Asymptotic Analysis: Linear Ordinary Differential Equations

Fedoryuk, Mikhail V. V.

ISBN 10: 3642634354 / ISBN 13: 9783642634352

Verlag: Springer, 2012

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Inhaltsangabe:

Fedoryuk's book is a unique reference for the asymptotic theory of ordinary differential equations given all the important formulae of this field. It is also an indispensable guide to the literature up to the most recent research.

Reseña del editor: 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.

Bibliografische Details

Titel: Asymptotic Analysis: Linear Ordinary ...
Verlag: Springer
Erscheinungsdatum: 2012
Einband: Softcover
Zustand: New