کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
1137181 | 1489152 | 2011 | 11 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: Stability of delay integro-differential equations using a spectral element method Stability of delay integro-differential equations using a spectral element method](/preview/png/1137181.png)
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.
Journal: Mathematical and Computer Modelling - Volume 54, Issues 9–10, November 2011, Pages 2493–2503