Applications of Lie Groups to Difference Equations

The book provides a systematic application of Lie groups to difference equations, difference meshes, and difference functionals. Besides the well-explained theoretical background and motivations, there is also a large number of concrete examples discussed in reasonable details. Due to the fairly broad introductory part, the book is indeed self-contained. The main ideas and concepts appear understandable not only to experts.—Vojtech Zadnik, Zentralblatt MATH 1236In recent years "difference geometry" and its applications to integrable systems and mathematical physics have attracted significant attention and this monograph will contribute to the ongoing developments in this general area. It is clearly written and largely self-contained … —Peter J. Vassiliou, Mathematical Reviews, 2012e

• Introduction. Finite differences and transformation groups in space of discrete variables. Invariance of finite difference equations and meshes. Invariant difference models of ordinary differential equations. Invariant difference models of partial differential equations. Combined models, admitting a transformation group. The discrete representation of a differential equation. Invariant variational problem and conservation laws for difference equations.