Extension of the spectral element method for stability analysis of time-periodic delay-differential equations with multiple and distributed delays

David Lehotzky, T. Insperger, G. Stépán

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

The spectral element method was introduced by Khasawneh and Mann (2013) for the stability analysis of time-periodic delay-differential equations (DDEs) with multiple delays. In this paper, this method is generalized for time-periodic DDEs with multiple delays and distributed delay. For this general case, an explicit formula is given for the construction of the matrix approximation of the monodromy operator. The derived formula enables the algorithmic application of the method to DDEs with general combinations of delays for arbitrary point sets and test functions. Stability analysis is demonstrated for specific case studies, and the computation code is provided for a complex example.

Original languageEnglish
Pages (from-to)177-189
Number of pages13
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume35
DOIs
Publication statusPublished - Jun 1 2016

Fingerprint

Spectral Element Method
Multiple Delays
Distributed Delay
Delay Differential Equations
Stability Analysis
Differential equations
Matrix Approximation
Monodromy
Test function
Point Sets
Explicit Formula
Arbitrary
Operator

Keywords

  • Spectral element
  • Stability
  • Time-delay system
  • Time-periodic system

ASJC Scopus subject areas

  • Modelling and Simulation
  • Numerical Analysis
  • Applied Mathematics

Cite this

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AU - Insperger, T.

AU - Stépán, G.

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Y1 - 2016/6/1

N2 - The spectral element method was introduced by Khasawneh and Mann (2013) for the stability analysis of time-periodic delay-differential equations (DDEs) with multiple delays. In this paper, this method is generalized for time-periodic DDEs with multiple delays and distributed delay. For this general case, an explicit formula is given for the construction of the matrix approximation of the monodromy operator. The derived formula enables the algorithmic application of the method to DDEs with general combinations of delays for arbitrary point sets and test functions. Stability analysis is demonstrated for specific case studies, and the computation code is provided for a complex example.

AB - The spectral element method was introduced by Khasawneh and Mann (2013) for the stability analysis of time-periodic delay-differential equations (DDEs) with multiple delays. In this paper, this method is generalized for time-periodic DDEs with multiple delays and distributed delay. For this general case, an explicit formula is given for the construction of the matrix approximation of the monodromy operator. The derived formula enables the algorithmic application of the method to DDEs with general combinations of delays for arbitrary point sets and test functions. Stability analysis is demonstrated for specific case studies, and the computation code is provided for a complex example.

KW - Spectral element

KW - Stability

KW - Time-delay system

KW - Time-periodic system

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