Skip to main content
SpringerLink
Log in
Book cover

Numerical Continuation Methods

An Introduction

  • Book
  • © 1990

Overview

Authors:
  1. Eugene L. Allgower

    1. Department of Mathematics, Colorado State University, Fort Collins, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

  2. Kurt Georg

    1. Department of Mathematics, Colorado State University, Fort Collins, USA

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (16 chapters)

  1. Front Matter

    Pages I-XIV
    Download chapter PDF

  2. Introduction

    • Eugene L. Allgower, Kurt Georg
    Pages 1-6

  3. The Basic Principles of Continuation Methods

    • Eugene L. Allgower, Kurt Georg
    Pages 7-16

  4. Newton’s Method as Corrector

    • Eugene L. Allgower, Kurt Georg
    Pages 17-27

  5. Solving the Linear Systems

    • Eugene L. Allgower, Kurt Georg
    Pages 28-36

  6. Convergence of Euler-Newton-Like Methods

    • Eugene L. Allower, Kurt Georg
    Pages 37-43

  7. Steplength Adaptations for the Predictor

    • Eugene L. Allower, Kurt Georg
    Pages 44-60

  8. Predictor-Corrector Methods Using Updating

    • Eugene L. Allgower, Kurt Georg
    Pages 61-74

  9. Detection of Bifurcation Points Along a Curve

    • Eugene L. Allower, Kurt Georg
    Pages 75-90

  10. Calculating Special Points of the Solution Curve

    • Eugene L. Allower, Kurt Georg
    Pages 91-95

  11. Large Scale Problems

    • Eugene L. Allower, Kurt Georg
    Pages 96-111

  12. Numerically Implementable Existence Proofs

    • Eugene L. Allower, Kurt Georg
    Pages 112-150

  13. PL Continuation Methods

    • Eugene L. Allower, Kurt Georg
    Pages 151-172

  14. PL Homotopy Algorithms

    • Eugene L. Allgower, Kurt Georg
    Pages 173-202

  15. General PL Algorithms on PL Manifolds

    • Eugene L. Allgower, Kurt Georg
    Pages 203-232

  16. Approximating Implicitly Defined Manifolds

    • Eugene L. Allower, Kurt Georg
    Pages 233-251

  17. Update Methods and their Numerical Stability

    • Eugene L. Allower, Kurt Georg
    Pages 252-265

  18. Back Matter

    Pages 346-388
    Download chapter PDF
Back to top

Keywords

About this book

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.

Authors and Affiliations

  • Department of Mathematics, Colorado State University, Fort Collins, USA

    Eugene L. Allgower, Kurt Georg

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation