Moving Boundary Problem Solved By
The Adomian Decomposition Method
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.
Related Book
Other papers in this volume
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