2D Discrete Differential Operators for Periodic Functions

This paper presents novel types of discrete differential operators for two-variable functions, periodic for each variable. They determine values of derivatives, both the first- as well the second, by the values of the function itself in a set of points uniformly distributed over the periods. Those operators relate the values of derivatives at each point to the values of the function in all selected points. Such operators allow creating easily finite difference equations for partial differential equations up to the second order, for solving boundary problems. They are addresses especially to nonlinear cases.