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Asymptotic Analysis

Linear Ordinary Differential Equations

  • Book
  • © 1993

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Authors:
  1. Mikhail V. Fedoryuk
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Table of contents (5 chapters)

  1. Front Matter

    Pages I-VIII
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  2. The Analytic Theory of Differential Equations

    • Mikhail V. Fedoryuk
    Pages 1-23

  3. Second-Order Equations on the Real Line

    • Mikhail V. Fedoryuk
    Pages 24-78

  4. Second-Order Equations in the Complex Plane

    • Mikhail V. Fedoryuk
    Pages 79-167

  5. Second-Order Equations with Turning Points

    • Mikhail V. Fedoryuk, Andrew Rodick
    Pages 168-226

  6. n th-Order Equations and Systems

    • Mikhail V. Fedoryuk
    Pages 227-351

  7. Back Matter

    Pages 352-363
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Keywords

About this book

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.

Bibliographic Information

  • Book Title: Asymptotic Analysis

  • Book Subtitle: Linear Ordinary Differential Equations

  • Authors: Mikhail V. Fedoryuk

  • DOI: https://doi.org/10.1007/978-3-642-58016-1

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1993

  • Hardcover ISBN: 978-3-540-54810-2Published: 03 May 1993

  • Softcover ISBN: 978-3-642-63435-2Published: 13 October 2012

  • eBook ISBN: 978-3-642-58016-1Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: VIII, 363

  • Additional Information: Original Russian edition published by Nauka, Moscow, 1983

  • Topics: Analysis

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