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Periodic solutions of nonlinear delay differential equations using spectral element method

Publication ,  Journal Article
Khasawneh, FA; Barton, DAW; Mann, BP
Published in: Nonlinear Dynamics
January 1, 2012

We extend the temporal spectral element method further to study the periodic orbits of general autonomous nonlinear delay differential equations (DDEs) with one constant delay. Although we describe the approach for one delay to keep the presentation clear, the extension to multiple delays is straightforward. We also show the underlying similarities between this method and the method of collocation. The spectral element method that we present here can be used to find both the periodic orbit and its stability. This is demonstrated with a variety of different examples, namely, the delayed versions of Mackey-Glass equation, Van der Pol equation, and Duffing equation. For each example, we show the method's convergence behavior using both p and h refinement and we provide comparisons between equal size meshes that have different distributions. © 2011 Springer Science+Business Media B.V.

Duke Scholars

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

January 1, 2012

Volume

67

Issue

1

Start / End Page

641 / 658

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences
 

Citation

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Khasawneh, F. A., Barton, D. A. W., & Mann, B. P. (2012). Periodic solutions of nonlinear delay differential equations using spectral element method. Nonlinear Dynamics, 67(1), 641–658. https://doi.org/10.1007/s11071-011-0017-3
Khasawneh, F. A., D. A. W. Barton, and B. P. Mann. “Periodic solutions of nonlinear delay differential equations using spectral element method.” Nonlinear Dynamics 67, no. 1 (January 1, 2012): 641–58. https://doi.org/10.1007/s11071-011-0017-3.
Khasawneh FA, Barton DAW, Mann BP. Periodic solutions of nonlinear delay differential equations using spectral element method. Nonlinear Dynamics. 2012 Jan 1;67(1):641–58.
Khasawneh, F. A., et al. “Periodic solutions of nonlinear delay differential equations using spectral element method.” Nonlinear Dynamics, vol. 67, no. 1, Jan. 2012, pp. 641–58. Scopus, doi:10.1007/s11071-011-0017-3.
Khasawneh FA, Barton DAW, Mann BP. Periodic solutions of nonlinear delay differential equations using spectral element method. Nonlinear Dynamics. 2012 Jan 1;67(1):641–658.
Journal cover image

Published In

Nonlinear Dynamics

DOI

ISSN

0924-090X

Publication Date

January 1, 2012

Volume

67

Issue

1

Start / End Page

641 / 658

Related Subject Headings

  • Acoustics
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 01 Mathematical Sciences