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A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations

  • Po-Wen Hsieh (a1), Yin-Tzer Shih (a2), Suh-Yuh Yang (a3) and Cheng-Shu You (a3)

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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Corresponding author

*Corresponding author. Email addresses:pwhsieh0209@gmail.com (P.-W. Hsieh), yintzer_shih@nchu.edu.tw (Y.-T. Shih), syyang@math.ncu.edu.tw (S.-Y. Yang), csdyou@gmail.com (C.-S. You)

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