@Article{CiCP-19-1287, author = {}, title = {A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations}, journal = {Communications in Computational Physics}, year = {2018}, volume = {19}, number = {5}, pages = {1287--1301}, abstract = {

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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.scpde14.21s}, url = {http://global-sci.org/intro/article_detail/cicp/11129.html} }