ON OPTIMALLY SCALED SYSTEMS FOR 2ND-ORDER SCALAR SINGULARLY PERTURBEDPROBLEMS

The conditioning of the singularly perturbed scalar Dirichlet problem is considered. It is shown haw this is related to the conditioning of an appropriate associated first-order system. Through this the dichoto my of the solution space (a concept that only makes sense in a vectori al setting) can be investigated. Two typical equations are studied in more detail, one with possible boundary layers on both sides of the in terval and one with an internal layer (i.e., the turning point case). The results are applied to obtain estimates of global discretization e rrors for difference methods. Several examples illustrate the analysis .