A Novel Technique for Constructing Difference Schemes for Systems of Singularly Perturbed Equations
2016 ◽
Vol 19
(5)
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pp. 1287-1301
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Keyword(s):
AbstractIn 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.
2008 ◽
Vol 48
(5)
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pp. 769-785
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2019 ◽
Vol 59
(12)
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pp. 2129-2129
Keyword(s):
2012 ◽
pp. 293-301
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2017 ◽
Vol 34
(1)
◽
pp. 121-144
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2019 ◽
Vol 59
(12)
◽
pp. 2057-2079
Keyword(s):