Applications of Lie Groups to Difference Equations (Differential and Integral Equations and Their Applications)
| Author | : | |
| Rating | : | 4.38 (596 Votes) |
| Asin | : | 1420083090 |
| Format Type | : | paperback |
| Number of Pages | : | 344 Pages |
| Publish Date | : | 2013-10-28 |
| Language | : | English |
DESCRIPTION:
Vassiliou, Mathematical Reviews, 2012e. 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 book provides a systematic application of Lie groups to difference equations, difference meshes, and difference functionals. It is clearly written and largely self-contained … Peter J. 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
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Keldysh Institute of Applied Mathematics, Moscow, Russia Russian Academy of Sciences, Moscow
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. In addition, the book develops difference mesh geometry based on a symmetry group, because different symmetries are shown to require different geometric mesh structures. In particular, there are new examples of invariant schemes for second-order ODEs, for the linear and nonlinear heat equation with a source, and for well-known equations including Burgers equation, the KdV equation, and the Schrödinger equation.. The method of finite-difference invariants provides the mesh generating equation, any special case of which guarantees the mesh invariance. The variational approach and Noether type theorems for difference equations are presented in the framework of the Lagrangian and Hamiltonian formalism for difference equations. Intended for researchers