The Magnus expansion for periodic delay differential equations

Árpád Takács, Eric A. Butcher, T. Insperger

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

Abstract

In this paper, the application of the Magnus expansion on periodic time-delayed differential equations is proposed, where an approximation technique of Chebyshev Spectral Continuous Time Approximation (CSCTA) is first used to convert a system of delayed differential equations (DDEs) into a system of ordinary differential equations (ODEs), whose solution are then obtained via the Magnus expansion. The stability and time response of this approach are investigated on two examples and compared with known results in the literature.

Original languageEnglish
Title of host publication9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers
Volume7 B
ISBN (Print)9780791855973
DOIs
Publication statusPublished - 2013
EventASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013 - Portland, OR, United States
Duration: Aug 4 2013Aug 7 2013

Other

OtherASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013
CountryUnited States
CityPortland, OR
Period8/4/138/7/13

Fingerprint

Magnus Expansion
Delayed Differential Equation
Delay Differential Equations
Differential equations
Approximation
Chebyshev
System of Ordinary Differential Equations
Ordinary differential equations
Response Time
Convert
Continuous Time

ASJC Scopus subject areas

  • Mechanical Engineering
  • Computer Graphics and Computer-Aided Design
  • Computer Science Applications
  • Modelling and Simulation

Cite this

Takács, Á., Butcher, E. A., & Insperger, T. (2013). The Magnus expansion for periodic delay differential equations. In 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (Vol. 7 B). [V07BT10A058] American Society of Mechanical Engineers. https://doi.org/10.1115/DETC2013-12304

The Magnus expansion for periodic delay differential equations. / Takács, Árpád; Butcher, Eric A.; Insperger, T.

9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 7 B American Society of Mechanical Engineers, 2013. V07BT10A058.

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

Takács, Á, Butcher, EA & Insperger, T 2013, The Magnus expansion for periodic delay differential equations. in 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. vol. 7 B, V07BT10A058, American Society of Mechanical Engineers, ASME 2013 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2013, Portland, OR, United States, 8/4/13. https://doi.org/10.1115/DETC2013-12304
Takács Á, Butcher EA, Insperger T. The Magnus expansion for periodic delay differential equations. In 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 7 B. American Society of Mechanical Engineers. 2013. V07BT10A058 https://doi.org/10.1115/DETC2013-12304
Takács, Árpád ; Butcher, Eric A. ; Insperger, T. / The Magnus expansion for periodic delay differential equations. 9th International Conference on Multibody Systems, Nonlinear Dynamics, and Control. Vol. 7 B American Society of Mechanical Engineers, 2013.
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