Novel Defect-correction High-order, in Space and Time, Accurate Schemes for Parabolic Singularly Perturbed Convection-diffusion Problems
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| 024 | 7 | 0 | |a 10.2478/cmam-2003-0025 |2 doi |
| 035 | |a (NATIONALLICENCE)gruyter-10.2478/cmam-2003-0025 | ||
| 245 | 0 | 0 | |a Novel Defect-correction High-order, in Space and Time, Accurate Schemes for Parabolic Singularly Perturbed Convection-diffusion Problems |h [Elektronische Daten] |
| 520 | 3 | |a 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. | |
| 540 | |a This article is distributed under the terms of the Creative Commons Attribution Non-Commercial License, which permits unrestricted non-commercial use, distribution, and reproduction in any medium, provided the original work is properly cited. | ||
| 690 | 7 | |a singular perturbation problem |2 nationallicence | |
| 690 | 7 | |a convection-diffusion equations |2 nationallicence | |
| 690 | 7 | |a ε-uniform fitted mesh method |2 nationallicence | |
| 690 | 7 | |a defect correction |2 nationallicence | |
| 690 | 7 | |a higher-order accuracy |2 nationallicence | |
| 700 | 1 | |a Hemker |D Pieter W. |u CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands. | |
| 700 | 1 | |a Shishkin |D Gregorii I. |u Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., 620219 Ekaterinburg, Russia. | |
| 700 | 1 | |a Shishkin |D Lidia P. |u Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., 620219 Ekaterinburg, Russia. | |
| 773 | 0 | |t Computational Methods in Applied Mathematics |d De Gruyter |g 3/3(2003), 387-404 |x 1609-4840 |q 3:3<387 |1 2003 |2 3 |o cmam | |
| 856 | 4 | 0 | |u https://doi.org/10.2478/cmam-2003-0025 |q text/html |z Onlinezugriff via DOI |
| 908 | |D 1 |a research article |2 jats | ||
| 950 | |B NATIONALLICENCE |P 856 |E 40 |u https://doi.org/10.2478/cmam-2003-0025 |q text/html |z Onlinezugriff via DOI | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Hemker |D Pieter W. |u CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Shishkin |D Gregorii I. |u Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., 620219 Ekaterinburg, Russia | ||
| 950 | |B NATIONALLICENCE |P 700 |E 1- |a Shishkin |D Lidia P. |u Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., 620219 Ekaterinburg, Russia | ||
| 950 | |B NATIONALLICENCE |P 773 |E 0- |t Computational Methods in Applied Mathematics |d De Gruyter |g 3/3(2003), 387-404 |x 1609-4840 |q 3:3<387 |1 2003 |2 3 |o cmam | ||
| 900 | 7 | |b CC0 |u http://creativecommons.org/publicdomain/zero/1.0 |2 nationallicence | |
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