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

Anwar, Sadath and Vyasarayani, C P (2015) Galerkin approximations for stability of delay differential equations with time periodic delays. Journal of Computational and Nonlinear Dynamics, 10 (6). pp. 1-7. ISSN 1555-1415

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Abstract

n this paper, we develop Galerkin approximations for determining the stability of delay differential equations (DDEs) with time periodic coefficients and time periodic delays. Using a transformation, we convert the DDE into a partial differential equation (PDE) along with a boundary condition (BC). The PDE and BC we obtain have time periodic coefficients. The PDE is discretized into a system of ordinary differential equations (ODEs) using the Galerkin method with Legendre polynomials as the basis functions. The boundary condition is imposed using the tau method. The resulting ODEs are time periodic in nature; thus, we resort to Floquet theory to determine the stability of the ODEs. We show through several numerical examples that the stability charts obtained from the Galerkin method agree closely with those obtained from direct numerical simulations.

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IITH Creators:

IITH Creators	ORCiD
Vyasarayani, Chandrika Prakash	http://orcid.org/0000-0002-3396-0484

Item Type:

Article

Uncontrolled Keywords:

Stability , Differential equations , Approximation , Delays , Galerkin method , Boundary-value problems , Computer simulation , Partial differential equations , Polynomials

Subjects:

Physics > Mechanical and aerospace

Divisions:

Department of Mechanical & Aerospace Engineering

Depositing User:

Team Library

Date Deposited:

23 Dec 2014 11:44

Last Modified:

04 Mar 2022 05:31

URI:

http://raiithold.iith.ac.in/id/eprint/1236