Vigo-aguiar and Natesan consider the numerical solution of a singularly perturbed, scalar, linear, second order ordinary differential equation (ODE) on [0,1], with linear boundary conditions.

Additional assumptions imply a weak boundary layer at 0, where the authors use an exponentially fitted difference scheme. The assumptions allow an upwind difference scheme to be used in the rest of the interval. The authors propose a domain decomposition scheme, using one processor for the boundary layer, and several for the rest of the interval. An outer solution is used as a guess for boundary values on each domain, though the authors do not discuss how to evaluate this outer solution numerically.