  This article complements recent results of the papers [J. Math. Phys. 41
(2000), 480; 45 (2004), 336] on the symmetry classification of second-order
ordinary difference equations and meshes, as well as the Lagrangian formalism
and Noether-type integration technique. It turned out that there exist
nonlinear superposition principles for solutions of special second-order
ordinary difference equations which possess Lie group symmetries. This
superposition springs from the linearization of second-order ordinary
difference equations by means of non-point transformations which act
simultaneously on equations and meshes. These transformations become some sort
of contact transformations in the continuous limit.
