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.