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Continuation Techniques and Bifurcation Problems

  • Book
  • © 1990

Overview

Editors:
  1. Hans D. Mittelmann

    1. Department of Mathematics, Arizona State University, Tempe, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Dirk Roose

    1. Department Computerwetenschappen, Katholieke Universiteit Leuven, Leuven, Belgium

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: International Series of Numerical Mathematics (ISNM, volume 92)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-2
    Download chapter PDF

  2. Large sparse continuation problems

    • E. L. Allgower, C.-S. Chien, K. Georg
    Pages 3-21

  3. Continuation for parametrized nonlinear variational inequalities

    • Erich Miersemann, Hans D. Mittelmann
    Pages 23-34

  4. A multi-grid continuation strategy for parameter-dependent variational inequalities

    • Ronald H. W. Hoppe, Hans D. Mittelmann
    Pages 35-46

  5. Continuation methods in semiconductor device simulation

    • W. M. Coughran Jr., M. R. Pinto, R. K. Smith
    Pages 47-65

  6. Stepsize selection in continuation procedures and damped Newton’s method

    • Randolph E. Bank, Hans D. Mittelmann
    Pages 67-77

  7. Symmetry breaking and semilinear elliptic equations

    • Chris Budd
    Pages 79-96

  8. Computational methods for bifurcation problems with symmetries—with special attention to steady state and Hopf bifurcation points

    • Michael Dellnitz, Bodo Werner
    Pages 97-123

  9. A note on the calculation of paths of Hopf bifurcations

    • A. Spence, K. A. Cliffe, A. D. Jepson
    Pages 125-131

  10. Computation of cusp singularities for operator equations and their discretizations

    • Andreas Griewank, George W. Reddien
    Pages 133-153

  11. Numerical computation of heteroclinic orbits

    • Eusebius J. Doedel, Mark J. Friedman
    Pages 155-170

  12. Interaction between fold and Hopf curves leads to new bifurcation phenomena

    • Bart De Dier, Dirk Roose, Paul Van Rompay
    Pages 171-186

  13. Bi-periodicity in an isothermal autocatalytic reaction-diffusion system

    • Christian Kaas-Petersen
    Pages 187-198

  14. Generic one-parameter bifurcations in the motion of a simple robot

    • E. Lindtner, A. Steindl, H. Troger
    Pages 199-218
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Keywords

About this book

The analysis of parameter-dependent nonlinear has received much attention in recent years. Numerical continuation techniques allow the efficient computation of solution branches in a one-parameter problem. In many cases continuation procedures are used as part of a more complete analysis of a nonlinear problem, based on bifurcation theory and singularity theory. These theories contribute to the understanding of many nonlinear phenomena in nature and they form the basis for various analytical and numerical tools, which provide qualitative and quantitative results about nonlinear systems. In this issue we have collected a number of papers dealing with continuation techniques and bifurcation problems. Readers familiar with the notions of continuation and bifurcation will find recent research results addressing a variety of aspects in this issue. Those who intend to learn about the field or a specific topic in it may find it useful to first consult earlier literature on the numerical treatment of these problems together with some theoretical background. The papers in this issue fall naturally into different groups.

Editors and Affiliations

  • Department of Mathematics, Arizona State University, Tempe, USA

    Hans D. Mittelmann

  • Department Computerwetenschappen, Katholieke Universiteit Leuven, Leuven, Belgium

    Dirk Roose

Bibliographic Information

  • Book Title: Continuation Techniques and Bifurcation Problems

  • Editors: Hans D. Mittelmann, Dirk Roose

  • Series Title: International Series of Numerical Mathematics

  • DOI: https://doi.org/10.1007/978-3-0348-5681-2

  • Publisher: Birkhäuser Basel

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Basel AG 1990

  • Softcover ISBN: 978-3-7643-2397-4Published: 01 January 1990

  • eBook ISBN: 978-3-0348-5681-2Published: 21 November 2013

  • Series ISSN: 0373-3149

  • Series E-ISSN: 2296-6072

  • Edition Number: 1

  • Number of Pages: V, 218

  • Number of Illustrations: 10 b/w illustrations

  • Topics: Science, Humanities and Social Sciences, multidisciplinary

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