TY - JOUR T1 - A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations AU - Po-Wen Hsieh, Yin-Tzer Shih, Suh-Yuh Yang & Cheng-Shu You JO - Communications in Computational Physics VL - 5 SP - 1287 EP - 1301 PY - 2018 DA - 2018/04 SN - 19 DO - http://doi.org/10.4208/cicp.scpde14.21s UR - https://global-sci.org/intro/article_detail/cicp/11129.html KW - AB -

In this paper, we propose a novel and simple technique to construct effective difference schemes for solving systems of singularly perturbed convection-diffusion-reaction equations, whose solutions may display boundary or interior layers. We illustrate the technique by taking the Il'in-Allen-Southwell scheme for 1-D scalar equations as a basis to derive a formally second-order scheme for 1-D coupled systems and then extend the scheme to 2-D case by employing an alternating direction approach. Numerical examples are given to demonstrate the high performance of the obtained scheme on uniform meshes as well as piecewise-uniform Shishkin meshes.