caa a22 4500 465751393 CHVBK 20180323111834.0 cr unu---uuuuu 170327e19901201xx s 000 0 eng 10.1007/BF02241272 doi (NATIONALLICENCE)springer-10.1007/BF02241272 Auzinger W. Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 6-10, A-1040, Wien, Austria aut On error structures and extrapolation for stiff systems, with application in the method of lines [Elektronische Daten] [W. Auzinger] Über Fehlerstrukturen und Extrapolation bei steifen Systemen, mit Anwendung bei der Linienmethode In this paper, which carries on the considerations in [1], the structure of the global error is studied for some time discretization schemes, applied to a class of stiff initial value problems as they typically arise from the semi-discretization of parabolic initial/boundary value problems (method of lines). The implicit Euler and trapezoidal schemes and a locally one-dimensional splitting method are considered, and ‘perturbed' asymptotic error expansions are derived which are valid independent of the stiffness (independent of the meshwidth in space). The key point within the analysis is a careful, quantitative description of the remainder term in such an expansion. The results are applicable in the method of lines setting and enable the prediction of the behavior of extrapolation algorithms for the class of problems under consideration. These theoretical considerations are illustrated by numerical examples. Springer-Verlag, 1990 Stiff systems nationallicence method of lines nationallicence error structures nationallicence extrapolation nationallicence Computing Springer-Verlag 44/4(1990-12-01), 331-356 0010-485X 44:4<331 1990 44 607 https://doi.org/10.1007/BF02241272 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF02241272 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Auzinger W. Institut für Angewandte und Numerische Mathematik, Technische Universität Wien, Wiedner Hauptstrasse 6-10, A-1040, Wien, Austria aut NATIONALLICENCE 773 0- Computing Springer-Verlag 44/4(1990-12-01), 331-356 0010-485X 44:4<331 1990 44 607 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer