Author : James Robert Buchanan
Publisher :
Page : 226 pages
File Size : 28,32 MB
Release : 1993
Category :
ISBN :
Author : Mikhail V. Fedoryuk
Publisher : Springer Science & Business Media
Page : 370 pages
File Size : 45,24 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642580165
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.
Author : Carlos Simpson
Publisher : Springer
Page : 144 pages
File Size : 50,98 MB
Release : 2006-11-14
Category : Mathematics
ISBN : 354046641X
This book concerns the question of how the solution of a system of ODE's varies when the differential equation varies. The goal is to give nonzero asymptotic expansions for the solution in terms of a parameter expressing how some coefficients go to infinity. A particular classof families of equations is considered, where the answer exhibits a new kind of behavior not seen in most work known until now. The techniques include Laplace transform and the method of stationary phase, and a combinatorial technique for estimating the contributions of terms in an infinite series expansion for the solution. Addressed primarily to researchers inalgebraic geometry, ordinary differential equations and complex analysis, the book will also be of interest to applied mathematicians working on asymptotics of singular perturbations and numerical solution of ODE's.
Author : Steve P. Riley
Publisher :
Page : 148 pages
File Size : 24,22 MB
Release : 2020-01-30
Category :
ISBN : 9781536172225
This book is designed to provide the reader with an exposition of some aspects of the oscillation theory of first order delay partial dynamic equations on time scales. Oscillation theory of differential equations, originated from the monumental paper of C. Sturm published in 1836, has now been recognised as an important branch of mathematical analysis from both theoretical and practical viewpoints. Asymptotic behavior in the deep Euclidean region of momenta for four-dimensional models of quantum field theory is studied through the system of Schwinger-Dyson equations. This system is truncated by a sequence of n-particle approximations in which n → ∞ goes into the complete system of Schwinger-Dyson equations. Lastly, the authors discuss the exact analytical solution of the Schrödinger equation corresponding to the hydrogen atom confined by four spherical potentials: infinite potential, parabolic potential, constant potential, and dielectric continuum.
Author : A. Georgescu
Publisher : CRC Press
Page : 282 pages
File Size : 31,6 MB
Release : 1995-05-15
Category : Mathematics
ISBN : 9780412558603
The main definitions and results of asymptotic analysis and the theory of regular and singular perturbations are summarized in this book. They are applied to the asymptotic study of several mathematical models from mechanics, fluid dynamics, statistical mechanics, meteorology and elasticity. Due to the generality of presentation this applications-oriented book is suitable for the solving of differential equations from any other field of interest.
Author : M.H. Lantsman
Publisher : Springer Science & Business Media
Page : 450 pages
File Size : 25,15 MB
Release : 2013-04-17
Category : Mathematics
ISBN : 9401597979
The asymptotic theory deals with the problern of determining the behaviour of a function in a neighborhood of its singular point. The function is replaced by another known function ( named the asymptotic function) close (in a sense) to the function under consideration. Many problems of mathematics, physics, and other divisions of natural sci ence bring out the necessity of solving such problems. At the present time asymptotic theory has become an important and independent branch of mathematical analysis. The present consideration is mainly based on the theory of asymp totic spaces. Each asymptotic space is a collection of asymptotics united by an associated real function which determines their growth near the given point and (perhaps) some other analytic properties. The main contents of this book is the asymptotic theory of ordinary linear differential equations with variable coefficients. The equations with power order growth coefficients are considered in detail. As the application of the theory of differential asymptotic fields, we also consider the following asymptotic problems: the behaviour of explicit and implicit functions, improper integrals, integrals dependent on a large parameter, linear differential and difference equations, etc .. The obtained results have an independent meaning. The reader is assumed to be familiar with a comprehensive course of the mathematical analysis studied, for instance at mathematical departments of universities. Further necessary information is given in this book in summarized form with proofs of the main aspects.
Author : Michel Marie Chipot
Publisher : World Scientific
Page : 283 pages
File Size : 32,1 MB
Release : 2024-04-15
Category : Mathematics
ISBN : 9811290458
The primary focus of the book is to explore the asymptotic behavior of problems formulated within cylindrical structures. Various physical applications are discussed, with certain topics such as fluid flows in channels being particularly noteworthy. Additionally, the book delves into the relevance of elasticity in the context of cylindrical bodies.In specific scenarios where the size of the cylinder becomes exceptionally large, the material's behavior is determined solely by its cross-section. The investigation centers around understanding these particular properties.Since the publication of the first edition, several significant advancements have been made, adding depth and interest to the content. Consequently, new sections have been incorporated into the existing edition, complemented by a comprehensive list of references.
Author : R. B. Paris
Publisher : Longman
Page : 364 pages
File Size : 44,26 MB
Release : 1986
Category : Asymptotic expansions
ISBN :
Author : R. B. White
Publisher : World Scientific
Page : 430 pages
File Size : 22,69 MB
Release : 2010
Category : Mathematics
ISBN : 1848166087
"This is a useful volume in which a wide selection of asymptotic techniques is clearly presented in a form suitable for both applied mathematicians and Physicists who require an introduction to asymptotic techniques." --Book Jacket.
Author : Wolfgang Wasow
Publisher : Courier Dover Publications
Page : 385 pages
File Size : 38,42 MB
Release : 2018-03-21
Category : Mathematics
ISBN : 0486824586
This outstanding text concentrates on the mathematical ideas underlying various asymptotic methods for ordinary differential equations that lead to full, infinite expansions. "A book of great value." — Mathematical Reviews. 1976 revised edition.
