Galerkin approximations for stability of delay differential equations with time periodic coefficients

Anwar Sadath, K T and Vyasarayani, C P (2015) Galerkin approximations for stability of delay differential equations with time periodic coefficients. Journal of Computational and Nonlinear Dynamics, 10 (2). pp. 1-14. ISSN 1555-1415

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Abstract

A numerical method to determine the stability of delay differential equations (DDEs) with time periodic coefficients is proposed. The DDE is converted into an equivalent partial differential equation (PDE) with a time periodic boundary condition (BC). The PDE, along with its BC, is then converted into a system of ordinary differential equations (ODEs) with time periodic coefficients using the Galerkin least squares approach. In the Galerkin approach, shifted Legendre polynomials are used as basis functions, allowing us to obtain explicit expressions for the approximate system of ODEs. We analyze the stability of the discretized ODEs, which represent an approximate model of the DDEs, using Floquet theory. We use numerical examples to show that the stability charts obtained with our method are in excellent agreement with those existing in the literature and those obtained from direct numerical simulation.

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IITH Creators:
IITH CreatorsORCiD
Vyasarayani, C Phttp://orcid.org/0000-0002-3396-0484
Item Type: Article
Additional Information: We are indebted to the anonymous reviewers for their extremely useful and insightful suggestions on this work, which has helped us to improve the quality of this paper significantly. We also thank Dr. Tamas Kalmar-Nagy for his help on this work
Subjects: Physics > Mechanical and aerospace
Divisions: Department of Mechanical & Aerospace Engineering
Depositing User: Team Library
Date Deposited: 23 Dec 2014 11:37
Last Modified: 11 Aug 2017 06:50
URI: http://raiith.iith.ac.in/id/eprint/1235
Publisher URL: https://doi.org/10.1115/1.4026989
OA policy: http://www.sherpa.ac.uk/romeo/issn/1555-1415/
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