Uniformly higher order accurate extrapolations to solutions of uniformly convergent discretization methods for singularly perturbed problems (Q1191601)

This paper deals with the Il'in-Allen-Southwell scheme for the nonselfadjoint problem \(\varepsilon u''+au'-b(x)u=f(x)\) for \(0<x<1\), \(u(0)\), \(u(1)\) given, \(\varepsilon\in (0,1]\), \(a>0\), and \(b(x)\geq 0\). The author proves that the extrapolation solution \(\bar u^ h(x)\) derived from the global error expansion of the scheme is uniformly convergent with order two. A numerical example is presented.