Standard finite difference scheme for a singularly perturbed elliptic convection-diffusion equation on a rectangle under computer perturbations

摘要

A singularly perturbed elliptic convection-diffusion equation with a perturbation parameter epsilon (epsilon a (0, 1]) is considered on a rectangle. As applied to this equation, a standard finite difference scheme on a uniform grid is studied under computer perturbations. This scheme is not epsilon-uniformly stable with respect to perturbations. The conditions imposed on a "computing system" are established under which a converging standard scheme (referred to as a computer difference scheme) remains stable.