Use of central‐difference operators for solution of singularly perturbed problems

Singularly perturbed second‐order elliptic equations with boundary layers are considered. These may be considered as model problems for the advection of some quantity such as heat or a pollutant in a flow field or as linear approximations to the Navier‐Stokes equations for fluid flow. Numerical methods composed of central‐difference operators on special piece‐wise‐uniform meshes are constructed for the above problems. Numerical results are obtained which show that these methods give approximate solutions with error estimates that are independent of the singular perturbation parameter. An open theoretical problem is posed.