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Comparative study of semi-analytical methods for the stability analysis of delay differential equations

Publication ,  Journal Article
Tweten, DJ; Lipp, GM; Khasawneh, FA; Mann, BP
Published in: Proceedings of the ASME Design Engineering Technical Conference
December 1, 2011

This paper describes and compares the zeroth-order 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 achieved and computing time required by each method are determined in two numerical studies consisting of a ship stability example and the delayed damped Mathieu equation. For each study, we present a stability diagram in parameter space and a convergence plot. The spectral element method is demonstrated to have the quickest convergence rate while the Legendre collocation method requires the least computing time. The zeroth-order semi-discretization method on the other hand has both the slowest convergence rate and requires the most computing time. Copyright © 2011 by ASME.

Duke Scholars

Published In

Proceedings of the ASME Design Engineering Technical Conference

DOI

Publication Date

December 1, 2011

Volume

4

Issue

PARTS A AND B

Start / End Page

447 / 456
 

Citation

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Tweten, D. J., Lipp, G. M., Khasawneh, F. A., & Mann, B. P. (2011). Comparative study of semi-analytical methods for the stability analysis of delay differential equations. Proceedings of the ASME Design Engineering Technical Conference, 4(PARTS A AND B), 447–456. https://doi.org/10.1115/DETC2011-47519
Tweten, D. J., G. M. Lipp, F. A. Khasawneh, and B. P. Mann. “Comparative study of semi-analytical methods for the stability analysis of delay differential equations.” Proceedings of the ASME Design Engineering Technical Conference 4, no. PARTS A AND B (December 1, 2011): 447–56. https://doi.org/10.1115/DETC2011-47519.
Tweten DJ, Lipp GM, Khasawneh FA, Mann BP. Comparative study of semi-analytical methods for the stability analysis of delay differential equations. Proceedings of the ASME Design Engineering Technical Conference. 2011 Dec 1;4(PARTS A AND B):447–56.
Tweten, D. J., et al. “Comparative study of semi-analytical methods for the stability analysis of delay differential equations.” Proceedings of the ASME Design Engineering Technical Conference, vol. 4, no. PARTS A AND B, Dec. 2011, pp. 447–56. Scopus, doi:10.1115/DETC2011-47519.
Tweten DJ, Lipp GM, Khasawneh FA, Mann BP. Comparative study of semi-analytical methods for the stability analysis of delay differential equations. Proceedings of the ASME Design Engineering Technical Conference. 2011 Dec 1;4(PARTS A AND B):447–456.

Published In

Proceedings of the ASME Design Engineering Technical Conference

DOI

Publication Date

December 1, 2011

Volume

4

Issue

PARTS A AND B

Start / End Page

447 / 456