Discrete differential operators for periodic and two-periodic time functions

• Tadeusz Sobczyk ^[1] ; Michał Radzik ^[2] ; Natalia Radwan-Pragłowska ^[1]
  1. [1] Cracow University of Technology

     Cracow University of Technology

     Kraków, Polonia

     
  2. [2] Technical Institute, State Higher Vocational School in Nowy Sacz, Polonia
• Localización: Compel: International journal for computation and mathematics in electrical and electronic engineering, ISSN 0332-1649, Vol. 38, Nº 1, 2019, págs. 325-347
• Idioma: inglés
• Enlaces
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• Resumen

  • Purpose – To identify the properties of novel discrete differential operators of the first- and the second-order for periodic and two-periodic time functions.

    Design/methodology/approach – The development of relations between the values of first and second derivatives of periodic and two-periodic functions, as well as the values of the functions themselves for a set of time instants. Numerical tests of discrete operators for selected periodic and two-periodic functions.

    Findings – Novel discrete differential operators for periodic and two-periodic time functions determining their first and the second derivatives at very high accuracy basing on relatively low number of points per highest harmonic.

    Research limitations/implications – Reduce the complexity of creation difference equations for ordinary non-linear differential equations used to find periodic or two-periodic solutions, when they exist.

    Practical implications – Application to steady-state analysis of non-linear dynamic systems for solutions predicted as periodic or two-periodic in time.

    Originality/value – Identify novel discrete differential operators for periodic and two-periodic time functions engaging a large set of time instants that determine the first and second derivatives with very high accuracy.