Author(s)

R. Grzymkowski & D. Słota

Abstract

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 approach is verified by comparing the results obtained with the analytical solution. Keywords: moving boundary problem, Stefan problem, Adomian decomposition method. 1 Introduction In the moving boundary problem the position of the boundary of the domain, which depends on time and space, has to be determined [5]. The example of this kind of problem is the Stefan problem. This name includes a wide range of mathematical models describing thermal or diffusion processes which are characterized by a phase change in which the heat of the phase transition is emitted or absorbed, such as solidification of metals, freezing of the ground and water, crystal growth, melting ice etc. The Stefan problem consists of finding the distribution of temperature in the domain and the position of the moving interface (the freezing front) [11, 10]. In this paper we solve the one-phase Stefan problem with Neumann’s boundary condition. The solution is based on the Adomian decomposition method and the gradient method for minimizing the functional. The Adomian decomposition method was developed by G. Adomian [1, 3]. This method is useful for solving a wide class of problems [3, 2, 4, 6, 9, 8, 7, 12].

Keywords

moving boundary problem, Stefan problem, Adomian decomposition method.