Summary: IMA Journal of Numerical Analysis Page 1 of 23
Linearly implicit methods for a semilinear parabolic system
arising in twophase flows
Computer Science Department, University of Ioannina,
45110 Ioannina, Greece.
DEMETRIOS T. PAPAGEORGIOU
Department of Mathematics, Imperial College London,
London, SW7 2AZ, UK.
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