High-order Time-accurate Schemes for Singularly Perturbed Parabolic Convection-diffusion Problems with Robin Boundary Conditions
Abstract: The boundary-value problem for a singularly perturbed parabolic PDE with convection is considered on an interval in the case of the singularly perturbed Robin boundary condition; the highest space derivatives in the equation and in the boundary condition are multiplied by the perturbation parameter ε. The order of convergence for the known ε-uniformly convergent schemes does not exceed 1. In this paper, using a defect correction technique, we construct ε-uniformly convergent schemes of highorder time-accuracy. The efficiency of the new defect-correction schemes is confirmed by numerical experiments. A new original technigue for experimental studying of convergence orders is developed for the cases where the orders of convergence in the x-direction and in the t-direction can be substantially different.
- Standort
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Deutsche Nationalbibliothek Frankfurt am Main
- Umfang
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Online-Ressource
- Sprache
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Englisch
- Erschienen in
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High-order Time-accurate Schemes for Singularly Perturbed Parabolic Convection-diffusion Problems with Robin Boundary Conditions ; volume:2 ; number:1 ; year:2002 ; pages:3-25
Computational methods in applied mathematics ; 2, Heft 1 (2002), 3-25
- Urheber
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Hemker, Pieter W.
Shishkin, Grigorii I.
Shishkina, Lidia P.
- DOI
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10.2478/cmam-2002-0001
- URN
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urn:nbn:de:101:1-2410261608257.319895150478
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
- 15.08.2025, 07:21 MESZ
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Beteiligte
- Hemker, Pieter W.
- Shishkin, Grigorii I.
- Shishkina, Lidia P.
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