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Asymptotic Behavior Of Solutions Of Differential Difference Equations
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Book Synopsis Asymptotic Behavior of Solutions of Differential-Difference Equations by : Richard Bellman
Download or read book Asymptotic Behavior of Solutions of Differential-Difference Equations written by Richard Bellman and published by American Mathematical Soc.. This book was released on 1959 with total page 99 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behavior of Solutions of Differential-difference Equations by :
Download or read book Asymptotic Behavior of Solutions of Differential-difference Equations written by and published by . This book was released on 1958 with total page 76 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Asymptotic Integration of Differential and Difference Equations by : Sigrun Bodine
Download or read book Asymptotic Integration of Differential and Difference Equations written by Sigrun Bodine and published by Springer. This book was released on 2015-05-26 with total page 411 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Differential-Difference Equations by : Bellman
Download or read book Differential-Difference Equations written by Bellman and published by Academic Press. This book was released on 1963-01-01 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential-Difference Equations
Book Synopsis Cohomology Theory and Algebraic Correspondences by : Ernst Snapper
Download or read book Cohomology Theory and Algebraic Correspondences written by Ernst Snapper and published by . This book was released on 1957 with total page 66 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behavior of Solutions of Ordinary Differential Equations Near Sets by : Taro Yoshizawa
Download or read book Asymptotic Behavior of Solutions of Ordinary Differential Equations Near Sets written by Taro Yoshizawa and published by . This book was released on 1961 with total page 21 pages. Available in PDF, EPUB and Kindle. Book excerpt: Asymptotic behavior of unperturbed systems of solutions of differential-difference equations.
Book Synopsis The Asymptotic and Oscillatory Behaviour of Difference and Differential Equations by : Shuhui Wu
Download or read book The Asymptotic and Oscillatory Behaviour of Difference and Differential Equations written by Shuhui Wu and published by GRIN Verlag. This book was released on 2022-03-04 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Doctoral Thesis / Dissertation from the year 2009 in the subject Mathematics - Applied Mathematics, London Metropolitan University, language: English, abstract: This thesis deals with the asymptotic and oscillatory behaviour of the solutions of certain differential and difference equations. It mainly consists of three parts. The first part is to study the asymptotic behaviour of certain differential equations. The second part is to look for oscillatory criteria for certain nonlinear neutral differential equations. And the third part is to establish new criteria for a class of nonlinear neutral difference equations of any order with continuous variable and another type of higher even order nonlinear neutral difference equations to be oscillatory. A functional differential equation is a differential equation involving the values of the unknown functions at present, as well as at past or future time. The word “time” here stands for the independent variable. In the thesis, the concept of a functional differential equation is confined to ordinary differential equations, although it suits partial ones as well. Functional differential equations can be classified into four types according to their deviations: retarded, advanced, neutral and mixed. A neutral equation is one in which derivative of functionals of the past history and the present state are involved, but no future states occur in the equation. The order of a differential equation is the order of the highest derivative of the unknown function. A difference equation is a specific type of recurrence relation, which is an equation that defines a sequence recursively: each term of the sequence is defined as a function of the preceding terms. On the other hand, difference equations can be thought of as the discrete analogue of the corresponding differential equations. By analogy with differential equations, difference equations also can be classified into four types: delay, advanced, neutral, and mixed. The order of a difference equation is the difference between the largest and the smallest values of the integer variable explicitly involved in the difference equation.
Book Synopsis Asymptotic Behavior of the Solutions of Differential-difference Equations by : J. K. Hale (Mathematician, United States)
Download or read book Asymptotic Behavior of the Solutions of Differential-difference Equations written by J. K. Hale (Mathematician, United States) and published by . This book was released on 1961 with total page 33 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Functional Differential Equations and Applications by : Alexander Domoshnitsky
Download or read book Functional Differential Equations and Applications written by Alexander Domoshnitsky and published by Springer Nature. This book was released on 2022-02-02 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses delay and integro-differential equations from the point of view of the theory of functional differential equations. This book is a collection of selected papers presented at the international conference of Functional Differential Equations and Applications (FDEA-2019), 7th in the series, held at Ariel University, Israel, from August 22–27, 2019. Topics covered in the book include classical properties of functional differential equations as oscillation/non-oscillation, representation of solutions, sign properties of Green's matrices, comparison of solutions, stability, control, analysis of boundary value problems, and applications. The primary audience for this book includes specialists on ordinary, partial and functional differential equations, engineers and doctors dealing with modeling, and researchers in areas of mathematics and engineering.
