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)=o, o⩽x⩽1y(o)=y(1), y′(o)=y′(1) under suitable conditions on ∂f/∂y and for y ϵ C4[0,1]. Some numerical examples are provided to illustrate the results.