# Difference Equations In Normed Spaces

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## Difference Equations in Normed Spaces

Author | : Michael Gil |

Publsiher | : Elsevier |

Total Pages | : 378 |

Release | : 2007-01-08 |

ISBN | : 9780080469355 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Difference Equations in Normed Spaces Book Excerpt:**

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

## New Trends in Differential and Difference Equations and Applications

Author | : Feliz Manuel Minhós,João Fialho |

Publsiher | : MDPI |

Total Pages | : 198 |

Release | : 2019-10-14 |

ISBN | : 3039215388 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**New Trends in Differential and Difference Equations and Applications Book Excerpt:**

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.

## Regularity of Difference Equations on Banach Spaces

Author | : Ravi P. Agarwal,Claudio Cuevas,Carlos Lizama |

Publsiher | : Springer |

Total Pages | : 208 |

Release | : 2014-06-13 |

ISBN | : 3319064479 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Regularity of Difference Equations on Banach Spaces Book Excerpt:**

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 area of difference equations, particularly those with advance knowledge of and interest in functional analysis.

## Differential and Difference Equations with Applications

Author | : Sandra Pinelas,John R. Graef,Stefan Hilger,Peter Kloeden,Christos Schinas |

Publsiher | : Springer Nature |

Total Pages | : 778 |

Release | : 2020-10-21 |

ISBN | : 3030563235 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Differential and Difference Equations with Applications Book Excerpt:**

This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019. First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. The book includes studies on boundary value problems; Markov models; time scales; non-linear difference equations; multi-scale modeling; and myriad applications.

## Well Posedness of Parabolic Difference Equations

Author | : A. Ashyralyev,P.E. Sobolevskii |

Publsiher | : Birkhäuser |

Total Pages | : 353 |

Release | : 2012-12-06 |

ISBN | : 3034885180 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Well Posedness of Parabolic Difference Equations Book Excerpt:**

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 of difference operators in Banach spaces, which allows one to deal with difference schemes of arbitrary order of accuracy. Establishing coercivity inequalities allows one to obtain sharp, that is, two-sided estimates of convergence rates. The proofs are based on results in interpolation theory of linear operators. This monograph will be of value to professional mathematicians as well as advanced students interested in the fields of functional analysis and partial differential equations.

## Difference Equations

Author | : Ronald E. Mickens |

Publsiher | : CRC Press |

Total Pages | : 555 |

Release | : 2015-03-06 |

ISBN | : 1482230798 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Difference Equations Book Excerpt:**

Difference Equations: Theory, Applications and Advanced Topics, Third Edition provides a broad introduction to the mathematics of difference equations and some of their applications. Many worked examples illustrate how to calculate both exact and approximate solutions to special classes of difference equations. Along with adding several advanced to

## Advances in Difference Equations and Discrete Dynamical Systems

Author | : Saber Elaydi,Yoshihiro Hamaya,Hideaki Matsunaga,Christian Pötzsche |

Publsiher | : Springer |

Total Pages | : 282 |

Release | : 2017-11-13 |

ISBN | : 9811064091 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Advances in Difference Equations and Discrete Dynamical Systems Book Excerpt:**

This volume contains the proceedings of the 22nd International Conference on Difference Equations and Applications, held at Osaka Prefecture University, Osaka, Japan, in July 2016. The conference brought together both experts and novices in the theory and applications of difference equations and discrete dynamical systems. The volume features papers in difference equations and discrete dynamical systems with applications to mathematical sciences and, in particular, mathematical biology and economics. This book will appeal to researchers, scientists, and educators who work in the fields of difference equations, discrete dynamical systems, and their applications.

## Form Symmetries and Reduction of Order in Difference Equations

Author | : Hassan Sedaghat |

Publsiher | : CRC Press |

Total Pages | : 325 |

Release | : 2011-05-24 |

ISBN | : 1439807647 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Form Symmetries and Reduction of Order in Difference Equations Book Excerpt:**

Form Symmetries and Reduction of Order in Difference Equations presents a new approach to the formulation and analysis of difference equations in which the underlying space is typically an algebraic group. In some problems and applications, an additional algebraic or topological structure is assumed in order to define equations and obtain significant results about them. Reflecting the author’s past research experience, the majority of examples involve equations in finite dimensional Euclidean spaces. The book first introduces difference equations on groups, building a foundation for later chapters and illustrating the wide variety of possible formulations and interpretations of difference equations that occur in concrete contexts. The author then proposes a systematic method of decomposition for recursive difference equations that uses a semiconjugate relation between maps. Focusing on large classes of difference equations, he shows how to find the semiconjugate relations and accompanying factorizations of two difference equations with strictly lower orders. The final chapter goes beyond semiconjugacy by extending the fundamental ideas based on form symmetries to nonrecursive difference equations. With numerous examples and exercises, this book is an ideal introduction to an exciting new domain in the area of difference equations. It takes a fresh and all-inclusive look at difference equations and develops a systematic procedure for examining how these equations are constructed and solved.

## Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces

Author | : Behzad Djafari Rouhani |

Publsiher | : CRC Press |

Total Pages | : 450 |

Release | : 2019-05-20 |

ISBN | : 148222819X |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Nonlinear Evolution and Difference Equations of Monotone Type in Hilbert Spaces Book Excerpt:**

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.

## Geometric Theory of Discrete Nonautonomous Dynamical Systems

Author | : Christian Pötzsche |

Publsiher | : Springer |

Total Pages | : 399 |

Release | : 2010-08-24 |

ISBN | : 3642142583 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Geometric Theory of Discrete Nonautonomous Dynamical Systems Book Excerpt:**

Nonautonomous dynamical systems provide a mathematical framework for temporally changing phenomena, where the law of evolution varies in time due to seasonal, modulation, controlling or even random effects. Our goal is to provide an approach to the corresponding geometric theory of nonautonomous discrete dynamical systems in infinite-dimensional spaces by virtue of 2-parameter semigroups (processes). These dynamical systems are generated by implicit difference equations, which explicitly depend on time. Compactness and dissipativity conditions are provided for such problems in order to have attractors using the natural concept of pullback convergence. Concerning a necessary linear theory, our hyperbolicity concept is based on exponential dichotomies and splittings. This concept is in turn used to construct nonautonomous invariant manifolds, so-called fiber bundles, and deduce linearization theorems. The results are illustrated using temporal and full discretizations of evolutionary differential equations.

## Difference Equations Discrete Dynamical Systems and Applications

Author | : Saber Elaydi,Christian Pötzsche,Adina Luminiţa Sasu |

Publsiher | : Springer |

Total Pages | : 382 |

Release | : 2019-06-29 |

ISBN | : 3030200167 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Difference Equations Discrete Dynamical Systems and Applications Book Excerpt:**

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 field.

## Partial Difference Equations

Author | : Sui Sun Cheng |

Publsiher | : CRC Press |

Total Pages | : 288 |

Release | : 2003-02-06 |

ISBN | : 9780415298841 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Partial Difference Equations Book Excerpt:**

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 equations.

## Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces

Author | : Anatoly M Samoilenko,Yuri V Teplinsky |

Publsiher | : World Scientific |

Total Pages | : 408 |

Release | : 2013-05-03 |

ISBN | : 9814434841 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Elements of Mathematical Theory of Evolutionary Equations in Banach Spaces Book Excerpt:**

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 of extendibility of the solutions in degenerate cases. For nonlinear differential equations in spaces of bounded number sequences, new results are obtained in the theory of countable-point boundary-value problems. The book contains new mathematical results that will be useful towards advances in nonlinear mechanics and theoretical physics. Contents:Reducibility Problems for Difference EquationsInvariant Tori of Difference Equations in the Space MPeriodic Solutions of Difference Equations. Extention of SolutionsCountable-Point Boundary-Value Problems for Nonlinear Differential Equations Readership: Graduate students and researchers working in the field of analysis and differential equations. Keywords:Differencial Equations;Difference Equations;Invariant Tori;Bounded Number Sequences;Banach Spaces;Periodic Solutions;ReducibilityKey Features:New theoretical results, complete with proofsTheory developed for equations in infinite-dimensional spacesWritten by leading specialists in the fieldReviews: “The chapters are written so that they are almost independent of each other. The present monograph is helpful to specialists who are concerned with the relevant mathematical problems.” Zentralblatt MATH

## Proceedings of the Sixth International Conference on Difference Equations Augsburg Germany 2001

Author | : Bernd Aulbach,Saber N. Elaydi,G. Ladas |

Publsiher | : CRC Press |

Total Pages | : 584 |

Release | : 2004-06-07 |

ISBN | : 9780203575437 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Proceedings of the Sixth International Conference on Difference Equations Augsburg Germany 2001 Book Excerpt:**

This volume comprises selected papers presented at the Sixth International Conference on Difference Equations which was held at Augsburg, Germany. It covers all themes in the fields of discrete dynamical systems and ordinary and partial difference equations, classical and contemporary, theoretical and applied. It provides a useful reference text for graduates and researchers working in this area of mathematics.

## The Theory of Difference Schemes

Author | : Alexander A. Samarskii |

Publsiher | : CRC Press |

Total Pages | : 786 |

Release | : 2001-03-29 |

ISBN | : 9780203908518 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**The Theory of Difference Schemes Book Excerpt:**

The Theory of Difference Schemes emphasizes solutions to boundary value problems through multiple difference schemes. It addresses the construction of approximate numerical methods and computer algorithms for solving mathematical physics problems. The book also develops mathematical models for obtaining desired solutions in minimal time using direct or iterative difference equations. Mathematical Reviews said it is "well-written [and] an excellent book, with a wealth of mathematical material and techniques."

