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

Eugene O'Riordan; Maria Pickett

doi:10.1016/j.cam.2018.08.004

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

Eugene O'Riordan, Maria Pickett

School of Mathematics & Physics

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Abstract

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.

Original language	English
Pages (from-to)	128-149
Number of pages	22
Journal	Journal of Computational and Applied Mathematics
Volume	347
Early online date	18 Aug 2018
DOIs	https://doi.org/10.1016/j.cam.2018.08.004
Publication status	Published - 1 Feb 2019

Keywords

singularly perturbed
two parameter
scaled first derivative

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10.1016/j.cam.2018.08.004

A_singularly_perturbed_problem_involving_two_singular_perturbation_parametersAccepted author manuscript (Post-print), 456 KBLicence: CC BY-NC-ND

Data availability statement for 'Numerical approximations to the scaled first derivatives of the solution to a two parameter singularly perturbed problem'.
O'Riordan, E. (Creator) & Pickett, M. (Creator), Elsevier BV, 18 Aug 2018
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title = "Numerical approximations to the scaled first derivatives of the solution to a two parameter singularly perturbed problem",

abstract = "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.",

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AB - 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.

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KW - scaled first derivative

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DO - 10.1016/j.cam.2018.08.004

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EP - 149

JO - Journal of Computational and Applied Mathematics

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

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