A higher accuracy exponential finite difference method for the numerical solution of second order elliptic partial differential equations

Abstract

In this article, we have developed a new exponential finite difference method of order four for the numerical solution of second order elliptic partial differential equations. We have presented the derivation and development of the method as well as have estimated the local truncation error in the method. Numerical examples are given to illustrate the performance of the method and its accuracy. The proposed method compares well with compact nine points fourth order method, it can be observed in numerical section of the article.