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• W2015773368 abstract "This paper provides the first comparison of the semi-discretization, spectral element, and Legendre collocation methods. Each method is a technique for solving delay differential equations (DDEs) as well as determining regions of stability in the DDE parameter space. We present the necessary concepts, assumptions, and equations required to implement each method. To compare the relative performance between the methods, the convergence rate and computational time for each method is compared in three numerical studies consisting of a ship stability example, the delayed damped Mathieu equation, and a helicopter rotor control problem. For each study, we present one or more stability diagrams in the parameter space and one or more convergence plots. The spectral element method is demonstrated to have the quickest convergence rate while the Legendre collocation method requires the least computational time. The semi-discretization method on the other hand has both the slowest convergence rate and requires the most computational time." @default.
• W2015773368 created "2016-06-24" @default.
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• W2015773368 date "2012-08-01" @default.
• W2015773368 modified "2023-09-27" @default.
• W2015773368 title "On the comparison of semi-analytical methods for the stability analysis of delay differential equations" @default.
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• W2015773368 doi "https://doi.org/10.1016/j.jsv.2012.04.009" @default.
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