Galerkin approximations for retarded delay differential equations with state-dependent delays

Vyasarayani, C P and Gupta, A and McPhee, J (2013) Galerkin approximations for retarded delay differential equations with state-dependent delays. Journal of Dynamic Systems, Measurement, and Control, 135 (6). pp. 1-6. ISSN 0022-0434

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Abstract

In this work, approximations for state dependent delay differential equations (DDEs) are developed using Galerkin's approach. The DDE is converted into an equivalent partial differential equation (PDE) with a moving boundary, where the length of the domain dependents on the solution of the PDE. The PDE is further reduced into a finite number of ordinary differential equations (ODEs) using Galerkin's approach with time dependent basis functions. The nonlinear boundary condition is represented by a Lagrange multiplier, whose expression is derived in closed form. We also demonstrate the validity of the developed method by comparing the numerical solution of the ODEs to that of the original DDE.

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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 thank Professor Sue Campbell of the applied mathematics department at the University of Waterloo for helpful suggestions.

Uncontrolled Keywords:

Delay differential equations; Galerkin approximations; Moving boundaries; Non-linear boundary conditions; Numerical solution; Partial differential equations (PDE); State-dependent delay; Time-dependent basis functions

Subjects:

Physics > Mechanical and aerospace

Divisions:

Department of Mechanical & Aerospace Engineering

Depositing User:

Team Library

Date Deposited:

18 Nov 2014 03:39

Last Modified:

04 Mar 2022 05:38

URI:

http://raiithold.iith.ac.in/id/eprint/838