IJPAM: Volume 58, No. 1 (2010)

VARIATIONAL ITERATION METHOD FOR SOLVING
SINGULARLY PERTURBED TWO-POINT
BOUNDARY VALUE PROBLEMS

Nurettin Dogan$^{1}$, Marwan Al-Quran$^{2}$, Vedat S. Ertürk$^3$, Shaher Momani$^4$
$^1$Department of Electronics and Computer Education
Faculty of Technical Education
Gazi University
Teknikokullar, Ankara, 06500, TURKEY
e-mail: ndogan@ymail.com
$^2$Jordan University of Science and Technology
P.O. Box 3030, Irbid, 22110, JORDAN
e-mail: marwan04@just.edu.jo
$^{3}$Department of Mathematics
Faculty of Arts and Sciences
Ondokuz Mayis University
Samsun, TURKEY
e-mail: vserturk@yahoo.com
$^{4}$Department of Mathematics
Faculty of Science
University of Jordan
Amman, 11942, JORDAN
e-mail: shahermm@yahoo.com


Abstract.In this work, He's variational iteration method is used for the solution of singularly perturbed two-point boundary value problems. Some problems are solved to demonstrate the applicability of the method. It is observed that a good choice of the freely selected initial approximation in the VIM leads to exact solutions for some examples or gives a very well approximate solutions by using only one iteration. VIM has been applied to the initial value problems until now. In this work, VIM is used for the solution of singularly perturbed two-point boundary value problems.

Received: November 11, 2009

AMS Subject Classification: 35A15, 34B10

Key Words and Phrases: variational iteration method, singularly perturbed two-point boundary value problems, approximate solution

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 58
Issue: 1