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Zusatztext 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 Informationen zum Autor Vladimir Dorodnitsyn Klappentext This book presents a survey of methods and results in a new application area of Lie groups to difference equations and difference meshes (lattices). It focuses on the formulation and mathematical substantiation of exact symmetry preservation in difference models! such as difference equations and meshes. Methods are illustrated with numerous examples and applications in heat and mass transfer! hydrodynamics! physics! and mechanics. To highlight the numerical aspect of the book! the author provides a short survey of methods and theory of finite difference schemes and meshes. He also explains other approaches to quality features of difference schemes! such as variational and moving frames methods. Zusammenfassung Presents a survey of methods and results in an application area of Lie groups to difference equations and difference meshes (lattices). This work focuses on the formulation and mathematical substantiation of exact symmetry preservation in difference models, such as difference equations and meshes. Inhaltsverzeichnis 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. ...
