Group properties of difference equations. (Q2782031)

The book is devoted to the study of continuous symmetries of finite-difference equations, difference networks, and difference functionals. Difference equations arise either as primary mathematical models in physics or as difference approximations of differential equations. On the whole, this book deals with constructions difference models which preserve symmetries of original continuous models. NEWLINENEWLINENEWLINEIn the first chapter ``Difference algebra and algebra of infinity small transformations of finite-difference variables'', the author studies properties of transformation groups of difference schemes. In the second chapter ``Transformation groups admissible by finite-difference equations. Invariant difference schemes'', symmetries of finite-difference equations are studied. Lie group classifications of second-order ordinary difference equations are given. The author considers many examples of finite-difference models entirely inheriting the continuous symmetry of original differential models. NEWLINENEWLINENEWLINEThe third chapter ``Invariant variational problems and conservative difference equations'' deals with invariant variational problems for difference functionals and Noether-type theorems for difference equations.