A Note on the Solutions of the Van der Pol and Duffing Equations Using a Linearisation Method
Joint Authors
Sibanda, Precious
Motsa, Sandile Sydney
Source
Mathematical Problems in Engineering
Issue
Vol. 2012, Issue 2012 (31 Dec. 2012), pp.1-10, 10 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2012-09-27
Country of Publication
Egypt
No. of Pages
10
Main Subjects
Abstract EN
We present a novel application of the successive linearisation method to the classical Van der Pol and Duffing oscillator equations.
By recasting the governing equations as nonlinear eigenvalue problems we obtain accurate values of the frequency and amplitude.
We demonstrate that the proposed method can be used to obtain the limit cycle and bifurcation diagrams of the governing equations.
Comparison with exact and other results in the literature shows that the method is accurate and effective in finding solutions of nonlinear equations with oscillatory solutions, nonlinear eigenvalue problems, and other nonlinear problems with bifurcations.
American Psychological Association (APA)
Motsa, Sandile Sydney& Sibanda, Precious. 2012. A Note on the Solutions of the Van der Pol and Duffing Equations Using a Linearisation Method. Mathematical Problems in Engineering،Vol. 2012, no. 2012, pp.1-10.
https://search.emarefa.net/detail/BIM-1001833
Modern Language Association (MLA)
Motsa, Sandile Sydney& Sibanda, Precious. A Note on the Solutions of the Van der Pol and Duffing Equations Using a Linearisation Method. Mathematical Problems in Engineering No. 2012 (2012), pp.1-10.
https://search.emarefa.net/detail/BIM-1001833
American Medical Association (AMA)
Motsa, Sandile Sydney& Sibanda, Precious. A Note on the Solutions of the Van der Pol and Duffing Equations Using a Linearisation Method. Mathematical Problems in Engineering. 2012. Vol. 2012, no. 2012, pp.1-10.
https://search.emarefa.net/detail/BIM-1001833
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1001833