promise to generalize the proposed method to cover higher dimensional problems.

collocation techniques, thin plate radial basis function, logarithmic radial basis function, phase change problems, mushy zone.