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.
Original language | English |
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Pages (from-to) | 1287-1301 |
Number of pages | 15 |
Journal | Communications in Computational Physics |
Volume | 19 |
Issue number | 5 |
DOIs | |
State | Published - 1 May 2016 |
Keywords
- Il'in-Allen-Southwell scheme
- System of singularly perturbed equations
- boundary layer
- formally second-order scheme
- interior layer
- system of viscous Burgers' equations