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• W2026087060 abstract "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." @default.
• W2026087060 created "2016-06-24" @default.
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• W2026087060 date "2011-11-01" @default.
• W2026087060 modified "2023-10-14" @default.
• W2026087060 title "Stability of delay integro-differential equations using a spectral element method" @default.
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• W2026087060 doi "https://doi.org/10.1016/j.mcm.2011.06.009" @default.
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