# Multiple Scale and Singular Perturbation Methods

• J. Kevorkian
• J. D. Cole
Book

Part of the Applied Mathematical Sciences book series (AMS, volume 114)

1. Front Matter
Pages i-viii
2. J. Kevorkian, J. D. Cole
Pages 1-35
3. J. Kevorkian, J. D. Cole
Pages 36-117
4. J. Kevorkian, J. D. Cole
Pages 118-266
5. J. Kevorkian, J. D. Cole
Pages 267-409
6. J. Kevorkian, J. D. Cole
Pages 410-521
7. J. Kevorkian, J. D. Cole
Pages 522-620
8. Back Matter
Pages 621-633

### Introduction

This book is a revised and updated version, including a substantial portion of new material, of our text Perturbation Methods in Applied Mathematics (Springer­ Verlag, 1981). We present the material at a level that assumes some familiarity with the basics of ordinary and partial differential equations. Some of the more advanced ideas are reviewed as needed; therefore this book can serve as a text in either an advanced undergraduate course or a graduate-level course on the subject. Perturbation methods, first used by astronomers to predict the effects of small disturbances on the nominal motions of celestial bodies, have now become widely used analytical tools in virtually all branches of science. A problem lends itself to perturbation analysis if it is "close" to a simpler problem that can be solved exactly. Typically, this closeness is measured by the occurrence of a small dimensionless parameter, E, in the governing system (consisting of differential equations and boundary conditions) so that for E = 0 the resulting system is exactly solvable. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of E. In a regular perturbation problem, a straightforward procedure leads to a system of differential equations and boundary conditions for each term in the asymptotic expansion. This system can be solved recursively, and the accuracy of the result improves as E gets smaller, for all values of the independent variables throughout the domain of interest. We discuss regular perturbation problems in the first chapter.

### Keywords

Layer differential equation mathematics model partial differential equation transformation

#### Authors and affiliations

• J. Kevorkian
• 1
• J. D. Cole
• 2
1. 1.Department of Applied MathematicsUniversity of WashingtonSeattleUSA
2. 2.Department of Mathematical SciencesRensselaer Polytechnic InstituteTroyUSA

### Bibliographic information

• DOI https://doi.org/10.1007/978-1-4612-3968-0
• Copyright Information Springer-Verlag New York 1996
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4612-8452-9
• Online ISBN 978-1-4612-3968-0
• Series Print ISSN 0066-5452
• Buy this book on publisher's site
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