Homotopy Continuation for Characteristic Roots of Delay Differential Equation

Samukham, S (2015) Homotopy Continuation for Characteristic Roots of Delay Differential Equation. Masters thesis, Indian Institute of Technology Hyderabad.

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In this thesis we develop a homotopy continuation method to find the characteristic roots of scalar delay differential equations with multiple delays. We introduce a homotopy parameter µ € [0;1] in such a way that for µ - 0, the characteristic equation contains only one delay term and for µ - 1 the original characteristic equation is recovered. By selecting µ - 0 allows us to express all the roots of the characteristic equation in closed form in terms of Lambert W function. A numerical continuation based scheme is then developed to trace the roots as µ is varied from 0 to 1. The roots of the characteristic equation for µ - 1 correspond to the characteristic roots of the delay differential equation. We show several numerical examples to demonstrate the developed method.

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IITH Creators:
IITH CreatorsORCiD
Item Type: Thesis (Masters)
Uncontrolled Keywords: Homotopy, Pseudo- Arc length, Characteristic roots; TD360
Subjects: Others > Mechanics
Divisions: Department of Physics
Depositing User: Library Staff
Date Deposited: 06 Jul 2015 05:53
Last Modified: 14 May 2019 10:57
URI: http://raiith.iith.ac.in/id/eprint/1652
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