Difference equations are playing an increasingly important role in
the natural sciences. Indeed many phenomena are inherently discrete
and are naturally described by difference equations. Phenomena
described by differential equations are therefore approximations of
more basic discrete ones. Moreover, in their study it is very often
necessary to resort to numerical methods. This always involves a
discretization of the differential equations involved, thus
replacing them by difference equations. This book shows how Lie
group and integrability techniques, originally developed for
differential equations, have been adapted to the case of difference
ones. Each of the eleven chapters is a self-contained treatment of
a topic, containing introductory material as well as the latest
research results. The book will be welcomed by graduate students
and researchers seeking an introduction to the field. As a survey
of the current state of the art it will also serve as a valuable
reference.
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