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Numerical Continuation Methods

An Introduction

  • Eugene L. Allgower
  • Kurt Georg

Part of the Springer Series in Computational Mathematics book series (SSCM, volume 13)

Table of contents

  1. Front Matter
    Pages I-XIV
  2. Eugene L. Allgower, Kurt Georg
    Pages 1-6
  3. Eugene L. Allgower, Kurt Georg
    Pages 7-16
  4. Eugene L. Allgower, Kurt Georg
    Pages 17-27
  5. Eugene L. Allgower, Kurt Georg
    Pages 28-36
  6. Eugene L. Allower, Kurt Georg
    Pages 37-43
  7. Eugene L. Allower, Kurt Georg
    Pages 44-60
  8. Eugene L. Allgower, Kurt Georg
    Pages 61-74
  9. Eugene L. Allower, Kurt Georg
    Pages 75-90
  10. Eugene L. Allower, Kurt Georg
    Pages 91-95
  11. Eugene L. Allower, Kurt Georg
    Pages 96-111
  12. Eugene L. Allower, Kurt Georg
    Pages 112-150
  13. Eugene L. Allower, Kurt Georg
    Pages 151-172
  14. Eugene L. Allgower, Kurt Georg
    Pages 173-202
  15. Eugene L. Allgower, Kurt Georg
    Pages 203-232
  16. Eugene L. Allower, Kurt Georg
    Pages 233-251
  17. Eugene L. Allower, Kurt Georg
    Pages 252-265
  18. Back Matter
    Pages 346-388

About this book

Introduction

Over the past fifteen years two new techniques have yielded extremely important contributions toward the numerical solution of nonlinear systems of equations. This book provides an introduction to and an up-to-date survey of numerical continuation methods (tracing of implicitly defined curves) of both predictor-corrector and piecewise-linear types. It presents and analyzes implementations aimed at applications to the computation of zero points, fixed points, nonlinear eigenvalue problems, bifurcation and turning points, and economic equilibria. Many algorithms are presented in a pseudo code format. An appendix supplies five sample FORTRAN programs with numerical examples, which readers can adapt to fit their purposes, and a description of the program package SCOUT for analyzing nonlinear problems via piecewise-linear methods. An extensive up-to-date bibliography spanning 46 pages is included. The material in this book has been presented to students of mathematics, engineering and sciences with great success, and will also serve as a valuable tool for researchers in the field.

Keywords

Algorithmus Approximation Numerical continuation Verzweigungspunkte bifurcation boundary element method complementary pivoting computation curve and surface approximation eigenvalue problem nichtlineare Differentialgleichung nonlinear systems nonlinear systems of equations numerische Kontinuitätsmethoden strategy

Authors and affiliations

  • Eugene L. Allgower
    • 1
  • Kurt Georg
    • 1
  1. 1.Department of MathematicsColorado State UniversityFort CollinsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-61257-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1990
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-64764-2
  • Online ISBN 978-3-642-61257-2
  • Series Print ISSN 0179-3632
  • Buy this book on publisher's site
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