Abstract
The differential equation of a Duffing oscillator is presented which exhibits an interesting branching behaviour. Depending on the frequency of the excitation, there is a great variety of different types of solutions. Extensive numerical results are obtained by the means of classical numerical analysis.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
6. References
R. Bulirsch: Die Mehrzielmethode zur numerischen Lösung von nichtlinearen Randwertproblemen und Aufgaben der optimalen Steuerung. Report der Carl-Cranz-Gesellschaft (1971)
R. Bulirsch, W. Oettli, J. Stoer (ed.): Optimization and optimal control. Proceedings of a conference held at Oberwolfach, 1974. Lecture Notes, Vol. 477, Springer, Berlin-Heidelberg-New York (1975)
R. Bulirsch, J. Stoer: Numerical treatment of ordinary differential equations by extrapolation methods. Numer. Math. 8 (1966), 1–13
R. Bulirsch, J. Stoer, P. Deuflhard: Numerical solution of nonlinear two-point boundary value problems I. to appear in Numer. Math., Handbook Series Approximation
P. Deuflhard: A modified Newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting. Numer. Math. 22 (1974) 289–315
P. Deuflhard: A relaxation strategy for the modified Newton method. in [2]
E. Fehlberg: Klassische Runge-Kutta Formeln fünfter und siebenter Ordnung mit Schrittweitenkontrolle. Computing 4 (1969), 93–106
P. Holmes: A nonlinear oscillator with a strange attractor. Phil. Trans. Roy. Soc. London A. 292 (1979), 419–448
H.G. Hussels: Schrittweitensteuerung bei der Integration gewöhnlicher Differentialgleichungen mit Extrapolationsverfahren. Universität zu Köln, Mathem. Institut, Diplomarbeit (1973)
R. Seydel: Numerical computation of branch points in ordinary differential equations. Numer. Math. 32 (1979), 51–68
R. Seydel: Programme zur numerischen Behandlung von Verzweigungsproblemen bei nichtlinearen Gleichungen und Differentialgleichungen. ISNM 54 (1980), 163–175
R. Seydel: The strange attractors of a Duffing equation-dependence on the exciting frequency. Technische Universität München, Institut für Mathematik, Bericht M8019 (1980)
J. Stoer, R. Bulirsch: Introduction to numerical analysis. Springer, Berlin-Heidelberg-New York (1980)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1981 Springer-Verlag
About this paper
Cite this paper
Becker, K.H., Seydel, R. (1981). A duffing equation with more than 20 branch points. In: Allgower, E.L., Glashoff, K., Peitgen, HO. (eds) Numerical Solution of Nonlinear Equations. Lecture Notes in Mathematics, vol 878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090677
Download citation
DOI: https://doi.org/10.1007/BFb0090677
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-10871-9
Online ISBN: 978-3-540-38781-7
eBook Packages: Springer Book Archive