Volume 19, Issue 5
A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations

Po-Wen Hsieh ,  Yin-Tzer Shih ,  Suh-Yuh Yang and Cheng-Shu You

10.4208/cicp.scpde14.21s

Commun. Comput. Phys., 19 (2016), pp. 1287-1301.

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  • Abstract

In this paper, we propose a novel and simple technique to construct effective difference schemes for solving systems of singularly perturbed convection-diffusionreaction 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.

  • History

Published online: 2018-04

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