Mathematical Modeling and Stability Analysis of Delay Differential Equations

Ahsan, Zaid (2015) Mathematical Modeling and Stability Analysis of Delay Differential Equations. Masters thesis, Indian Institute of Technology Hyderabad.

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Abstract

Finite-dimensional approximations are developed for retarded delay differential equations (DDEs). The DDE system is equivalently posed as an initial–boundary value problem consisting of hyperbolic partial differential equations (PDEs). By exploting the equivalence of partial derivatives in space and time, we develop a new PDE representation for the DDEs that is devoid of boundary conditions. The resulting boundary condition–free PDEs are discretized using the Galerkin method with Legendre polynomials as the basis functions, whereupon we obtain a system of ordinary differential equations (ODEs) that is a finite-dimensional approximation of the original DDE system.

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IITH Creators:
IITH CreatorsORCiD
Item Type: Thesis (Masters)
Uncontrolled Keywords: partial differential equations, ordinary differential equations, Dynamics, Control, Stability, TD420
Subjects: Others > Mechanics
Divisions: Department of Physics
Depositing User: Library Staff
Date Deposited: 31 Jul 2015 09:03
Last Modified: 06 Jun 2017 10:20
URI: http://raiith.iith.ac.in/id/eprint/1741
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