The Chebyshev spectral continuous time approximation for periodic delay differential equations

Eric A. Butcher, Oleg A. Bobrenkov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Scopus citations

Abstract

In this paper, the approximation technique proposed in [1] for converting a system of constant-coefficient delay differential equations (DDEs) into a system of ordinary differential equations (ODEs) using pseudospectral differencing is applied to both constant and periodic systems of DDEs. Specifically, the use of Chebyshev spectral collocation is proposed in order to obtain the "spectral accurac" convergence behavior shown in [1], The proposed technique is used to study the stability of first and second order constant coefficient DDEs with one or two fixed delays with or without cubic nonlinearity and parametric sinusoidal excitation, as well as of the delayed Mathieu's equation. In all the examples, the results of the approximation by the proposed method show good agreement with either analytical results, or the results obtained before by other reliable approximation methods. In particular, the greater accuracy and convergence properties of this method compared to the finite difference-based continuous time approximation proposed recently in [2] is shown.

Original languageEnglish (US)
Title of host publicationProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009
Pages633-643
Number of pages11
EditionPART A
DOIs
StatePublished - 2010
Externally publishedYes
Event2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009 - San Diego, CA, United States
Duration: Aug 30 2009Sep 2 2009

Publication series

NameProceedings of the ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference 2009, DETC2009
NumberPART A
Volume4

Conference

Conference2009 ASME International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, DETC2009
CountryUnited States
CitySan Diego, CA
Period8/30/099/2/09

ASJC Scopus subject areas

  • Computer Networks and Communications
  • Hardware and Architecture
  • Electrical and Electronic Engineering

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