On the numerical integration of a class of singular perturbation problems
A three-point difference scheme recently proposed by \textit{M. K. Kadalbajoo} and \textit{Y. N. Reddy} [ibid. 51, 441-452 (1986; Zbl 0579.65081)] for the numerical solution of a class of linear, singularly perturbed, two-point boundary-value problems is investigated. The scheme is derived from a first-order approximation to the original problem with a small deviating argument. It is shown here that, in the limit, as the deviating argument tends to zero, the difference scheme converges to one- sided approximation to the original singularly perturbed equation in conservation form. The limiting scheme is shown to be stable on any uniform grid. Therefore, no advantage arises from using the deviating argument, and the most accurate and efficient results are obtained with the deviation at its zero limit.
scientific article; zbMATH DE number 4030872