UID:
edoccha_9959186004002883
Format:
1 online resource (VI, 142 p.)
Edition:
1st ed. 1991.
Edition:
Online edition Springer Lecture Notes Archive ; 041142-5
ISBN:
3-540-46641-X
Series Statement:
Lecture Notes in Mathematics, 1502
Content:
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.
Note:
Bibliographic Level Mode of Issuance: Monograph
,
Ordinary differential equations on a Riemann surface -- Laplace transform, asymptotic expansions, and the method of stationary phase -- Construction of flows -- Moving relative homology chains -- The main lemma -- Finiteness lemmas -- Sizes of cells -- Moving the cycle of integration -- Bounds on multiplicities -- Regularity of individual terms -- Complements and examples -- The Sturm-Liouville problem.
,
English
In:
Springer eBooks
Additional Edition:
ISBN 3-540-55009-7
Language:
English
URL:
http://dx.doi.org/10.1007/BFb0094551
