Non-polynomial spline finite difference method for solving second order boundary value problem

Abstract

        Second -order two-point boundary value problems (BVPs) were solved based on a  of non-polynomial spline general functions with finite difference method.In this paper we discusses a method depended on using special finite-difference approximations for derivatives and formatting a formula that can be deal with endpoints that exceed the usual finite-difference formula for derivatives. Convergence analysis of the  method is discussed. The numerical description of the method is shown by four examples. So the results obtained by our method are very encouraging over other existing methods.