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In this article, a new exponential finite difference scheme for  the numerical solution of two point boundary value problems with Dirichlet's boundary conditions is proposed. The scheme is based on an exponential approximation of the Taylor expansion for the discretized derivative .The convergence of the scheme discussed under appropriate condition .The theoretical and numerical results  show that this new scheme is efficient and at least fourth order accurate

Solving Two Point Boundary Value Problems for Ordinary Differential Equations Using Exponential Finite Difference Method