Perturbation Methods, Bifurcation Theory and Computer Algebra

  • Richard H. Rand
  • Dieter Armbruster

Part of the Applied Mathematical Sciences book series (AMS, volume 65)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Richard H. Rand, Dieter Armbruster
    Pages 1-26
  3. Richard H. Rand, Dieter Armbruster
    Pages 27-49
  4. Richard H. Rand, Dieter Armbruster
    Pages 50-88
  5. Richard H. Rand, Dieter Armbruster
    Pages 89-106
  6. Richard H. Rand, Dieter Armbruster
    Pages 107-131
  7. Richard H. Rand, Dieter Armbruster
    Pages 132-154
  8. Richard H. Rand, Dieter Armbruster
    Pages 155-214
  9. Back Matter
    Pages 215-244

About this book


Perturbation methods have always been an important tool for treating nonlinear differential equations. Now the drudgery associated with them has been eliminated! This book offers computer algebra (MACSYMA) programs which implement the most popular perturbation methods. Not only does this avoid the errors associated with hand computation, but the increase in efficiency permits more complicated problems to be tackled. This book is useful both for the beginner learning perturbation methods for the first time, as well as for the researcher. Methods covered include: Lindstedt's method, center manifolds, normal forms, two variable expansion method (method of multiple scales), averaging, Lie transforms and Liapunov-Schmidt reduction. For each method the book includes an introduction and some example problems solved both by hand and by machine. The examples feature common bifurcations such as the pitchfork and the Hopf. The MACSYMA code for each method is given and suggested exercises are provided at the end of each Chapter. An Appendix offers a brief introduction to MACSYMA.


Algebra bifurcation computer algebra differential equation manifold nonlinear differential equation transform theory

Authors and affiliations

  • Richard H. Rand
    • 1
  • Dieter Armbruster
    • 2
  1. 1.Department of Theoretical & Applied MechanicsCornell UniversityIthacaUSA
  2. 2.Institut für Informations-verarbeitungUniversität Tübingen74 Tübingen 1Germany

Bibliographic information

  • DOI
  • Copyright Information Springer-Verlag New York, Inc. 1987
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-0-387-96589-5
  • Online ISBN 978-1-4612-1060-3
  • Series Print ISSN 0066-5452
  • Buy this book on publisher's site