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A multi-interval Chebyshev collocation approach for the stability of periodic delay systems with discontinuities

Publication ,  Journal Article
Khasawneh, FA; Mann, BP; Butcher, EA
Published in: Communications in Nonlinear Science and Numerical Simulation
November 1, 2011

This paper investigates the stability of periodic delay systems with non-smooth coefficients using a multi-interval Chebyshev collocation approach (MIC). In this approach, each piecewise continuous interval is expanded in a Chebyshev basis of the first order. The boundaries of these intervals are placed at the points of discontinuity to recover the fast convergence properties of spectral methods. Stability is examined for a set of case studies that contain the complexities of periodic coefficients, delays and discontinuities. The new approach is also compared to the conventional Chebyshev collocation method. © 2011 Elsevier B.V.

Duke Scholars

Published In

Communications in Nonlinear Science and Numerical Simulation

DOI

ISSN

1007-5704

Publication Date

November 1, 2011

Volume

16

Issue

11

Start / End Page

4408 / 4421

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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ICMJE
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Khasawneh, F. A., Mann, B. P., & Butcher, E. A. (2011). A multi-interval Chebyshev collocation approach for the stability of periodic delay systems with discontinuities. Communications in Nonlinear Science and Numerical Simulation, 16(11), 4408–4421. https://doi.org/10.1016/j.cnsns.2011.03.025
Khasawneh, F. A., B. P. Mann, and E. A. Butcher. “A multi-interval Chebyshev collocation approach for the stability of periodic delay systems with discontinuities.” Communications in Nonlinear Science and Numerical Simulation 16, no. 11 (November 1, 2011): 4408–21. https://doi.org/10.1016/j.cnsns.2011.03.025.
Khasawneh FA, Mann BP, Butcher EA. A multi-interval Chebyshev collocation approach for the stability of periodic delay systems with discontinuities. Communications in Nonlinear Science and Numerical Simulation. 2011 Nov 1;16(11):4408–21.
Khasawneh, F. A., et al. “A multi-interval Chebyshev collocation approach for the stability of periodic delay systems with discontinuities.” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 11, Nov. 2011, pp. 4408–21. Scopus, doi:10.1016/j.cnsns.2011.03.025.
Khasawneh FA, Mann BP, Butcher EA. A multi-interval Chebyshev collocation approach for the stability of periodic delay systems with discontinuities. Communications in Nonlinear Science and Numerical Simulation. 2011 Nov 1;16(11):4408–4421.
Journal cover image

Published In

Communications in Nonlinear Science and Numerical Simulation

DOI

ISSN

1007-5704

Publication Date

November 1, 2011

Volume

16

Issue

11

Start / End Page

4408 / 4421

Related Subject Headings

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