Stefan problem solved by Adomian decomposition method

Abstract

The solution of the one-phase Stefan problem is presented. This problem consists of finding the distribution of temperature in the domain and the position of the moving interface (freezing front). The proposed solution is based on the Adomian decomposition method and optimalization. The validity of the approach is verified by comparing the results obtained with the analytical solution.

Comparison of the Adomian decomposition method and the variational iteration method in solving the moving boundary problem

“…According to the ADM method [1,2,8,9], we seek the approximate solution of the problem considered in the form of a function series:…”

“…Both of the methods examined have found application in determining the approximate solutions of different technical problems. Examples of these applications are considered in, among other work, [8][9][10][11][12]. Adaptation of the VIM method for solving the heat conduction problem is also discussed by Chun in [13], whereas application of the VIM method for solving direct and inverse Stefan problems is presented by Słota in [14].…”

Variational Iteration Method A Tools For Solving Partial Differential Equations

“…Further we compare the result with given solutions using ADM [2,3,4]. The paper has been organized as follows.…”

One-phase inverse stefan problem solved by adomian decomposition method

“…In papers [28,29], authors consider solving the inverse problems for the differential equations by the Adomian decomposition method. This method is also used for an approximate solution of the Stefan problem [30].…”