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Journal of Applied Mathematics
Volume 2012, Article ID 704138, 12 pages
Research Article

Application of the Variational Iteration Method to Strongly Nonlinear 𝑞 -Difference Equations

Department of Mathematics and Information Education, National Taipei University of Education, Taipei 106, Taiwan

Received 30 July 2011; Accepted 30 November 2011

Academic Editor: Debasish Roy

Copyright © 2012 Hsuan-Ku Liu. 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.


The theory of approximate solution lacks development in the area of nonlinear 𝑞 -difference equations. One of the difficulties in developing a theory of series solutions for the homogeneous equations on time scales is that formulas for multiplication of two 𝑞 -polynomials are not easily found. In this paper, the formula for the multiplication of two 𝑞 -polynomials is presented. By applying the obtained results, we extend the use of the variational iteration method to nonlinear 𝑞 -difference equations. The numerical results reveal that the proposed method is very effective and can be applied to other nonlinear 𝑞 -difference equations.