In this paper the possibility of application of the Adomian decomposition method for solving the moving boundary problem is presented. As an example of the moving boundary problem we consider a one-phase Stefan problem with Neumann’s boundary condition. This problem consists of finding the distribution of temperature in the domain and position of the moving interface. The validity of the approa...

We present time-parallel multigrid methods for the eecient numerical solution of moving boundary problems of two-phase Stefan type describing heat transfer processes with a change of phase. Using either a direct approach to the nonlinear enthalpy formulation of the problem or a linearization thereof based on semigroup theory, parallelism comes in by the simultaneous application of multigrid met...

Salva and Tarzia, [N.N. Salva, D.A. Tarzia, J. Math. Anal. Appl. 379 (2011) 240 244], gave explicit solutions of a similarity type for a class of free boundary problem for a semi-infinite material. In this paper, through an elementary approach and less stringent assumption on data, we obtain more general results than those given by their central result, and thereby construct explicit solutions ...

In this paper we propose a new algorithm for the well known elliptic obstacle problem and for parabolic variational inequalities like oneand two-phase Stefan problem and of obstacle type. Our approach enters the category of xed domain methods and solves just linear elliptic or parabolic equations and their discretization at each iteration. We prove stability and convergence properties. The appr...