Difference And Differential Equations
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Differential Difference Equations
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Author : Richard Bellman
language : en
Publisher:
Release Date : 1963
Differential Difference Equations written by Richard Bellman and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1963 with Mathematics categories.
Asymptotic Integration Of Differential And Difference Equations
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Author : Sigrun Bodine
language : en
Publisher: Springer
Release Date : 2015-05-26
Asymptotic Integration Of Differential And Difference Equations written by Sigrun Bodine and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-26 with Mathematics categories.
This book presents the theory of asymptotic integration for both linear differential and difference equations. This type of asymptotic analysis is based on some fundamental principles by Norman Levinson. While he applied them to a special class of differential equations, subsequent work has shown that the same principles lead to asymptotic results for much wider classes of differential and also difference equations. After discussing asymptotic integration in a unified approach, this book studies how the application of these methods provides several new insights and frequent improvements to results found in earlier literature. It then continues with a brief introduction to the relatively new field of asymptotic integration for dynamic equations on time scales. Asymptotic Integration of Differential and Difference Equations is a self-contained and clearly structured presentation of some of the most important results in asymptotic integration and the techniques used in this field. It will appeal to researchers in asymptotic integration as well to non-experts who are interested in the asymptotic analysis of linear differential and difference equations. It will additionally be of interest to students in mathematics, applied sciences, and engineering. Linear algebra and some basic concepts from advanced calculus are prerequisites.
Oscillation Theory For Difference And Functional Differential Equations
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Author : R.P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Oscillation Theory For Difference And Functional Differential Equations written by R.P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-29 with Mathematics categories.
This monograph is devoted to a rapidly developing area of research of the qualitative theory of difference and functional differential equations. In fact, in the last 25 years Oscillation Theory of difference and functional differential equations has attracted many researchers. This has resulted in hundreds of research papers in every major mathematical journal, and several books. In the first chapter of this monograph, we address oscillation of solutions to difference equations of various types. Here we also offer several new fundamental concepts such as oscillation around a point, oscillation around a sequence, regular oscillation, periodic oscillation, point-wise oscillation of several orthogonal polynomials, global oscillation of sequences of real valued functions, oscillation in ordered sets, (!, R, ~)-oscillate, oscillation in linear spaces, oscillation in Archimedean spaces, and oscillation across a family. These concepts are explained through examples and supported by interesting results. In the second chapter we present recent results pertaining to the oscil lation of n-th order functional differential equations with deviating argu ments, and functional differential equations of neutral type. We mainly deal with integral criteria for oscillation. While several results of this chapter were originally formulated for more complicated and/or more general differ ential equations, we discuss here a simplified version to elucidate the main ideas of the oscillation theory of functional differential equations. Further, from a large number of theorems presented in this chapter we have selected the proofs of only those results which we thought would best illustrate the various strategies and ideas involved.
Advanced Topics In Difference Equations
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Author : R.P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Advanced Topics In Difference Equations written by R.P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
. The theory of difference equations, the methods used in their solutions and their wide applications have advanced beyond their adolescent stage to occupy a central position in Applicable Analysis. In fact, in the last five years, the proliferation of the subject is witnessed by hundreds of research articles and several monographs, two International Conferences and numerous Special Sessions, and a new Journal as well as several special issues of existing journals, all devoted to the theme of Difference Equations. Now even those experts who believe in the universality of differential equations are discovering the sometimes striking divergence between the continuous and the discrete. There is no doubt that the theory of difference equations will continue to play an important role in mathematics as a whole. In 1992, the first author published a monograph on the subject entitled Difference Equations and Inequalities. This book was an in-depth survey of the field up to the year of publication. Since then, the subject has grown to such an extent that it is now quite impossible for a similar survey, even to cover just the results obtained in the last four years, to be written. In the present monograph, we have collected some of the results which we have obtained in the last few years, as well as some yet unpublished ones.
Focal Boundary Value Problems For Differential And Difference Equations
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Author : R.P. Agarwal
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Focal Boundary Value Problems For Differential And Difference Equations written by R.P. Agarwal and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
The last fifty years have witnessed several monographs and hundreds of research articles on the theory, constructive methods and wide spectrum of applications of boundary value problems for ordinary differential equations. In this vast field of research, the conjugate (Hermite) and the right focal point (Abei) types of problems have received the maximum attention. This is largely due to the fact that these types of problems are basic, in the sense that the methods employed in their study are easily extendable to other types of prob lems. Moreover, the conjugate and the right focal point types of boundary value problems occur frequently in real world problems. In the monograph Boundary Value Problems for Higher Order Differential Equations published in 1986, we addressed the theory of conjugate boundary value problems. At that time the results on right focal point problems were scarce; however, in the last ten years extensive research has been done. In Chapter 1 of the mono graph we offer up-to-date information of this newly developed theory of right focal point boundary value problems. Until twenty years ago Difference Equations were considered as the dis cretizations of the differential equations. Further, it was tacitly taken for granted that the theories of difference and differential equations are parallel. However, striking diversities and wide applications reported in the last two decades have made difference equations one of the major areas of research.
Difference Equations
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Author : Ronald E. Mickens
language : en
Publisher: Van Nostrand Reinhold Company
Release Date : 1987
Difference Equations written by Ronald E. Mickens and has been published by Van Nostrand Reinhold Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1987 with Mathematics categories.
Nonstandard Finite Difference Models Of Differential Equations
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Author : Ronald E. Mickens
language : en
Publisher: World Scientific
Release Date : 1994
Nonstandard Finite Difference Models Of Differential Equations written by Ronald E. Mickens and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of the book is to show that discrete models of differential equations exist such that the elementary types of numerical instabilities do not occur. A consequence of this result is that in general bigger step-sizes can often be used in actual calculations and/or finite difference schemes can be constructed that are conditionally stable in many instances whereas in using standard techniques no such schemes exist. The theoretical basis of this work is centered on the concepts of ?exact? and ?best? finite difference schemes. In addition, a set of rules is given for the discrete modeling of derivatives and nonlinear expressions that occur in differential equations. These rules often lead to a unique nonstandard finite difference model for a given differential equation.
Introduction To Difference Equations
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Author : Samuel Goldberg
language : en
Publisher: Courier Corporation
Release Date : 1986-01-01
Introduction To Difference Equations written by Samuel Goldberg and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986-01-01 with Mathematics categories.
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.
Modelling With Differential And Difference Equations
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Author : Glenn Fulford
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-12
Modelling With Differential And Difference Equations written by Glenn Fulford and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-12 with Mathematics categories.
Any student wishing to solve problems via mathematical modelling will find that this book provides an excellent introduction to the subject.
Finite Difference Methods For Ordinary And Partial Differential Equations
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Author : Randall J. LeVeque
language : en
Publisher: SIAM
Release Date : 2007-01-01
Finite Difference Methods For Ordinary And Partial Differential Equations written by Randall J. LeVeque and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.
This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.