caa a22 4500 445862165 CHVBK 20180317145447.0 cr unu---uuuuu 170323e20110601xx s 000 0 eng 10.1007/s10092-010-0033-6 doi (NATIONALLICENCE)springer-10.1007/s10092-010-0033-6 Linearly implicit schemes foraclass ofdispersive-dissipative systems [Elektronische Daten] [Georgios Akrivis, Yiorgos-Sokratis Smyrlis] We consider initial value problems for semilinear parabolic equations, which possess a dispersive term, nonlocal in general. This dispersive term is not necessarily dominated by the dissipative term. In our numerical schemes, the time discretization is done by linearly implicit schemes. More specifically, we discretize the initial value problem by the implicit-explicit Euler scheme and by the two-step implicit-explicit BDF scheme. In this work, we extend the results in Akrivis et al. (Math. Comput. 67:457-477, 1998; Numer. Math. 82:521-541, 1999), where the dispersive term (if present) was dominated by the dissipative one and was integrated explicitly. We also derive optimal order error estimates. We provide various physically relevant applications of dispersive-dissipative equations and systems fitting in our abstract framework. Springer-Verlag, 2010 Dispersive-dissipative systems nationallicence Semilinear parabolic equations nationallicence Kuramoto-Sivashinsky equation nationallicence Linearly implicit schemes nationallicence Backward differentiation formulas (BDF) methods nationallicence Error estimates nationallicence Akrivis Georgios Computer Science Department, University of Ioannina, 451 10, Ioannina, Greece aut Smyrlis Yiorgos-Sokratis Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus aut Calcolo Springer Milan 48/2(2011-06-01), 145-172 0008-0624 48:2<145 2011 48 10092 https://doi.org/10.1007/s10092-010-0033-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10092-010-0033-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Akrivis Georgios Computer Science Department, University of Ioannina, 451 10, Ioannina, Greece aut NATIONALLICENCE 700 1- Smyrlis Yiorgos-Sokratis Department of Mathematics and Statistics, University of Cyprus, P.O. Box 20537, 1678, Nicosia, Cyprus aut NATIONALLICENCE 773 0- Calcolo Springer Milan 48/2(2011-06-01), 145-172 0008-0624 48:2<145 2011 48 10092 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer