High order discrete method for a class of two-point boundary value problems with periodic boundary conditions

In this paper, we present a new 3-point finite difference scheme for the class of two-point boundary value problems with periodic boundary conditions: y″ + (x,y) = 0, 0 ≤ x ≤ 1, y(0) = y(1), y′(0) = y′(1). Under suitable conditions on ∂f∂y, and for y ∈ C6[0, 1], it is shown that our finite difference method (based on three evaluations of f) is O(h4)-convergent. The results are illustrated by several numerical examples.