ON THE CONVERGENCE OF FINITE DIFFERENCE METHODS FOR A CLASS OF TWO-POINT BOUNDARY VALUE PROBLEMS WITH PERIODIC BOUNDARY CONDITIONS

摘要

In this paper we present a detailed convergence analysis to establish second-order convergence for a three-point two parameter family of finite difference methods (based on one evaluation of f) for the class of two-point boundary value problems (TPBVPs) 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-4[0, 1]. Some numerical examples are provided to illustrate the results. [References: 18]