One-phase inverse stefan problem solved by adomian decomposition method

In this paper, the solution of one-phase inverse Stefan problem is presented. The problem consists of the reconstruction of the function which describes the distribution of temperature on the boundary, when the position of the moving interface is well-known. The proposed solution is based on the Adomian decomposition method and the least square method. (~) 2006 Elsevier Ltd. All rights reserved. 1. INTRODUCTION The inverse problems for differential equations consist of stating the boundary conditions, ther-mophysical properties of the body or initial conditions. The insufficiency of input information is compensated by some additional information on the effects of the input conditions. For the inverse Stefan problem, this additional information is the position of the freezing front, its velocity in normal direction, or temperature in selected points of the domain. Most published materials involve the reconstruction of temperature or heat flux on the boundary of a domain. In papers [1,2], the problem is reduced to a system of integral equations. In paper [3], the solution is found in terms of an infinite series of one-dimensional integrals. Jochum considers the inverse Stefan problem as a problem of nonlinear approximation theory (see [4,5]). In paper [6], for solutions of one-phase two-dimensional problems, authors used a complete family of solutions to the heat equation to minimize the maximal defect in the initial-boundary data. Similar method was used in [7,8] for two-and multi-phase problems. The solution in this method is found in a linear combination form of the functions satisfying the equation of heat conduction. The coefficients of this combination are determined by the least square method for the boundary of a domain. In papers [9-11], authors used dynamic programming or minimization techniques in *Author to whom all correspondence should be addressed. The authors wish to thank the reviewers for their valuable criticisms and suggestions, leading to the present improved version of our paper, 0898-1221/06/$-see front matter (~) 2006 Elsevier Ltd, All rights reserved.