• DocumentCode
    856162
  • Title

    The operational matrices of integration and differentiation for the Fourier sine-cosine and exponential series

  • Author

    Paraskevopoulos, P.N.

  • Author_Institution
    National Technical University of Athens, Zographou, Greece
  • Volume
    32
  • Issue
    7
  • fYear
    1987
  • fDate
    7/1/1987 12:00:00 AM
  • Firstpage
    648
  • Lastpage
    651
  • Abstract
    For the Fourier sine-cosine series basis vector \\varphi (t) and the Fourier exponential series basis vector \\psi(t) , a linear nonsingular transfor-marion T is determined such that \\psi(t) = T\\varphi (t) . This result is then used to show that the operational matrices of integration P and Q for \\varphi (t) and \\psi(t) , respectively, are related by the expression TP = QT . Analogous results are derived for the corresponding operational matrices of differentiation D and R . General expressions are derived for T,P,Q,D, and R .
  • Keywords
    Fourier series; Integration (mathematics); Matrices; Chebyshev approximation; Computer science; Genetic expression; Jacobian matrices; Optimal control; Sensitivity analysis; Vectors;
  • fLanguage
    English
  • Journal_Title
    Automatic Control, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9286
  • Type

    jour

  • DOI
    10.1109/TAC.1987.1104663
  • Filename
    1104663
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=856162