A parameter uniform essentially first-order convergent numerical method for a parabolic system of singularly perturbed differential equations of reaction–diffusion type with initial and Robin boundary conditions
2019 ◽
Vol 12
(01)
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pp. 1950001
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Keyword(s):
In this paper, a class of linear parabolic systems of singularly perturbed second-order differential equations of reaction–diffusion type with initial and Robin boundary conditions is considered. The components of the solution [Formula: see text] of this system are smooth, whereas the components of [Formula: see text] exhibit parabolic boundary layers. A numerical method composed of a classical finite difference scheme on a piecewise uniform Shishkin mesh is suggested. This method is proved to be first-order convergent in time and essentially first-order convergent in the space variable in the maximum norm uniformly in the perturbation parameters.
2017 ◽
Vol 35
(3_4)
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pp. 277-302
Keyword(s):
2021 ◽
Vol 1850
(1)
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pp. 012063
2016 ◽
Vol 33
(1)
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pp. 67-92
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2019 ◽
Vol 5
(3)
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2017 ◽
Vol 41
(4)
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pp. 1683-1696
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