Perturbation Methods in Applied Mathematics

• J. Kevorkian
• J. D. Cole
Book

Part of the Applied Mathematical Sciences book series (AMS, volume 34)

1. Front Matter
Pages i-x
2. J. Kevorkian, J. D. Cole
Pages 1-16
3. J. Kevorkian, J. D. Cole
Pages 17-104
4. J. Kevorkian, J. D. Cole
Pages 105-329
5. J. Kevorkian, J. D. Cole
Pages 330-480
6. J. Kevorkian, J. D. Cole
Pages 481-545
7. Back Matter
Pages 546-559

Introduction

This book is a revised and updated version, including a substantial portion of new material, of J. D. Cole's text Perturbation Methods in Applied Mathe­ matics, Ginn-Blaisdell, 1968. We present the material at a level which 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. The applied mathematician, attempting to understand or solve a physical problem, very often uses a perturbation procedure. In doing this, he usually draws on a backlog of experience gained from the solution of similar examples rather than on some general theory of perturbations. The aim of this book is to survey these perturbation methods, especially in connection with differ­ ential equations, in order to illustrate certain general features common to many examples. The basic ideas, however, are also applicable to integral equations, integrodifferential equations, and even to_difference equations. In essence, a perturbation procedure consists of constructing the solution for a problem involving a small parameter B, either in the differential equation or the boundary conditions or both, when the solution for the limiting case B = 0 is known. The main mathematical tool used is asymptotic expansion with respect to a suitable asymptotic sequence of functions of B.

Keywords

Asymptotische Darstellung Differentialgleichung Perturbation Störung (Math.) differential equation ordinary differential equation partial differential equation

Authors and affiliations

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

Bibliographic information

• DOI https://doi.org/10.1007/978-1-4757-4213-8
• Copyright Information Springer-Verlag New York 1981
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4419-2812-2
• Online ISBN 978-1-4757-4213-8
• Series Print ISSN 0066-5452
• Buy this book on publisher's site