ABSTRACT
In this chapter, we use the mathematical technique developed in the preceding chapter to study the symmetry properties of finite-difference models, i.e., difference equations considered together with difference meshes. The main theorem proved in this chapter deals with necessary and sufficient conditions for the invariance of difference equations and meshes. We develop a simple algorithm, called the method of finite-difference invariants, for constructing invariant difference model from a given differential equation and admitted transformation group. We also consider several examples of constructing finite-difference models, where we completely preserve the symmetry of the original differential equations. We show that symmetries of difference models permits symmetry reduction by means of subgroups (just as in the case of differential equations). In addition, we present an example where the group admitted by a difference model is calculated.
