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Differential-Difference Equations

Author: Bellman

Publisher: Academic Press

ISBN:

Category: Mathematics

Page: 461

View: 911

Differential-Difference Equations

Asymptotic behavior of solutions of differential-difference equations

Author: Richard Ernest Bellman

Publisher:

ISBN:

Category: Differential-difference equations

Page: 91

View: 817

In this paper, the problem was considered of determining the asymptotic behavior of solutions of linear differentialdifference equations whose coefficients possess asymptotic series. Although the problem is considerably more complicated than the corresponding problem for ordinary differential equations, by means of a sequence of transformations the problem was reduced to a form where the standard techniques of ordinary differential equation theory could be employed. The differential-difference equation was transformed into an integral equation which was trans formed into an integro-differential equation. At this point the Liouville transformation plays a vital role. Although the guiding ideas were simple, the analysis became formidable. For this reason, only some of the more immediate aspects of the problem were considered.

Differential-Difference Equations/Differential-Differenzengleichungen

Applications and Numerical Problems/Anwendungen und numerische Probleme

Author: COLLATZ

Publisher: Birkhäuser

ISBN:

Category: Juvenile Nonfiction

Page: 196

View: 484

A nonlinear system of differential-difference equations

Author: Virginia Walbran Noonburg

Publisher:

ISBN:

Category: Mathematics

Page: 168

View: 666

Difference Equations and Their Applications

Author: A.N. Sharkovsky

Publisher: Springer Science & Business Media

ISBN:

Category: Mathematics

Page: 358

View: 799

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.

Asymptotic Behavior of Solutions of Differential-difference Equations

Author: Richard Ernest Bellman

Publisher:

ISBN:

Category: Asymptotic expansions

Page: 91

View: 514

In this paper, the problem was considered of determining the asymptotic behavior of solutions of linear differentialdifference equations whose coefficients possess asymptotic series. Although the problem is considerably more complicated than the corresponding problem for ordinary differential equations, by means of a sequence of transformations the problem was reduced to a form where the standard techniques of ordinary differential equation theory could be employed. The differential-difference equation was transformed into an integral equation which was trans formed into an integro-differential equation. At this point the Liouville transformation plays a vital role. Although the guiding ideas were simple, the analysis became formidable. For this reason, only some of the more immediate aspects of the problem were considered.

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations

Positive Solutions

Author: Johnny Henderson

Publisher: Academic Press

ISBN:

Category: Mathematics

Page: 322

View: 940

Boundary Value Problems for Systems of Differential, Difference and Fractional Equations: Positive Solutions discusses the concept of a differential equation that brings together a set of additional constraints called the boundary conditions. As boundary value problems arise in several branches of math given the fact that any physical differential equation will have them, this book will provide a timely presentation on the topic. Problems involving the wave equation, such as the determination of normal modes, are often stated as boundary value problems. To be useful in applications, a boundary value problem should be well posed. This means that given the input to the problem there exists a unique solution, which depends continuously on the input. Much theoretical work in the field of partial differential equations is devoted to proving that boundary value problems arising from scientific and engineering applications are in fact well-posed. Explains the systems of second order and higher orders differential equations with integral and multi-point boundary conditions Discusses second order difference equations with multi-point boundary conditions Introduces Riemann-Liouville fractional differential equations with uncoupled and coupled integral boundary conditions

Modelling with Differential and Difference Equations

Author: Glenn Fulford

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page: 405

View: 584

The theme of this book is modeling the real world using mathematics. The authors concentrate on the techniques used to set up mathematical models and describe many systems in full detail, covering both differential and difference equations in depth. Among the broad spectrum of topics studied in this book are: mechanics, genetics, thermal physics, economics and population studies.

Optimal Control of Systems Described by Differential Difference Equations

Author: Stanford University. Division of Engineering Mechanics

Publisher:

ISBN:

Category: Mathematical optimization

Page: 113

View: 737

Symmetries and Integrability of Difference Equations

Author: Decio Levi

Publisher: Cambridge University Press

ISBN:

Category: Mathematics

Page:

View: 656

Difference equations are playing an increasingly important role in the natural sciences. Indeed many phenomena are inherently discrete and are naturally described by difference equations. Phenomena described by differential equations are therefore approximations of more basic discrete ones. Moreover, in their study it is very often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference equations. This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference ones. Each of the eleven chapters is a self-contained treatment of a topic, containing introductory material as well as the latest research results. The book will be welcomed by graduate students and researchers seeking an introduction to the field. As a survey of the current state of the art it will also serve as a valuable reference.

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