, Volume 55, Issue 2, pp 163–180 | Cite as

On the stability of numerical methods of Hopf points using backward error analysis

  • G. W. Reddien


Backward error analysis is used to analyze the behavior of selected one-step and multi-step methods for ordinary differential equations at weakly attracting fixed points and weakly attracting periodic solutions. For many methods, a Hopf bifurcation for maps occurs. The effect of an adaptive mesh selection procedure on these results is presented for a special case.

AMS Subject Classification


Key words

Hopf bifurcation Runge-Kutta Poincare map 

Stabilitätsuntersuchung numerischer Methoden an Hopf-Verzweigungspunkten mittels Rückwärtsanalyse des Fehlers


Um das Verhalten bestimmter Ein- und Mehrschrittverfahren für gewöhnliche Differentialgleichungen an schwach anziehenden Fixpunkten bzw. schwach anziehenden periodischen Lösungen zu untersuchen, wird Rückwärts-Fehleranalyse eingesetzt. Bei vielen Methoden tritt eine Hopf-Verzweigung auf; der Effekt einer adaptiven Gitteranpassung für solche Situationen wird an einem Spezialfall demonstriert.


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Copyright information

© Springer-Verlag 1995

Authors and Affiliations

  • G. W. Reddien
    • 1
  1. 1.Mathematics DepartmentSouthern Methodist UniversityDallasUSA

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