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Discrete differential operators for periodic and two-periodic time functions

Tadeusz Sobczyk (Institute of Electromechanical Energy Conversion, Cracow University of Technology, Cracow, Poland)
Michał Radzik (Technical Institute, State Higher Vocational School in Nowy Sącz, Nowy Sącz, Poland)
Natalia Radwan-Pragłowska (Institute of Electromechanical Energy Conversion, Cracow University of Technology, Cracow, Poland)

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering

ISSN: 0332-1649

Article publication date: 23 November 2018

Issue publication date: 24 January 2019

111

Abstract

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.

Keywords

Citation

Sobczyk, T., Radzik, M. and Radwan-Pragłowska, N. (2019), "Discrete differential operators for periodic and two-periodic time functions", COMPEL - The international journal for computation and mathematics in electrical and electronic engineering, Vol. 38 No. 1, pp. 325-347. https://doi.org/10.1108/COMPEL-03-2018-0123

Publisher

:

Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

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