Description
Book SynopsisIntended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. A guide to methods and results in a new area of application of Lie groups to difference equations, difference meshes (lattices), and difference functionals, this book focuses on the preservation of complete symmetry of original differential equations in numerical schemes. This symmetry preservation results in symmetry reduction of the difference model along with that of the original partial differential equations and in order reduction for ordinary difference equations.
A substantial part of the book is concerned with conservation laws and first integrals for difference models. The variational approach and Noether type theorems for di
Trade Review
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 1236
In 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
Table of ContentsIntroduction. 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.
