A Completely Exponentially Fitted Difference Scheme for a Singular Perturbation Problem

Abstract

A completely exponentially fitted difference scheme is considered for the singular perturbation problem: $\epsilon U^{''}+a(x) U^{'}-b(x) U=f(x) \ {\rm for}  \ 0 \lt x \lt 1$, with U(0), and U(1) given, $\epsilon \in (0,1]$ and $a(x) \gt α \gt 0, b(x)\geq 0$. It is proven that the scheme is uniformly second-order accurate.