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Mathematical Problems in Engineering
Volume 2012, Article ID 791026, 10 pages
http://dx.doi.org/10.1155/2012/791026
Research Article

The Analytical and a Higher-Accuracy Numerical Solution of a Free Boundary Problem in a Class of Discontinuous Functions

Department of Mathematics and Computing, Beykent University, 34396 Istanbul, Turkey

Received 8 July 2011; Revised 10 September 2011; Accepted 8 October 2011

Academic Editor: Ezzat G. Bakhoum

Copyright © 2012 Bahaddin Sinsoysal. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A new method is suggested for obtaining the exact and numerical solutions of the initial-boundary value problem for a nonlinear parabolic type equation in the domain with the free boundary. With this aim, a special auxiliary problem having some advantages over the main problem and being equivalent to the main problem in a definite sense is introduced. The auxiliary problem allows us to obtain the weak solution in a class of discontinuous functions. Moreover, on the basis of the auxiliary problem a higher-resolution numerical method is developed so that the solution accurately describes all physical properties of the problem. In order to extract the significance of the numerical solutions obtained by using the suggested auxiliary problem, some computer experiments are carried out.