On Boundary Layer Approximations in the Numerical Solution of Certain Stiff Boundary Value Problems

Abstract

It is shown that an additional condition, related to a condition of Kreiss, is required in the algorithm of O’Malley and Flaherty in order to achieve uniformly valid approximate solutions to certain mth order stiff boundary value problems. This additional condition need be considered only if one seeks approximations that remain valid within the boundary layers. The condition amounts to the requirement that the variation of the large roots of the characteristic equation (along with the variation of certain of their derivatives) should not be excessively large.