## THERMAL SCIENCE

International Scientific Journal

### SOLUTION OF ONE-DIMENSIONAL MOVING BOUNDARY PROBLEM WITH PERIODIC BOUNDARY CONDITIONS BY VARIATIONAL ITERATION METHOD

**ABSTRACT**

In this paper, the solution of the one dimensional moving boundary problem with periodic boundary conditions is obtained with the help of variational iterational method. By using initial and boundary values, the explicit solutions of the equations have been derived, which accelerate the rapid convergence of the series solution. The method performs extremely well in terms of efficiency and simplicity. The temperature distribution and the position of moving boundary are evaluated and numerical results are presented graphically.

**KEYWORDS**

PAPER SUBMITTED: 2008-08-14

PAPER REVISED: 2008-10-05

PAPER ACCEPTED: 2008-10-09

**THERMAL SCIENCE** YEAR

**2009**, VOLUME

**13**, ISSUE

**2**, PAGES [199 - 204]

- Crank, J., Free and Moving Boundary Value Problem, Oxford University Press, Oxford, U. K., 1984
- Hill, J. M., One-Dimensional Stefan Problems, an Introduction, Longman Scientific and Technical, New York, USA, 1987
- Asaithambi, N. S., A Variable Time Step Galerkin Method for One Dimensional Stefan Problem, Appl. Math. Comput., 81 (1997), 2-3, pp. 189-200
- Rizwan-Uddin, A Nodal Method for Phase Change Moving Boundary Problems, Int. J. Comp. Fluid Dynamics, 11 (1999), 3, pp. 211-221
- Rizwan-Uddin, One Dimensional Phase Change Problem with Periodic Boundary Conditions, Numerical Heat Transfer A, 35 (1999), 4, pp. 361-372
- Savovic, S., Caldwell, J., Finite Difference Solution of One-Dimensional Stefan Problem with Periodic Boundary Conditions, Int. J. Heat and Mass Transfer, 46 (2003), 15, pp. 2911-2916
- Ahmed, S. G., A New Algorithm for Moving Boundary Problem Subject to Periodic Boundary Conditions, Int. J. of Numerical Method for Heat and Flow, 16 (2006), 1, pp. 18-27
- He, J. H., Approximate Solution of Nonlinear Differential Equations with Convolution Product nonlinearities, Comput. Methods Appl. Mech. Engg., 167 (1998), 1-2, pp. 69-73
- He, J. H., Variational Iteration Method - a Kind of Nonlinear Analytical Technique: Some Examples, Internat. J. Nonlinear Mech., 34 (1999), 4, pp. 699-708
- He, J. H., Variational Iteration Method for Autonomous Ordinary Differential Systems, Appl. Math. Comput., 114 (2000), 2-3, pp.115-123
- He, J. H., Some Asymptotic Methods for Strongly Nonlinear Equations, Internat. J. Modern Phys. B 20 (2006), 10, pp. 1141-1199
- Golbabai, A., Javidi, M., A Variational Iteration Method for Solving Parabolic Partial Differential Equations, Int. J. Computers & Mathematics with Applications, 54 (2007), 7-8, pp. 987-992.
- Abassy, T. A., El-Tawil M. A., El-Zoheiry, H., Exact Solution of Some Non Linear Partial Differential Equations Using the Variational Iteration Method Linked with Laplace Transforms and the Pade Technique, Computers and Mathematics with Applications, 54 (2007), 7-8, pp. 940-954
- Soliman, A. A., Abdou, M. A., Numerical Solutions of Nonlinear Evolution Equations Using Variational Iteration Method, Journal of Computational and Applied Mathematics, 207 (2007), 1, pp. 111-120
- Yao, L. S., Prusa, J., Melting and Freezing, in: Advances in Heat Transfer, Academic Press, New York, USA Vol. 19, 1989, pp. 1-95