Application of the variational iteration method to strongly nonlinear \(q\)-difference equations
Summary: 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.
scientific article; zbMATH DE number 6021745