caa a22 4500 37885772X CHVBK 20180305123339.0 cr unu---uuuuu 161128s2003 xx s 000 0 eng 10.2478/cmam-2003-0025 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2003-0025 Novel Defect-correction High-order, in Space and Time, Accurate Schemes for Parabolic Singularly Perturbed Convection-diffusion Problems [Elektronische Daten] 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. 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. singular perturbation problem nationallicence convection-diffusion equations nationallicence ε-uniform fitted mesh method nationallicence defect correction nationallicence higher-order accuracy nationallicence Hemker Pieter W. CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands. Shishkin Gregorii I. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., 620219 Ekaterinburg, Russia. Shishkin Lidia P. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., 620219 Ekaterinburg, Russia. Computational Methods in Applied Mathematics De Gruyter 3/3(2003), 387-404 1609-4840 3:3<387 2003 3 cmam https://doi.org/10.2478/cmam-2003-0025 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2003-0025 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Hemker Pieter W. CWI, P.O. Box 94079, 1090 GB Amsterdam, The Netherlands NATIONALLICENCE 700 1- Shishkin Gregorii I. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., 620219 Ekaterinburg, Russia NATIONALLICENCE 700 1- Shishkin Lidia P. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, 16 S. Kovalevskaya Str., 620219 Ekaterinburg, Russia NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 3/3(2003), 387-404 1609-4840 3:3<387 2003 3 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter