Summary: LINEARLY IMPLICIT SCHEMES
FOR A CLASS OF DISPERSIVE­DISSIPATIVE SYSTEMS
GEORGIOS AKRIVIS AND YIORGOS­SOKRATIS SMYRLIS
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 implicit­explicit Euler scheme and by the two­
step implicit­explicit BDF scheme. In this work, we extend the results in [2, 3],
where the dispersive term (if present) was dominated by the dissipative one and
was not integrated implicitly. We also derive optimal order error estimates. We
provide various physically relevant applications of dispersive­dissipative equations
and systems fitting in our abstract framework.
1. Introduction
1.1. Dispersive­dissipative systems. We consider the time discretization of initial
value problems of the form
(1.1)
u (t) + Lu(t) = B t, u(t) , 0 < t < T,
u(0) = u0
,

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

Collections: Computer Technologies and Information Sciences