Novel Defect-correction High-order, in Space and Time, Accurate Schemes for Parabolic Singularly Perturbed Convection-diffusion Problems
Abstract: New high-order accurate finite difference schemes based on defect correction are considered for an initial boundary-value problem on an interval for singularly perturbed parabolic PDEs with convection; the highest space derivative in the equation is multiplied by the perturbation parameter ε. Solutions of the well-known classical numerical schemes for such problems do not converge ε-uniformly (the errors of such schemes depend on the value of the parameter ε and are comparable with the solution itself for small values of ε). The convergence order of the existing ε-uniformly convergent schemes does not exceed 1 in space and time. In this paper, using a defect correction technique, we construct a special difference scheme that converges ε-uniformly with the second (up to a logarithmic factor) order of accuracy with respect to x and with the second order of accuracy and higher with respect to t.
- 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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Novel Defect-correction High-order, in Space and Time, Accurate Schemes for Parabolic Singularly Perturbed Convection-diffusion Problems ; volume:3 ; number:3 ; year:2003 ; pages:387-404
Computational methods in applied mathematics ; 3, Heft 3 (2003), 387-404
- Urheber
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Hemker, Pieter W.
Shishkin, Gregorii I.
Shishkin, Lidia P.
- DOI
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10.2478/cmam-2003-0025
- URN
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urn:nbn:de:101:1-2410261609346.332485044473
- Rechteinformation
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Open Access; Der Zugriff auf das Objekt ist unbeschränkt möglich.
- Letzte Aktualisierung
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15.08.2025, 07:25 MESZ
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Beteiligte
- Hemker, Pieter W.
- Shishkin, Gregorii I.
- Shishkin, Lidia P.
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