Numerical approximations to the scaled first derivatives of the solution to a two parameter singularly perturbed problem

A singularly perturbed problem involving two singular perturbation parameters is discretized using the classical upwinded finite difference scheme on an appropriate piecewise-uniform Shishkin mesh. Scaled discrete derivatives (with scaling only used within the layers) are shown to be parameter unifo...

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Bibliographic Details
Published in:Journal of computational and applied mathematics 2019-02, Vol.347, p.128-149
Main Authors: O’Riordan, E., Pickett, M.L.
Format: Article
Language:English
Subjects:
Scaled first derivative
Singularly perturbed
Two parameter
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Summary:A singularly perturbed problem involving two singular perturbation parameters is discretized using the classical upwinded finite difference scheme on an appropriate piecewise-uniform Shishkin mesh. Scaled discrete derivatives (with scaling only used within the layers) are shown to be parameter uniformly convergent to the scaled first derivatives of the continuous solution.
ISSN:0377-0427
1879-1778
DOI:10.1016/j.cam.2018.08.004