The solution of one-phase inverse Stefan problem by homotopy analysis method

Abstract

In this paper we obtain the solution of one-phase inverse Stefan problem by homotopy analysis method. The distribution of temperature on the boundary such that () () t v t u = , 0 , along with the temperature distribution () t x u , are obtained. The moving front () t s is given as additional information. There are advantages to using the homotopy analysis method (HAM), firstly it is independent of small/large physical parameter, there is always a guarantee of convergence; there is flexibility on the choice of base function and the initial guess of solution and lastly there is great generality. The numerical results obtained will show high accuracy and a strong rate of convergence.

INverse problem of identifying a time-dependent coefficient and free boundary in heat conduction equation by using the meshless local Petrov-Galerkin (MLPG) method via moving least squares approximation

“…In recent years, several methods have been employed for solving the inverse problem of heat conduction equation and Stefan problems numerically, such as the homotopy analysis method [27,42,48], Lie-group shooting method [36], finite difference method and finite element method [56] and variational iteration method [51]. Grzymkowski and Slota [23,24] investigated the direct and inverse one-phase Stefan problems by applying the Adomian decomposition method (ADM), and Slota [52] used the homotopy perturbation method for one-phase inverse Stefan problem.…”

Meshless Local Petrov–Galerkin Formulation of Inverse Stefan Problem via Moving Least Squares Approximation

“…The existence and uniqueness of the solution to these problems are investigated in References [2,3,5]. In recent years, several methods have been employed for solving the Stefan problems numerically, such as the homotopy analysis method [6,7], Lie-group shooting method [8], finite difference and finite element methods [9] and the variational iteration method [10]. Grzymkowski and Slota [11,12] applied the Adomian decomposition method (ADM) to solve one-phase Stefan problems and Slota [13] used the homotopy perturbation method for one-phase inverse Stefan problems.…”