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Stability of delay integro-differential equations using a spectral element method

Publication ,  Journal Article
Khasawneh, FA; Mann, BP
Published in: Mathematical and Computer Modelling
November 1, 2011

This paper describes a spectral element approach for studying the stability of delay integro-differential equations (DIDEs). In contrast to delay differential equations (DDEs) with discrete delays that act point-wise, the delays in DIDEs are distributed over a period of time through an integral term. Although both types of delays lead to an infinite dimensional state-space, the analysis of DDEs with distributed delays is far more involved. Nevertheless, the approach that we describe here is applicable to both autonomous and non-autonomous DIDEs with smooth bounded kernel functions. We also describe the stability analysis of DIDEs with special kernels (gamma-type kernel functions) via converting the DIDE into a higher order DDE with only discrete delays. This case of DIDEs is of practical importance, e.g., in modeling wheel shimmy phenomenon. A set of case studies are then provided to show the effectiveness of the proposed approach. © 2011 Elsevier Ltd.

Duke Scholars

Published In

Mathematical and Computer Modelling

DOI

ISSN

0895-7177

Publication Date

November 1, 2011

Volume

54

Issue

9-10

Start / End Page

2493 / 2503

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 4613 Theory of computation
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics
 

Citation

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Khasawneh, F. A., & Mann, B. P. (2011). Stability of delay integro-differential equations using a spectral element method. Mathematical and Computer Modelling, 54(9–10), 2493–2503. https://doi.org/10.1016/j.mcm.2011.06.009
Khasawneh, F. A., and B. P. Mann. “Stability of delay integro-differential equations using a spectral element method.” Mathematical and Computer Modelling 54, no. 9–10 (November 1, 2011): 2493–2503. https://doi.org/10.1016/j.mcm.2011.06.009.
Khasawneh FA, Mann BP. Stability of delay integro-differential equations using a spectral element method. Mathematical and Computer Modelling. 2011 Nov 1;54(9–10):2493–503.
Khasawneh, F. A., and B. P. Mann. “Stability of delay integro-differential equations using a spectral element method.” Mathematical and Computer Modelling, vol. 54, no. 9–10, Nov. 2011, pp. 2493–503. Scopus, doi:10.1016/j.mcm.2011.06.009.
Khasawneh FA, Mann BP. Stability of delay integro-differential equations using a spectral element method. Mathematical and Computer Modelling. 2011 Nov 1;54(9–10):2493–2503.
Journal cover image

Published In

Mathematical and Computer Modelling

DOI

ISSN

0895-7177

Publication Date

November 1, 2011

Volume

54

Issue

9-10

Start / End Page

2493 / 2503

Related Subject Headings

  • Numerical & Computational Mathematics
  • 4903 Numerical and computational mathematics
  • 4901 Applied mathematics
  • 4613 Theory of computation
  • 0802 Computation Theory and Mathematics
  • 0103 Numerical and Computational Mathematics
  • 0102 Applied Mathematics