TY - BOOK ID - 80821763 TI - Symmetries and integrability of difference equations PY - 2011 SN - 9780511997136 9780521136587 9781139117098 1139117092 9781139127752 1139127756 0511997132 1139114921 9781139114929 052113658X 110721324X 1280776099 1139122835 9786613686480 1139112732 9781280776090 9781139122832 6613686484 9781139112734 PB - Cambridge : Cambridge University Press, DB - UniCat KW - Difference equations. KW - Symmetry (Mathematics) KW - Integrals. KW - Calculus, Integral KW - Invariance (Mathematics) KW - Group theory KW - Automorphisms KW - Calculus of differences KW - Differences, Calculus of KW - Equations, Difference UR - https://www.unicat.be/uniCat?func=search&query=sysid:80821763 AB - 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. ER -