## Mathematics Without Boundaries

Author | : Panos M. Pardalos,Themistocles M. Rassias |

Publsiher | : Springer |

Total Pages | : 648 |

Release | : 2014-09-16 |

ISBN | : 1493911244 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Mathematics Without Boundaries Book Excerpt:**

This volume consists of chapters written by eminent scientists and engineers from the international community and present significant advances in several theories, methods and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, Discrete Mathematics and Geometry, as well as several applications to a large variety of concrete problems, including applications of computers to the study of smoothness and analyticity of functions, applications to epidemiological diffusion, networks, mathematical models of elastic and piezoelectric fields, optimal algorithms, stability of neutral type vector functional differential equations, sampling and rational interpolation for non-band-limited signals, recurrent neural network for convex optimization problems and experimental design. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical and Engineering subjects and especially to graduate students who search for the latest information.

## Mathematical Analysis in Interdisciplinary Research

Author | : Ioannis N. Parasidis |

Publsiher | : Springer Nature |

Total Pages | : 135 |

Release | : 2022 |

ISBN | : 3030847217 |

Category | : Electronic Book |

Language | : EN, FR, DE, ES & NL |

**Mathematical Analysis in Interdisciplinary Research Book Excerpt:**

## Systems of Quasilinear Equations and Their Applications to Gas Dynamics

Author | : Boris Leonidovich Rozhdestvenski_,Nikola_ Nikolaevich I_Anenko |

Publsiher | : American Mathematical Soc. |

Total Pages | : 676 |

Release | : 1983-12-31 |

ISBN | : 9780821898062 |

Category | : Science |

Language | : EN, FR, DE, ES & NL |

**Systems of Quasilinear Equations and Their Applications to Gas Dynamics Book Excerpt:**

This book is essentially a new edition, revised and augmented by results of the last decade, of the work of the same title published in 1968 by ``Nauka.'' It is devoted to mathematical questions of gas dynamics. Topics covered include Foundations of the Theory of Systems of Quasilinear Equations of Hyperbolic Type in Two Independent Variables; Classical and Generalized Solutions of One-Dimensional Gas Dynamics; Difference Methods for Solving the Equations of Gas Dynamics; and Generalized Solutions of Systems of Quasilinear Equations of Hyperbolic Type.

## Frontiers in Functional Equations and Analytic Inequalities

Author | : George A. Anastassiou,John Michael Rassias |

Publsiher | : Springer Nature |

Total Pages | : 753 |

Release | : 2019-11-23 |

ISBN | : 3030289508 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Frontiers in Functional Equations and Analytic Inequalities Book Excerpt:**

This volume presents cutting edge research from the frontiers of functional equations and analytic inequalities active fields. It covers the subject of functional equations in a broad sense, including but not limited to the following topics: Hyperstability of a linear functional equation on restricted domains Hyers–Ulam’s stability results to a three point boundary value problem of nonlinear fractional order differential equations Topological degree theory and Ulam’s stability analysis of a boundary value problem of fractional differential equations General Solution and Hyers-Ulam Stability of Duo Trigintic Functional Equation in Multi-Banach Spaces Stabilities of Functional Equations via Fixed Point Technique Measure zero stability problem for the Drygas functional equation with complex involution Fourier Transforms and Ulam Stabilities of Linear Differential Equations Hyers–Ulam stability of a discrete diamond–alpha derivative equation Approximate solutions of an interesting new mixed type additive-quadratic-quartic functional equation. The diverse selection of inequalities covered includes Opial, Hilbert-Pachpatte, Ostrowski, comparison of means, Poincare, Sobolev, Landau, Polya-Ostrowski, Hardy, Hermite-Hadamard, Levinson, and complex Korovkin type. The inequalities are also in the environments of Fractional Calculus and Conformable Fractional Calculus. Applications from this book's results can be found in many areas of pure and applied mathematics, especially in ordinary and partial differential equations and fractional differential equations. As such, this volume is suitable for researchers, graduate students and related seminars, and all science and engineering libraries. The exhibited thirty six chapters are self-contained and can be read independently and interesting advanced seminars can be given out of this book.

## Difference Schemes

Author | : S.K. Godunov,V.S. Ryabenkii |

Publsiher | : Elsevier |

Total Pages | : 488 |

Release | : 1987-05-01 |

ISBN | : 9780080875408 |

Category | : Mathematics |

Language | : EN, FR, DE, ES & NL |

**Difference Schemes Book Excerpt:**

Much applied and theoretical research in natural sciences leads to boundary-value problems stated in terms of differential equations. When solving these problems with computers, the differential problems are replaced approximately by difference schemes. This book is an introduction to the theory of difference schemes, and was written as a textbook for university mathematics and physics departments and for technical universities. Some sections of the book will be of interest to computations specialists. While stressing a mathematically rigorous treatment of model problems, the book also demonstrates the relation between theory and computer experiments, using difference schemes created for practical computations.