Application of discrete differential operators of periodic functions to solve 1D boundary-value problems

What is it about?

Discrete differential operators of periodic time functions are effective tools for determining periodic steady states solutions of nonlinear ordinary differential equations. This paper concentrates on application of such types of operators for solving boundary value problems for the same class of differential equations. For that, a solution of the boundary problem is treated as periodic over an interval between boundaries, assuming that this solution is repeated outside the interval. Generally, such solution should be foreseen as a non-continuous function at the boundaries. It is known that approximations of non-continuous periodic functions based on the Fourier approach leads to, so called, Gibbs effects at discontinuities. The paper shows how to omit this problem for various types of boundary conditions.

Featured Image