Discrete differential operators for periodic and two-periodic time functions
ISSN: 0332-1649
Article publication date: 23 November 2018
Issue publication date: 24 January 2019
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