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题名/责任者:

Applications of Lie groups to difference equations / Vladimir Dorodnitsyn.

出版发行项:

Boca Raton, FL : Chapman & Hall/CRC, c2011.

ISBN:

9781420083095 (hardback)

ISBN:

1420083090 (hardback)

ISBN:

9781420083101 (electronic bk.)

ISBN:

1420083104 (electronic bk.)

载体形态项:

lxxx, 264 p. : ill. ; 27 cm.

丛编说明:

Differential and integral equations and their applications ; v. 8

丛编统一题名:

Differential and integral equations and their applications ; v. 8.

个人责任者:

Dorodnitsyn, V. A. (Vladimir Anatol evich), 1947-

论题主题:

Difference equations.

中图法分类号:

O241.8

书目附注:

Includes bibliographical references and index.

摘要附注:

"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 mesn 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 Schr dinger equation".

摘要附注:

"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".

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