1D and 2D finite-difference operators for periodic functions on arbitrary mesh

This paper presents novel discrete differential operators for periodic functions of one-and two-variables, which relate the values of the derivatives to the values of the function itself for a set of arbitrarily chosen points over the function's area. It is very characteristic, that the values of the derivatives at each point depend on the function values at all points in that area. Such operators allow one to easily create finite-difference equations for boundary-value problems. The operators are addressed especially to nonlinear differential equations.