Discrete differential operators for periodic and two-periodic time functions

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.