Rational finite difference approximation of high order accuracy for nonlinear two point boundary value problems

Abstract

In this paper, we present a new method for solving nonlinear general two point boundary value problems. A method based on finite differences and rational function approximation and we call this method as rational approximation method. A rational approximation method is applied to construct the numerical solution for two point boundary value problems. The novel method is tested on three model problems. Thus the numerical results obtained for these model problems show the performance and efficiency of the developed method.