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dc.contributor.authorAkrivis, Georgiosen
dc.contributor.authorPapageorgiou, Demetrios T.en
dc.contributor.authorSmyrlis, Yiorgos-Sokratisen
dc.creatorAkrivis, Georgiosen
dc.creatorPapageorgiou, Demetrios T.en
dc.creatorSmyrlis, Yiorgos-Sokratisen
dc.description.abstractWe study the discretization of a nonlinear parabolic system arising in two-phase flows, which in a special case reduces to the Kuramoto-Sivashinsky equation, by linearly implicit methods and, in particular, by implicit-explicit multistep methods. We carry out extensive numerical experiments to investigate the accuracy and efficiency of these algorithms with extremely satisfactory results. These numerical experiments establish the analyticity of the solution and the existence of global attractors (rigorous proofs of such results for this system are not available). Our numerical experiments yield a sharp estimate for the band of analyticity of the solutions as the parameters vary. The accuracy of the schemes enables, in general, the exhaustive numerical study of such systems and the full classification of the inertial manifold. We provide numerical examples of travelling time-periodic attractors as well as quasi-periodic and chaotic attractors. © 2009 The author. Published by Oxford University Press on behalf of the Institute of Mathematics and its Applications. All rights reserved.en
dc.sourceIMA Journal of Numerical Analysisen
dc.subjectKuramoto-Sivashinsky equationen
dc.subjectdissipative infinite-dimensional dynamical systemsen
dc.subjectimplicit-explicit Backward Differentiation Formulæ schemesen
dc.subjectlinearly implicit schemesen
dc.subjectsemilinear parabolic systemsen
dc.titleLinearly implicit methods for a semilinear parabolic system arising in two-phase flowsen
dc.description.endingpage321Σχολή Θετικών και Εφαρμοσμένων Επιστημών / Faculty of Pure and Applied SciencesΤμήμα Μαθηματικών και Στατιστικής / Department of Mathematics and Statistics
dc.description.notes<p>Cited By :12</p>en
dc.source.abbreviationIMA J.Numer.Anal.en
dc.contributor.orcidSmyrlis, Yiorgos-Sokratis [0000-0001-9126-2441]

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