USE OF CENTRAL-DIFFERENCE OPERATORS FOR SOLUTION OF SINGULARLY PERTURBED PROBLEMS

Singularly perturbed second-order elliptic equations with boundary lay ers 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 sp ecial piece-wise-uniform meshes are constructed for the above problems . Numerical results are obtained which show that these methods give ap proximate solutions with error estimates that are independent of the s ingular perturbation parameter. An open theoretical problem is posed.