Cantitate/Preț
Produs

Applications of Lie Groups to Difference Equations: Differential and Integral Equations and Their Applications

Autor Vladimir Dorodnitsyn
en Limba Engleză Paperback – 16 iun 2017
Intended 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 difference equations are presented in the framework of the Lagrangian and Hamiltonian formalism for difference equations.
In addition, the book develops difference mesh geometry based on a symmetry group, because different symmetries are shown to require different geometric mesh structures. The method of finite-difference invariants provides the mesh generating equation, any special case of which guarantees the mesh invariance. A number of examples of invariant meshes is presented. In particular, and with numerous applications in numerics for continuous media, that most evolution PDEs need to be approximated on moving meshes.
Based on the developed method of finite-difference invariants, the practical sections of the book present dozens of examples of invariant schemes and meshes for physics and mechanics. 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.
Citește tot Restrânge

Din seria Differential and Integral Equations and Their Applications

Preț: 42718 lei

Preț vechi: 55256 lei
-23% Nou

Puncte Express: 641

Preț estimativ în valută:
8176 8499$ 6773£

Carte tipărită la comandă

Livrare economică 05-19 februarie 25

Preluare comenzi: 021 569.72.76

Specificații

ISBN-13: 9781138118232
ISBN-10: 1138118230
Pagini: 344
Ilustrații: 31
Dimensiuni: 178 x 254 mm
Greutate: 0.45 kg
Ediția:1
Editura: CRC Press
Colecția Chapman and Hall/CRC
Seria Differential and Integral Equations and Their Applications


Public țintă

Professional

Cuprins

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.

Recenzii

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

Descriere

This guide presents methods and results in a new area of application of Lie groups to difference equations, difference meshes (lattices), and difference functional. It is perhaps the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. It focuses on the preservation of complete symmetry of original differential equations in numerical schemes. A substantial part of the text is concerned with conservation laws and first integrals for difference models. The book also includes dozens of examples of invariant schemes and meshes for physics and mechanics.