Application of the variational iteration method to strongly nonlinear q-difference equations

Abstract

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. Copyright © 2012 Hsuan-Ku Liu.