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A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays

Publication ,  Journal Article
Khasawneh, FA; Mann, BP
Published in: Communications in Nonlinear Science and Numerical Simulation
August 1, 2013

This paper describes a general spectral element approach to study the stability of multiple time delay systems (MTDS). We show, for the first time, how this approach can be applied to periodic MTDS where the delays and the period are incommensurate. In contrast to prior works on MTDS, the spectral element approach is applicable to both autonomous as well as non-autonomous MTDS. Both MTDS of first order or higher can be obtained and systems with or without damping can be investigated. Since the spectral element approach uses efficient interpolation and a set of well-distributed interpolation points, the size of the matrices necessary for convergence is kept small. Further, since the spectral element approach is a semi-analytical procedure, it avoids the need to use tedious time marching algorithms to explore the stability behavior of the system. © 2012 Elsevier B.V.

Duke Scholars

Published In

Communications in Nonlinear Science and Numerical Simulation

DOI

ISSN

1007-5704

Publication Date

August 1, 2013

Volume

18

Issue

8

Start / End Page

2129 / 2141

Related Subject Headings

  • Mathematical Physics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Khasawneh, F. A., & Mann, B. P. (2013). A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays. Communications in Nonlinear Science and Numerical Simulation, 18(8), 2129–2141. https://doi.org/10.1016/j.cnsns.2012.11.030
Khasawneh, F. A., and B. P. Mann. “A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays.” Communications in Nonlinear Science and Numerical Simulation 18, no. 8 (August 1, 2013): 2129–41. https://doi.org/10.1016/j.cnsns.2012.11.030.
Khasawneh FA, Mann BP. A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays. Communications in Nonlinear Science and Numerical Simulation. 2013 Aug 1;18(8):2129–41.
Khasawneh, F. A., and B. P. Mann. “A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays.” Communications in Nonlinear Science and Numerical Simulation, vol. 18, no. 8, Aug. 2013, pp. 2129–41. Scopus, doi:10.1016/j.cnsns.2012.11.030.
Khasawneh FA, Mann BP. A spectral element approach for the stability analysis of time-periodic delay equations with multiple delays. Communications in Nonlinear Science and Numerical Simulation. 2013 Aug 1;18(8):2129–2141.
Journal cover image

Published In

Communications in Nonlinear Science and Numerical Simulation

DOI

ISSN

1007-5704

Publication Date

August 1, 2013

Volume

18

Issue

8

Start / End Page

2129 / 2141

Related Subject Headings

  • Mathematical Physics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics