Analysis of a finite-difference scheme for a singularly perturbed problem with two small parameters. (Q1425119)

The authors discuss a model of convection-diffusion-reaction problem where both the diffusion term and the convection term are multiplied by small parameters. A difference scheme for this boundary value problem is proposed and a comparison principle is stated. Sharp bounds for the derivatives of the solution are derived using a barrier-technique. The behavior of the difference scheme on special layer-adapted meshes, so-called Shishkin meshes, is discussed. Independently of the two small parameters, the difference scheme is first-order convergent. Numerical experiments are performed.