Book Synopsis Asymptotic Behavior of Solutions of Differential-difference Equations by Richard Bellman and Kenneth L. Cooke by :
Download or read book Asymptotic Behavior of Solutions of Differential-difference Equations by Richard Bellman and Kenneth L. Cooke written by and published by . This book was released on 1959 with total page 95 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Existence and Asymptotic Behavior of Solutions to Linear Integro-differential-difference Equations by : Bhagat Singh
Download or read book Existence and Asymptotic Behavior of Solutions to Linear Integro-differential-difference Equations written by Bhagat Singh and published by . This book was released on 1971 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Survey of the Theory of the Boundedness, Stability, and Asymptotic Behavior of Solutions of Linear and Non-linear Differential and Difference Equations by : Richard Bellman
Download or read book A Survey of the Theory of the Boundedness, Stability, and Asymptotic Behavior of Solutions of Linear and Non-linear Differential and Difference Equations written by Richard Bellman and published by . This book was released on 1949 with total page 168 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Global Behavior of Nonlinear Difference Equations of Higher Order with Applications by : V.L. Kocic
Download or read book Global Behavior of Nonlinear Difference Equations of Higher Order with Applications written by V.L. Kocic and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear difference equations of order greater than one are of paramount impor tance in applications where the (n + 1)st generation (or state) of the system depends on the previous k generations (or states). Such equations also appear naturally as discrete analogues and as numerical solutions of differential and delay differential equations which model various diverse phenomena in biology, ecology, physiology, physics, engineering and economics. Our aim in this monograph is to initiate a systematic study of the global behavior of solutions of nonlinear scalar difference equations of order greater than one. Our primary concern is to study the global asymptotic stability of the equilibrium solution. We are also interested in whether the solutions are bounded away from zero and infinity, in the description of the semi cycles of the solutions, and in the existence of periodic solutions. This monograph contains some recent important developments in this area together with some applications to mathematical biology. Our intention is to expose the reader to the frontiers of the subject and to formulate some important open problems that require our immediate attention.
Book Synopsis The Asymptotic Behavior of the Solutions of Linear and Non-linear Differential-difference Equations by : Kenneth L. Cooke
Download or read book The Asymptotic Behavior of the Solutions of Linear and Non-linear Differential-difference Equations written by Kenneth L. Cooke and published by . This book was released on 1951 with total page 600 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis On the Asymptotic Behavior of the Solutions of Boundary Problems for Quasilinear Differential Equations by : M. I. Vishik
Download or read book On the Asymptotic Behavior of the Solutions of Boundary Problems for Quasilinear Differential Equations written by M. I. Vishik and published by . This book was released on 1967 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Asymptotic Behavior of the Solutions of Differential - Difference Equations by : JACK K. HALE
Download or read book Asymptotic Behavior of the Solutions of Differential - Difference Equations written by JACK K. HALE and published by . This book was released on 1961 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory on perturbed differential-difference equations is given. The use of ordinary differential equations is necessary in the testing of perturbation functions by use of the Lyapunov functional. The advantages in using this particular function are two-fold. First, the unperturbed eq ation may be either linear or nonlinear. Secondly, there is no need f r an integral representation for the soluti ns. AD- 64 6059N>A -264 606Div. 15U (TIPSP/MFA) OTS price $1.60 RIAS, Inc., Baltimore, Md. ON THE GLOBAL STABILITY OF AN AUTONO OUS SYSTEM ON THE PLANE, by Czeslaw Olech. 1961, 16p. (Technical rept. no. 61-12) (Contract AF 49(638)382) (AFOSR 1130)Unclassified report ESCRIPTORS: (*Nu erical analysis, *Curve fitting, *Spheres, Linear systems.) (Func tions, Equations, *Differential equations, Par tia differential equations, Matrix algebra, Green's function.) Open-ended Terms: Jacobian matrix, Global sta ility, Plane. A discussion is presented on global asymptotic stability in the large or systems of ordinary differential equations. Problems and proofs are given.
Book Synopsis Asymptotic Analysis by : Mikhail V. Fedoryuk
Download or read book Asymptotic Analysis written by Mikhail V. Fedoryuk and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 370 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we present the main results on the asymptotic theory of ordinary linear differential equations and systems where there is a small parameter in the higher derivatives. We are concerned with the behaviour of solutions with respect to the parameter and for large values of the independent variable. The literature on this question is considerable and widely dispersed, but the methods of proofs are sufficiently similar for this material to be put together as a reference book. We have restricted ourselves to homogeneous equations. The asymptotic behaviour of an inhomogeneous equation can be obtained from the asymptotic behaviour of the corresponding fundamental system of solutions by applying methods for deriving asymptotic bounds on the relevant integrals. We systematically use the concept of an asymptotic expansion, details of which can if necessary be found in [Wasow 2, Olver 6]. By the "formal asymptotic solution" (F.A.S.) is understood a function which satisfies the equation to some degree of accuracy. Although this concept is not precisely defined, its meaning is always clear from the context. We also note that the term "Stokes line" used in the book is equivalent to the term "anti-Stokes line" employed in the physics literature.
