Linearly implicit schemes for a class of dispersive---dissipative systems

Authors:
Georgios Akrivis;Yiorgos-Sokratis Smyrlis
Affiliations:
Computer Science Department, University of Ioannina, Ioannina, Greece 451 10;Department of Mathematics and Statistics, University of Cyprus, Nicosia, Cyprus 1678
Venue:
Calcolo: a quarterly on numerical analysis and theory of computation
Year:
2011

Citing 3
Cited 1

Implicit-explicit multistep finite element methods for nonlinear parabolic problems

Mathematics of Computation
Implicit-explicit BDF methods for the Kuramoto-Sivashinsky equation

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Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)

Galerkin Finite Element Methods for Parabolic Problems (Springer Series in Computational Mathematics)

Computational Study of the Dispersively Modified Kuramoto-Sivashinsky Equation

SIAM Journal on Scientific Computing

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Abstract

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.