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Difference Equations in Normed Spaces

Difference Equations in Normed Spaces
  • Author : Michael Gil
  • Publsiher : Elsevier
  • Release : 08 January 2007
  • ISBN : 9780080469355
  • Pages : 378 pages
  • Rating : 4/5 from 21 ratings
GET THIS BOOKDifference Equations in Normed Spaces

Summary:
Difference equations appear as natural descriptions of observed evolution phenomena because most measurements of time evolving variables are discrete. They also appear in the applications of discretization methods for differential, integral and integro-differential equations. The application of the theory of difference equations is rapidly increasing to various fields, such as numerical analysis, control theory, finite mathematics, and computer sciences. This book is devoted to linear and nonlinear difference equations in a normed space. The main methodology presented in this book is based on a combined use of recent norm estimates for operator-valued functions with the following methods and results: The freezing method The Liapunov type equation The method of majorants The multiplicative representation of solutions Deals systematically with difference equations in normed spaces Considers new classes of equations that could not be studied in the frameworks of ordinary and partial difference equations Develops the freezing method and presents recent results on Volterra discrete equations Contains an approach based on the estimates for norms of operator functions


Difference Equations in Normed Spaces

Difference Equations in Normed Spaces
  • Author : Michael Gil
  • Publisher : Elsevier
  • Release : 08 January 2007
GET THIS BOOKDifference Equations in Normed Spaces

Difference equations appear as natural descriptions of observed evolution phenomena because most measurements of time evolving variables are discrete. They also appear in the applications of discretization methods for differential, integral and integro-differential equations. The application of the theory of difference equations is rapidly increasing to various fields, such as numerical analysis, control theory, finite mathematics, and computer sciences. This book is devoted to linear and nonlinear difference equations in a normed space. The main methodology presented in this book


Regularity of Difference Equations on Banach Spaces

Regularity of Difference Equations on Banach Spaces
  • Author : Ravi P. Agarwal,Claudio Cuevas,Carlos Lizama
  • Publisher : Springer
  • Release : 13 June 2014
GET THIS BOOKRegularity of Difference Equations on Banach Spaces

This work introduces readers to the topic of maximal regularity for difference equations. The authors systematically present the method of maximal regularity, outlining basic linear difference equations along with relevant results. They address recent advances in the field, as well as basic semi group and cosine operator theories in the discrete setting. The authors also identify some open problems that readers may wish to take up for further research. This book is intended for graduate students and researchers in the


Partial Difference Equations

Partial Difference Equations
  • Author : Sui Sun Cheng
  • Publisher : CRC Press
  • Release : 06 February 2003
GET THIS BOOKPartial Difference Equations

Partial Difference Equations treats this major class of functional relations. Such equations have recursive structures so that the usual concepts of increments are important. This book describes mathematical methods that help in dealing with recurrence relations that govern the behavior of variables such as population size and stock price. It is helpful for anyone who has mastered undergraduate mathematical concepts. It offers a concise introduction to the tools and techniques that have proven successful in obtaining results in partial difference


Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces

Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces
  • Author : Anatoly M Samoilenko,Yuri V Teplinsky
  • Publisher : World Scientific
  • Release : 03 May 2013
GET THIS BOOKElements of Mathematical Theory of Evolutionary Equations in Banach Spaces

Evolutionary equations are studied in abstract Banach spaces and in spaces of bounded number sequences. For linear and nonlinear difference equations, which are defined on finite-dimensional and infinite-dimensional tori, the problem of reducibility is solved, in particular, in neighborhoods of their invariant sets, and the basics for a theory of invariant tori and bounded semi-invariant manifolds are established. Also considered are the questions on existence and approximate construction of periodic solutions for difference equations in infinite-dimensional spaces and the problem


Difference Equations, Discrete Dynamical Systems and Applications

Difference Equations, Discrete Dynamical Systems and Applications
  • Author : Saber Elaydi,Christian Pötzsche,Adina Luminiţa Sasu
  • Publisher : Springer
  • Release : 29 June 2019
GET THIS BOOKDifference Equations, Discrete Dynamical Systems and Applications

The book presents the proceedings of the 23rd International Conference on Difference Equations and Applications, ICDEA 2017, held at the West University of Timișoara, Romania, under the auspices of the International Society of Difference Equations (ISDE), July 24 - 28, 2017. It includes new and significant contributions in the field of difference equations, discrete dynamical systems and their applications in various sciences. Disseminating recent studies and related results and promoting advances, the book appeals to PhD students, researchers, educators and practitioners in the


Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces

Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces
  • Author : Behzad Djafari Rouhani
  • Publisher : CRC Press
  • Release : 15 March 2019
GET THIS BOOKNonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces

This book is devoted to the study of non-linear evolution and difference equations of first or second order governed by maximal monotone operator. This class of abstract evolution equations contains ordinary differential equations, as well as the unification of some important partial differential equations including heat equation, wave equation, Schrodinger equation, etc. The book contains a collection of the authors' work and applications in this field, as well as those of other authors.




Techniques of Functional Analysis for Differential and Integral Equations

Techniques of Functional Analysis for Differential and Integral Equations
  • Author : Paul Sacks
  • Publisher : Academic Press
  • Release : 16 May 2017
GET THIS BOOKTechniques of Functional Analysis for Differential and Integral Equations

Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical



Topological Methods for Differential Equations and Inclusions

Topological Methods for Differential Equations and Inclusions
  • Author : John R. Graef,Johnny Henderson,Abdelghani Ouahab
  • Publisher : CRC Press
  • Release : 25 September 2018
GET THIS BOOKTopological Methods for Differential Equations and Inclusions

Topological Methods for Differential Equations and Inclusions covers the important topics involving topological methods in the theory of systems of differential equations. The equivalence between a control system and the corresponding differential inclusion is the central idea used to prove existence theorems in optimal control theory. Since the dynamics of economic, social, and biological systems are multi-valued, differential inclusions serve as natural models in macro systems with hysteresis.


Functional Analysis, Sobolev Spaces and Partial Differential Equations

Functional Analysis, Sobolev Spaces and Partial Differential Equations
  • Author : Haim Brezis
  • Publisher : Springer Science & Business Media
  • Release : 02 November 2010
GET THIS BOOKFunctional Analysis, Sobolev Spaces and Partial Differential Equations

This textbook is a completely revised, updated, and expanded English edition of the important Analyse fonctionnelle (1983). In addition, it contains a wealth of problems and exercises (with solutions) to guide the reader. Uniquely, this book presents in a coherent, concise and unified way the main results from functional analysis together with the main results from the theory of partial differential equations (PDEs). Although there are many books on functional analysis and many on PDEs, this is the first to cover


Well-Posedness of Parabolic Difference Equations

Well-Posedness of Parabolic Difference Equations
  • Author : A. Ashyralyev,P.E. Sobolevskii
  • Publisher : Birkhäuser
  • Release : 06 December 2012
GET THIS BOOKWell-Posedness of Parabolic Difference Equations

A well-known and widely applied method of approximating the solutions of problems in mathematical physics is the method of difference schemes. Modern computers allow the implementation of highly accurate ones; hence, their construction and investigation for various boundary value problems in mathematical physics is generating much current interest. The present monograph is devoted to the construction of highly accurate difference schemes for parabolic boundary value problems, based on Padé approximations. The investigation is based on a new notion of positivity