Some sufficient conditions are considered, under which the solutions of a class of incompletely exponentially fitted difference schemes converge uniformly in e, with orders one and two, to the solution of the singular perturbation problem: eu"+a(x)u'-b(x)u=f(x), for 0a>0, b(x)≥0. From these conditions.an incompletely exponentially fitted second-order scheme is derived. Finally, the results of some numerical experiments are given.
Lorenz,J.,Stability and consistency analysis of difference methods for singular perturbation problems,Proc.Conf.on Analytical and Numerical Approaches to Asymptotic Problems in Analysis,June(1980),9-13,University of Nijmegen,The Netherlands(O.Axelsson,L.Frank and A.Van der Sluis,Eds.)North-Holland,Amsterdam(1981).
Doolan,E.P.,J.J.H.Miller and W.H.A.Schilders,Uniform Numerical Methods for Problems with Initial and Boundary Layers,Boole Press,Dublin(1980).