Advertisement

Asymptotic Analysis

Linear Ordinary Differential Equations

  • Authors
  • Mikhail V. Fedoryuk

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Mikhail V. Fedoryuk
    Pages 1-23
  3. Mikhail V. Fedoryuk
    Pages 24-78
  4. Mikhail V. Fedoryuk
    Pages 79-167
  5. Mikhail V. Fedoryuk, Andrew Rodick
    Pages 168-226
  6. Mikhail V. Fedoryuk
    Pages 227-351
  7. Back Matter
    Pages 352-363

About this book

Introduction

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.

Keywords

Analytic Theory Analytische Theorie Asymptotic Behavior of Solutions Asymptotisches Verhalten von Lösungen Eigenvalue Linear Ordinary Differential Equations Quasiklassische Näherung Scattering Theory Streutheorie Sturm-Liouvillesche-Gleichung Transition Point differential equation operator ordinary differential equation Übergangspunkt

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-58016-1
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-63435-2
  • Online ISBN 978-3-642-58016-1
  • Buy this book on publisher's site
Industry Sectors
Pharma
Finance, Business & Banking
Electronics
Aerospace
Oil, Gas & Geosciences