caa a22 4500 378936433 CHVBK 20180305123641.0 cr unu---uuuuu 161128s2004 xx s 000 0 eng 10.2478/cmam-2004-0020 doi (NATIONALLICENCE)gruyter-10.2478/cmam-2004-0020 Vulanović Relja Kent State University Stark Campus, 6000 Frank Ave. NW, Canton, OH 44720-7599, USA. An Almost Sixth-Order Finite-Difference Method for Semilinear Singular Perturbation Problems [Elektronische Daten] [Relja Vulanović] The discretization meshes of the Shishkin type are more suitable for high- order finite-difference schemes than Bakhvalov-type meshes. This point is illustrated by the construction of a hybrid scheme for a class of semilinear singularly perturbed reaction-diffusion problems. A sixth-order five-point equidistant scheme is used at most of the mesh points inside the boundary layers, whereas lower-order three-point schemes are used elsewhere. It is proved under certain conditions that this combined scheme is almost sixth-order accurate and that its error does not increase when the perturbation parameter tends to zero. 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. finite differences nationallicence semilinear boundary value problem nationallicence Shishkin mesh nationallicence singular perturbation nationallicence Computational Methods in Applied Mathematics De Gruyter 4/3(2004), 368-383 1609-4840 4:3<368 2004 4 cmam https://doi.org/10.2478/cmam-2004-0020 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.2478/cmam-2004-0020 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Vulanović Relja Kent State University Stark Campus, 6000 Frank Ave. NW, Canton, OH 44720-7599, USA NATIONALLICENCE 773 0- Computational Methods in Applied Mathematics De Gruyter 4/3(2004), 368-383 1609-4840 4:3<368 2004 4 cmam CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter