THERMAL SCIENCE
International Scientific Journal
SOLUTION OF THE TWO-PHASE STEFAN PROBLEM BY USING THE PICARD'S ITERATIVE METHOD
ABSTRACT
In this paper, an application of the Picard's iterative method for finding the solution of two phase Stefan problem is presented. In the proposed method an iterative connection is formulated, which allows to determine the temperature distribution in considered domain. Another unknown function, describing position of the moving interface, is approximated with the aid of linear combination of some base functions. Coefficients of this combination are determined by minimizing a properly constructed functional.
KEYWORDS
PAPER SUBMITTED: 2010-04-29
PAPER REVISED: 2010-07-27
PAPER ACCEPTED: 2010-11-18
THERMAL SCIENCE YEAR
2011, VOLUME
15, ISSUE
Supplement 1, PAGES [S21 - S26]
- Gupta, S. C., The Classical Stefan Problem. Basic Concepts, Modelling and Analysis, Elsevier, Amsterdam, The Netherlands, 2003
- Alexiades, V., Solomon, A. D., Mathematical Modeling of Melting and Freezing Processes, Hemisphere Publ. Corp., Washington, USA, 1993
- Feulvarch, E., Bergheau, J. M., An Implicit Fixed-Grid Method for the Finite-Element Analysis of Heat Transfer Involving Phase Changes, Numerical Heat Transfer Part B, 51 (2007), 6, pp. 585-610
- Savović, S., Caldwell, J., Numerical Solutions of the Stefan Problem with Time-Dependent Boundary Conditions by Variable Space Grid Method, Thermal Science, 13 (2009), 4, pp. 165-174
- Grzymkowski, R., Słota, D., Stefan Problem Solved by Adomian Decomposition Method, International Journal of Computer Mathematics, 82 (2005), 7, pp. 851-856
- He, J.-H., Non-Perturbative Methods for Strongly Nonlinear Problems, Dissertation.de-Verlag at Internet GmbH, Berlin, Germany, 2006
- He, J.-H., Variational Iteration Method - Some Recent Results and New Interpretations, Journal of Computational and Applied Mathematics, 207 (2007), 1, pp. 3-17
- He, J.-H., Wu, X.-H., Variational Iteration Method: New Development and Applications, Computers & Mathematics with Applications, 54 (2007), 7-8, pp. 881-894
- He, J.-H., Lee, E. W. M., A Constrained Variational Principle for Heat Conduction, Physics Letters A, 373 (2009), 31, pp. 2614-2615
- Słota, D., Direct and Inverse One-Phase Stefan Problem Solved by Variational Iteration Method, Computers & Mathematics with Applications, 54 (2007), 7-8, pp. 1139-1146
- Hetmaniok, E., Słota, D., Zielonka, A., Solution of the Solidification Problem by Using the Variational Iteration Method, Archives of Foundry Engineering, 9 (2009), 4, pp. 63-68
- Słota, D., Zielonka, A., A New Application of He's Variational Iteration Method for the Solution of the One-Phase Stefan Problem, Computers & Mathematics with Applications, 58 (2009), 11-12, pp. 2489-2494
- Ganji, D. D., Hosseini, M. J., Shayegh, J., Some Nonlinear Heat Transfer Equations Solved by Three Approximate Methods, International Communications in Heat and Mass Transfer, 34 (2007), 8, pp. 1003-1016
- Dehghan, M., Shakeri, F., Application of He's Variational Iteration Method for Solving the Cauchy Reaction-Diffusion Problem, Journal of Computational and Applied Mathematics, 214 (2008), 2, pp. 435-446
- Ramos, J. I., Picard's Iterative Method for Nonlinear Advection-Reaction-Diffusion Equations, Applied Mathematics and Computation, 215 (2009), 4, pp. 1526-1536
- Wituła, R., et al, Application of the Picard's Iterative Method for the Solution of One-Phase Stefan Problem, Archives of Foundry Engineering, 10 (2010), sp. issue 4, pp. 83-88
