Difference Equations and Their Applications - Couverture souple

Sharkovsky, A.N.; Maistrenko, Y. L.; Romanenko, E.Yu

Couverture souple

ISBN 10 : 940104774X ISBN 13 : 9789401047746

Editeur : Springer, 2012

Synopsis

The theory of difference equations is now enjoying a period of Renaissance. Witness the large number of papers in which problems, having at first sight no common features, are reduced to the investigation of subsequent iterations of the maps f- IR. m IR. m, m > 0, or (which is, in fact, the same) to difference equations The world of difference equations, which has been almost hidden up to now, begins to open in all its richness. Those experts, who usually use differential equations and, in fact, believe in their universality, are now discovering a completely new approach which re- sembles the theory of ordinary differential equations only slightly. Difference equations, which reflect one of the essential properties of the real world-its discreteness-rightful- ly occupy a worthy place in mathematics and its applications. The aim of the present book is to acquaint the reader with some recently discovered and (at first sight) unusual properties of solutions for nonlinear difference equations. These properties enable us to use difference equations in order to model complicated os- cillating processes (this can often be done in those cases when it is difficult to apply ordinary differential equations). Difference equations are also a useful tool of syn- ergetics- an emerging science concerned with the study of ordered structures. The application of these equations opens up new approaches in solving one of the central problems of modern science-the problem of turbulence.

A propos du livre

Présentation de l'éditeur

This book presents an exposition of recently discovered, unusual properties of difference equations. Even in the simplest scalar case, nonlinear difference equations have been proved to exhibit surprisingly varied and qualitatively different solutions. The latter can readily be applied to the modelling of complex oscillations and the description of the process of fractal growth and the resulting fractal structures. Difference equations give an elegant description of transitions to chaos and, furthermore, provide useful information on reconstruction inside chaos. In numerous simulations of relaxation and turbulence phenomena the difference equation description is therefore preferred to the traditional differential equation-based modelling. This monograph consists of four parts. The first part deals with one-dimensional dynamical systems, the second part treats nonlinear scalar difference equations of continuous argument. Parts three and four describe relevant applications in the theory of difference-differential equations and in the nonlinear boundary problems formulated for hyperbolic systems of partial differential equations. The book is intended not only for mathematicians but also for those interested in mathematical applications and computer simulations of nonlinear effects in physics, chemistry, biology and other fields.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2012
• Langue: anglais
• ISBN 10: 940104774X
• ISBN 13: 9789401047746
• Reliure: Broché
• Nombre de pages: 376
• Coordonnées du fabricant: ProductSafety@springernature.com; ProductSafety@springernature.com; ; Poststr. 9; Darmstadt; 64293; Allemagne