Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 857296, 10 pages
Effects of Nonlinearity on the Variational Iteration Solutions of Nonlinear Two-Point Boundary Value Problems with Comparison with Respect to Finite Element Analysis
1Department of Mathematics, Nigde University, Nigde 51245, Turkey
2Department of Civil Engineering, Nigde University, Nigde 51245, Turkey
Received 12 December 2006; Accepted 10 January 2008
Academic Editor: Katica Hedrih
Copyright © 2008 MehmetTarık Atay and SafaBozkurt Coşkun. 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.
Solution of a nonlinear two-point boundary value problem is studied using variational iteration method (VIM) considering its convergence behavior due to the changing nonlinearity effects in the equation. To achieve this, steady Burger equation is first solved by using finite element method (FEM) with a very fine mesh for the comparison of results obtained from VIM. Effect of the nonlinear term in the equation that is multiplied by a constant is taken into account for five different cases by changing the corresponding constant. Results have shown that VIM is a flexible, easy to apply, and promising method for the analysis of nonlinear two-point boundary value problems with the fact that the larger the effect of the nonlinear term of the equation, the slower the convergence rate when compared to FEM solutions.