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 Creators	ORCiD
Vyasarayani, Chandrika Prakash	http://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:

04 Mar 2022 05:30

URI:

http://raiithold.iith.ac.in/id/eprint/1235