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

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Khasawneh, FA; Mann, BP

Published Date

  • 2011

Published In

Volume / Issue

  • 54 / 9-10

Start / End Page

  • 2493 - 2503

International Standard Serial Number (ISSN)

  • 0895-7177

Digital Object Identifier (DOI)

  • 10.1016/j.mcm.2011.06.009