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.