Skip to main content

Abstract

This paper is concerned in a class of bifurcation problems in ordinary differential equations. It is shown how some basic aspects of bifurcation can be handled by standard methods of numerical analysis. The procedure is illustrated by four examples.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
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

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. R. Bulirsch: Lecture on the Working Conference on Codes for Boundary Value Problems in ODE’s. May 14–17, 1978 in Houston. To be published in Springer Lecture Notes.

    Google Scholar 

  2. R. Bulirsch, J. Stoer, P. Deuflhard: Numerical Solution of Nonlinear Two-Point Boundary Value Problems I. To appear in Numer. Math., Handbook Series Approximation.

    Google Scholar 

  3. M.A. Krasnosel’skii: Topological Methods in the Theory of Nonlinear Integral Equations. New York: Pergamon Press 1964.

    Google Scholar 

  4. W.F. Langford: Numerical Solution of Bifurcation Problems for Ordinary Differential Equations. Numer. Math. 28, 171–190 (1977).

    Article  Google Scholar 

  5. W.E. Olmstead: Extent of the Left Branching Solution to Certain Bifurcation Problems. SIAM J. Math.Anal. 8, 392–401 (1977).

    Article  Google Scholar 

  6. G.H. Pimbley: Eigenfunction Branches of Nonlinear Operators, and their Bifurcations. Lecture Notes, Vol. 104. Berlin-Heidelberg-New York: Springer 1969.

    Book  Google Scholar 

  7. J. Scheurle: Ein selektives Projektions-Iterationsverfahren und Anwendungen auf Verzweigungsprobleme. Numer. Math. 29, 11–35 (1977).

    Article  Google Scholar 

  8. R. Seydel: Numerical Computation of Branch Points in Ordinary Differential Equations. Numer. Math. 31 or 32.

    Google Scholar 

  9. J. Stoer, R. Bulirsch: Einführung in die numerische Mathematik II. Heidelberger Taschenbuch, Band 114. Berlin-Heidelberg-New York: Springer 1973.

    Book  Google Scholar 

  10. H. Unger: Nichtlineare Behandlung von Eigenwertaufgaben. ZAMM 30, 281–282 (1950).

    Article  Google Scholar 

  11. M.M. Vainberg: Variational Methods for the Study of Nonlinear Operators. San Francisco-London-Amsterdam: Holden-Day 1964.

    Google Scholar 

  12. H. Wielandt: Das Iterationsverfahren bei nicht selbstadjungierten linearen Eigenwertaufgaben. Math. Zeitschrift 50, 93–143 (1944).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1979 Springer Basel AG

About this chapter

Cite this chapter

Seydel, R. (1979). Numerical Computation of Primary Bifurcation Points in Ordinary Differential Equations. In: Albrecht, J., Collatz, L., Kirchgässner, K. (eds) Constructive Methods for Nonlinear Boundary Value Problems and Nonlinear Oscillations. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Serie Internationale D’Analyse Numerique, vol 48. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6283-7_13

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-6283-7_13

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-7643-1098-1

  • Online ISBN: 978-3-0348-6283-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics