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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.
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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
Table of contents (5 chapters)
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
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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