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A spectral element approach for the stability of delay systems

Publication ,  Journal Article
Khasawneh, FA; Mann, BP
Published in: International Journal for Numerical Methods in Engineering
August 12, 2011

We describe a spectral element approach to study the stability and equilibria solutions of Delay differential equations (DDEs). In contrast to the prototypical temporal finite element analysis (TFEA), the described spectral element approach admits spectral rates of convergence and allows exploiting hp-convergence schemes. The described approach also avoids the limitations of analytical integrations in TFEA by using highly accurate numerical quadratures-enabling the study of more complicated DDEs. The effectiveness of this new approach is compared with well-established methods in the literature using various case studies. Specifically, the stability results are compared with the conventional TFEA and Legendre collocation methods whereas the equilibria solutions are compared with the numerical simulations and the homotopy perturbation method (HPM) solutions. Our results reveal that the presented approach can have higher rates of convergence than both collocation methods and the HPM. Copyright © 2011 John Wiley & Sons, Ltd.

Duke Scholars

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

August 12, 2011

Volume

87

Issue

6

Start / End Page

566 / 592

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering
 

Citation

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ICMJE
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Khasawneh, F. A., & Mann, B. P. (2011). A spectral element approach for the stability of delay systems. International Journal for Numerical Methods in Engineering, 87(6), 566–592. https://doi.org/10.1002/nme.3122
Khasawneh, F. A., and B. P. Mann. “A spectral element approach for the stability of delay systems.” International Journal for Numerical Methods in Engineering 87, no. 6 (August 12, 2011): 566–92. https://doi.org/10.1002/nme.3122.
Khasawneh FA, Mann BP. A spectral element approach for the stability of delay systems. International Journal for Numerical Methods in Engineering. 2011 Aug 12;87(6):566–92.
Khasawneh, F. A., and B. P. Mann. “A spectral element approach for the stability of delay systems.” International Journal for Numerical Methods in Engineering, vol. 87, no. 6, Aug. 2011, pp. 566–92. Scopus, doi:10.1002/nme.3122.
Khasawneh FA, Mann BP. A spectral element approach for the stability of delay systems. International Journal for Numerical Methods in Engineering. 2011 Aug 12;87(6):566–592.
Journal cover image

Published In

International Journal for Numerical Methods in Engineering

DOI

EISSN

1097-0207

ISSN

0029-5981

Publication Date

August 12, 2011

Volume

87

Issue

6

Start / End Page

566 / 592

Related Subject Headings

  • Applied Mathematics
  • 40 Engineering
  • 09 Engineering