# Asymptotic Methods for Ordinary Differential Equations

Part of the Mathematics and Its Applications book series (MAIA, volume 512)

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Part of the Mathematics and Its Applications book series (MAIA, volume 512)

In this book we consider a Cauchy problem for a system of ordinary differential equations with a small parameter. The book is divided into th ree parts according to three ways of involving the small parameter in the system. In Part 1 we study the quasiregular Cauchy problem. Th at is, a problem with the singularity included in a bounded function j , which depends on time and a small parameter. This problem is a generalization of the regu larly perturbed Cauchy problem studied by Poincare [35]. Some differential equations which are solved by the averaging method can be reduced to a quasiregular Cauchy problem. As an example, in Chapter 2 we consider the van der Pol problem. In Part 2 we study the Tikhonov problem. This is, a Cauchy problem for a system of ordinary differential equations where the coefficients by the derivatives are integer degrees of a small parameter.

Cauchy problem differential equation ordinary differential equation

- DOI https://doi.org/10.1007/978-94-015-9347-2
- Copyright Information Springer Science+Business Media B.V. 2000
- Publisher Name Springer, Dordrecht
- eBook Packages Springer Book Archive
- Print ISBN 978-90-481-5500-2
- Online ISBN 978-94-015-9347-2
- Buy this book on publisher's site

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