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Difference Equations, Second Edition

Author: R Mickens

Publisher: CRC Press

Published: 1991-01-01

Total Pages: 470

ISBN-13: 9780442001360

In recent years, the study of difference equations has acquired a new significance, due in large part to their use in the formulation and analysis of discrete-time systems, the numerical integration of differential equations by finite-difference schemes, and the study of deterministic chaos. The second edition of Difference Equations: Theory and Applications provides a thorough listing of all major theorems along with proofs. The text treats the case of first-order difference equations in detail, using both analytical and geometrical methods. Both ordinary and partial difference equations are considered, along with a variety of special nonlinear forms for which exact solutions can be determined. Numerous worked examples and problems allow readers to fully understand the material in the text. They also give possible generalization of the theorems and application models. The text's expanded coverage of application helps readers appreciate the benefits of using difference equations in the modeling and analysis of "realistic" problems from a broad range of fields. The second edition presents, analyzes, and discusses a large number of applications from the mathematical, biological, physical, and social sciences. Discussions on perturbation methods and difference equation models of differential equation models of differential equations represent contributions by the author to the research literature. Reference to original literature show how the elementary models of the book can be extended to more realistic situations. Difference Equations, Second Edition gives readers a background in discrete mathematics that many workers in science-oriented industries need as part of their general scientific knowledge. With its minimal mathematical background requirements of general algebra and calculus, this unique volume will be used extensively by students and professional in science and technology, in areas such as applied mathematics, control theory, population science, economics, and electronic circuits, especially discrete signal processing.

Differential Equations: Theory and Applications

Author: David Betounes

Publisher: Springer Science & Business Media

Published: 2013-06-29

Total Pages: 686

ISBN-13: 1475749716

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This book provides a comprehensive introduction to the theory of ordinary differential equations with a focus on mechanics and dynamical systems as important applications of the theory. The text is written to be used in the traditional way or in a more applied way. The accompanying CD contains Maple worksheets for the exercises, and special Maple code for performing various tasks. In addition to its use in a traditional one or two semester graduate course in mathematics, the book is organized to be used for interdisciplinary courses in applied mathematics, physics, and engineering.

Theory and Applications of Differential and Difference Equations

Author: Adalynn West

Publisher: Clanrye International

Published: 2023-09-26

Total Pages: 0

ISBN-13: 9781647266530

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A differential equation is an equation in which an equality is expressed in terms of a function of one or more independent variables and derivatives of the function with respect to one or more of those independent variables. These equations play a prominent role in signal and system analysis because they describe the dynamic behavior of continuous-time (CT) physical systems. There are several applications of differential equations in different fields such as applied mathematics, science and engineering. The equation in which an equality is expressed in terms of a function of one or more independent variables and finite differences of the function is referred to as a difference equation. Differential and difference equations, both are essential for signal and system analysis because they can explain the dynamic behavior of discrete-time (DT) systems. Different approaches, evaluations, methodologies, and advanced studies on differential and difference equations have been included in this book. Its extensive content will provide the students of advanced mathematics with a thorough understanding of the subject.

Differential and Difference Equations with Applications

Author: Sandra Pinelas

Publisher: Springer Science & Business Media

Published: 2013-09-21

Total Pages: 639

ISBN-13: 1461473330

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The volume contains carefully selected papers presented at the International Conference on Differential & Difference Equations and Applications held in Ponta Delgada – Azores, from July 4-8, 2011 in honor of Professor Ravi P. Agarwal. The objective of the gathering was to bring together researchers in the fields of differential & difference equations and to promote the exchange of ideas and research. The papers cover all areas of differential and difference equations with a special emphasis on applications.

Difference and Differential Equations with Applications in Queueing Theory

Author: Aliakbar Montazer Haghighi

Publisher: John Wiley & Sons

Published: 2013-07-10

Total Pages: 419

ISBN-13: 1118393244

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A Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models Difference and Differential Equations with Applications in Queueing Theory presents the unique connections between the methods and applications of differential equations, difference equations, and Markovian queues. Featuring a comprehensive collection of topics that are used in stochastic processes, particularly in queueing theory, the book thoroughly discusses the relationship to systems of linear differential difference equations. The book demonstrates the applicability that queueing theory has in a variety of fields including telecommunications, traffic engineering, computing, and the design of factories, shops, offices, and hospitals. Along with the needed prerequisite fundamentals in probability, statistics, and Laplace transform, Difference and Differential Equations with Applications in Queueing Theory provides: A discussion on splitting, delayed-service, and delayed feedback for single-server, multiple-server, parallel, and series queue models Applications in queue models whose solutions require differential difference equations and generating function methods Exercises at the end of each chapter along with select answers The book is an excellent resource for researchers and practitioners in applied mathematics, operations research, engineering, and industrial engineering, as well as a useful text for upper-undergraduate and graduate-level courses in applied mathematics, differential and difference equations, queueing theory, probability, and stochastic processes.

Applied Theory of Functional Differential Equations

Author: V. Kolmanovskii

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 246

ISBN-13: 9401580847

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This volume provides an introduction to the properties of functional differential equations and their applications in diverse fields such as immunology, nuclear power generation, heat transfer, signal processing, medicine and economics. In particular, it deals with problems and methods relating to systems having a memory (hereditary systems). The book contains eight chapters. Chapter 1 explains where functional differential equations come from and what sort of problems arise in applications. Chapter 2 gives a broad introduction to the basic principle involved and deals with systems having discrete and distributed delay. Chapters 3-5 are devoted to stability problems for retarded, neutral and stochastic functional differential equations. Problems of optimal control and estimation are considered in Chapters 6-8. For applied mathematicians, engineers, and physicists whose work involves mathematical modeling of hereditary systems. This volume can also be recommended as a supplementary text for graduate students who wish to become better acquainted with the properties and applications of functional differential equations.

Differential-Difference Equations

Author: Bellman

Publisher: Academic Press

Published: 1963-01-01

Total Pages: 484

ISBN-13: 0080955142

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Differential-Difference Equations

Introduction to Difference Equations

Author: Samuel Goldberg

Publisher: Courier Corporation

Published: 1986-01-01

Total Pages: 292

ISBN-13: 0486650847

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Exceptionally clear exposition of an important mathematical discipline and its applications to sociology, economics, and psychology. Topics include calculus of finite differences, difference equations, matrix methods, and more. 1958 edition.

New Trends in Differential and Difference Equations and Applications

Author: Feliz Manuel Minhós

Publisher: MDPI

Published: 2019-10-14

Total Pages: 198

ISBN-13: 3039215388

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This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

Difference Equations and Their Applications

Author: A.N. Sharkovsky

Publisher: Springer Science & Business Media

Published: 1993-03-31

Total Pages: 374

ISBN-13: 9780792321941

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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.