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A novel technique for constructing difference schemes for systems of singularly perturbed equations

Po-Wen Hsieh Chung Yuan Christian University Yin-Tzer Shih National Chung Hsing University Suh-Yuh Yang National Central University Cheng-Shu You National Central University

Numerical Analysis and Scientific Computing mathscidoc:1703.25024

Communications in Computational Physics , 19, 2016.5
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.
system of singularly perturbed equations, system of viscous Burgers’ equations, boundary layer, interior layer, Il’in-Allen-Southwell scheme, formally second-order scheme
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@inproceedings{po-wen2016a,
  title={A novel technique for constructing difference schemes for systems of singularly perturbed equations},
  author={Po-Wen Hsieh, Yin-Tzer Shih, Suh-Yuh Yang, and Cheng-Shu You},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170314095953203483693},
  booktitle={Communications in Computational Physics },
  volume={19},
  year={2016},
}
Po-Wen Hsieh, Yin-Tzer Shih, Suh-Yuh Yang, and Cheng-Shu You. A novel technique for constructing difference schemes for systems of singularly perturbed equations. 2016. Vol. 19. In Communications in Computational Physics . http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170314095953203483693.
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