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2014 Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method
Xiao-Ying Qin, Yue-Xing Duan, Mao-Ren Yin
J. Appl. Math. 2014: 1-6 (2014). DOI: 10.1155/2014/391606

Abstract

An Adomian decomposition method (ADM) is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.

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Xiao-Ying Qin. Yue-Xing Duan. Mao-Ren Yin. "Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method." J. Appl. Math. 2014 1 - 6, 2014. https://doi.org/10.1155/2014/391606

Information

Published: 2014
First available in Project Euclid: 2 March 2015

zbMATH: 07131564
MathSciNet: MR3226307
Digital Object Identifier: 10.1155/2014/391606

Rights: Copyright © 2014 Hindawi

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