Summary: IMA Journal of Numerical Analysis Page 1 of 23
doi:10.1093/imanum/drnxxx
Linearly implicit methods for a semilinear parabolic system
arising in two­phase flows
GEORGIOS AKRIVIS
Computer Science Department, University of Ioannina,
45110 Ioannina, Greece.
DEMETRIOS T. PAPAGEORGIOU
Department of Mathematics, Imperial College London,
London, SW7 2AZ, UK.
YIORGOS­SOKRATIS SMYRLIS§
Department of Mathematics and Statistics, University of Cyprus,
P. O. Box 20537, 1678 Nicosia, Cyprus.
[Received on January 15, 2009]
We study the discretization of a nonlinear parabolic system arising in two­phase flows, which in a spe-
cial case reduces to the Kuramoto­Sivashinsky equation, by linearly implicit methods, and in particular
by implicit­explicit multistep methods. We carry out extensive numerical experiments to investigate the
accuracy and efficiency of these algorithms with extremely satisfactory results. These numerical exper-
iments 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

Source: Akrivis, Georgios - Department of Computer Science, University of Ioannina

Collections: Computer Technologies and Information Sciences