Email this article Discrete Spline Solution of Singularly Perturbed Problem with Two Small Parameters on a Shishkin-Type Mesh
- Authors: Zahra W.K.1, Van Daele M.2
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Affiliations:
- Faculty of Engineering, Tanta University
- Department of Applied Mathematics, Computer Science and Statistics, Ghent University
- Issue: Vol 29, No 3 (2018)
- Pages: 367-381
- Section: Article
- URL: https://journal-vniispk.ru/1046-283X/article/view/247774
- DOI: https://doi.org/10.1007/s10598-018-9416-3
- ID: 247774
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Abstract
We consider singularly perturbed problems of convection-diffusion-reaction type which involve two small parameters. A new discrete cubic spline method is developed for the solution of this problem on a Shishkin mesh. A convergence analysis is given and the method is shown to be almost second-order uniformly convergent with respect to the perturbation parameters ????d and ????c. Numerical results are presented to validate the theoretical results as well as the robustness of the method.
About the authors
W. K. Zahra
Faculty of Engineering, Tanta University
Author for correspondence.
Email: wzahra@f-eng.tanta.edu.eg
Egypt, Tanta
M. Van Daele
Department of Applied Mathematics, Computer Science and Statistics, Ghent University
Email: wzahra@f-eng.tanta.edu.eg
Belgium, Krijgslaan
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