Fractional Chebyshev collocation method for solving linear fractional-order delay-differential equations

Arman Dabiri, Eric Butcher

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

3 Scopus citations

Abstract

An efficient numerical method, the fractional Chebyshev collocation method, is proposed for obtaining the solution of a system of linear fractional order delaydifferential equations (FDDEs). It is shown that the proposed method overcomes several limitations of current numerical methods for solving linear FDDEs. For instance, the proposed method can be used for linear incommensurate order fractional differential equations and FDDEs, has spectral convergence (unlike finite differences), and does not require a canonical form. To accomplish this, a fractional differentiation matrix is derived at the Chebyshev-Gauss-Lobatto collocation points by using the discrete orthogonal relationship of the Chebyshev polynomials. Then, using two proposed discretization operators for matrix functions results in an explicit form of solution for a system of linear FDDEs with discrete delays. The advantages of using the fractional Chebyshev collocation method are demonstrated in two numerical examples in which the proposed method is compared with the Adams- Bashforth-Moulton method.

Original languageEnglish (US)
Title of host publication13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
PublisherAmerican Society of Mechanical Engineers (ASME)
Volume6
ISBN (Electronic)9780791858202
DOIs
StatePublished - Jan 1 2017
EventASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2017 - Cleveland, United States
Duration: Aug 6 2017Aug 9 2017

Other

OtherASME 2017 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, IDETC/CIE 2017
CountryUnited States
CityCleveland
Period8/6/178/9/17

ASJC Scopus subject areas

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

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    Dabiri, A., & Butcher, E. (2017). Fractional Chebyshev collocation method for solving linear fractional-order delay-differential equations. In 13th International Conference on Multibody Systems, Nonlinear Dynamics, and Control (Vol. 6). American Society of Mechanical Engineers (ASME). https://doi.org/10.1115/DETC2017-68333