Journal ArticleDOI
Stefan problem solved by Adomian decomposition method
R. Grzymkowski,Damian Słota +1 more
TLDR
The solution of the one-phase Stefan problem is presented, based on the Adomian decomposition method and optimalization, which consists of finding the distribution of temperature in the domain and the position of the moving interface.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.read more
Citations
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Journal ArticleDOI
Direct and inverse one-phase Stefan problem solved by the variational iteration method
TL;DR: The proposed solution is based on the variational iteration method, after the application of which the solution is obtained in the form of continuous functions.
Journal ArticleDOI
One-phase inverse stefan problem solved by adomian decomposition method
R. Grzymkowski,D. Sota +1 more
TL;DR: The proposed solution is based on the Adomian decomposition method and the least square method for the reconstruction of the function which describes the distribution of temperature on the boundary.
Journal ArticleDOI
The application of the homotopy perturbation method to one-phase inverse Stefan problem
TL;DR: In this paper, the application of the homotopy perturbation method for solving the inverse Stefan problem is presented, which consists in the calculation of temperature distribution in the domain, as well as in the reconstruction of the functions describing temperature and heat flux on the boundary, when the position of the moving interface is known.
Journal ArticleDOI
Series solution of nonlinear differential equations by a novel extension of the Laplace transform method
TL;DR: By developing several theorems, which incorporate the Adomian polynomials, the Laplace transformation of nonlinear expressions is made possible and the proposed approach is analytical, accurate, and free of integration.
Direct and inverse one-phase Stefan problem solved by the variational iteration method
TL;DR: In this paper, the authors proposed a variational iteration method to solve one-phase direct and inverse Stefan problems, where the direct problem consists in a calculation of temperature distribution and of a function which describes the position of the moving interface.
References
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Book
Optimization: Foundations and Applications
TL;DR: This paper presents a meta-modelling procedure called "Constrained Maximization and Minimization of Linear Equations", which automates the very labor-intensive and therefore time-heavy process of solving nonlinear Equations problems.
Journal ArticleDOI
Solution of a system of Volterra integral equations of the first kind by Adomian method
TL;DR: The Adomian decomposition method is being used to solve linear and non-linear systems of Volterra integral equations of the first kind to show the efficiency and simplicity of the method.