HIGH-ORDER DISCRETE METHOD FOR A CLASS OF 2-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'' + f(x, y) = 0, 0 less than or equal to x less than or equal to 1, y(0) = y(1), y'(0) = y'(1). Under suitable conditions on partial derivative f/partial derivative y, and for y is an element of C-6[0, 1], it is shown that ayl our finite difference method (based on three evaluations of f) is O(h(4))-convergent. The results are illustrated by several numerical examples.