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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 & Cheng-Shu You

DOI: 10.4208/cicp.scpde14.21s

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

Published online: 2018-04

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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-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.

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@Article{CiCP-19-1287, author = {Po-Wen Hsieh, Yin-Tzer Shih, Suh-Yuh Yang and Cheng-Shu You}, 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} }
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.

Po-Wen Hsieh, Yin-Tzer Shih, Suh-Yuh Yang and Cheng-Shu You. (2018). A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations. Communications in Computational Physics. 19 (5). 1287-1301. doi:10.4208/cicp.scpde14.21s
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