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On the comparison of semi-analytical methods for the stability analysis of delay differential equations

Publication ,  Journal Article
Tweten, DJ; Lipp, GM; Khasawneh, FA; Mann, BP
Published in: Journal of Sound and Vibration
August 13, 2012

This paper provides the first comparison of the semi-discretization, spectral element, and Legendre collocation methods. Each method is a technique for solving delay differential equations (DDEs) as well as determining regions of stability in the DDE parameter space. We present the necessary concepts, assumptions, and equations required to implement each method. To compare the relative performance between the methods, the convergence rate and computational time for each method is compared in three numerical studies consisting of a ship stability example, the delayed damped Mathieu equation, and a helicopter rotor control problem. For each study, we present one or more stability diagrams in the parameter space and one or more convergence plots. The spectral element method is demonstrated to have the quickest convergence rate while the Legendre collocation method requires the least computational time. The semi-discretization method on the other hand has both the slowest convergence rate and requires the most computational time. © 2012 Elsevier Ltd.

Duke Scholars

Published In

Journal of Sound and Vibration

DOI

EISSN

1095-8568

ISSN

0022-460X

Publication Date

August 13, 2012

Volume

331

Issue

17

Start / End Page

4057 / 4071

Related Subject Headings

  • Acoustics
  • 51 Physical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
 

Citation

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ICMJE
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Tweten, D. J., Lipp, G. M., Khasawneh, F. A., & Mann, B. P. (2012). On the comparison of semi-analytical methods for the stability analysis of delay differential equations. Journal of Sound and Vibration, 331(17), 4057–4071. https://doi.org/10.1016/j.jsv.2012.04.009
Tweten, D. J., G. M. Lipp, F. A. Khasawneh, and B. P. Mann. “On the comparison of semi-analytical methods for the stability analysis of delay differential equations.” Journal of Sound and Vibration 331, no. 17 (August 13, 2012): 4057–71. https://doi.org/10.1016/j.jsv.2012.04.009.
Tweten DJ, Lipp GM, Khasawneh FA, Mann BP. On the comparison of semi-analytical methods for the stability analysis of delay differential equations. Journal of Sound and Vibration. 2012 Aug 13;331(17):4057–71.
Tweten, D. J., et al. “On the comparison of semi-analytical methods for the stability analysis of delay differential equations.” Journal of Sound and Vibration, vol. 331, no. 17, Aug. 2012, pp. 4057–71. Scopus, doi:10.1016/j.jsv.2012.04.009.
Tweten DJ, Lipp GM, Khasawneh FA, Mann BP. On the comparison of semi-analytical methods for the stability analysis of delay differential equations. Journal of Sound and Vibration. 2012 Aug 13;331(17):4057–4071.
Journal cover image

Published In

Journal of Sound and Vibration

DOI

EISSN

1095-8568

ISSN

0022-460X

Publication Date

August 13, 2012

Volume

331

Issue

17

Start / End Page

4057 / 4071

Related Subject Headings

  • Acoustics
  • 51 Physical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences