A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations (Communications in Computational Physics, 2020)
In this paper, we propose a novel and simple technique to construct effectivedifference schemes for solving systems of singularly perturbed convection-diffusion-reactionequations, whose solutions may display boundary or interior layers. We illustratethe technique by taking the Il'in-Allen-Southwell scheme for 1-D scalar equationsas a basis to derive a formally second-order scheme for 1-D coupled systems andthen extend the scheme to 2-D case by employing an alternating direction approach.Numerical examples are given to demonstrate the high performance of the obtainedscheme on uniform meshes as well as piecewise-uniform Shishkin meshes.