  We explore the evolution of the eccentricity of an accretion disc perturbed
by an embedded planet whose mass is sufficient to open a large gap in the disc.
Various methods for representing the orbit-averaged motion of an eccentric disc
are discussed. We characterize the linear instability which leads to the growth
of eccentricity by means of hydrodynamical simulations. We numerically recover
the known result that eccentricity growth in the disc is possible when the
planet-to-star mass ratio exceeds 0.003. For mass ratios larger than this
threshold, the precession rates and growth rates derived from simulations, as
well as the shape of the eccentric mode, compare well with the predictions of a
linear theory of eccentric discs. We study mechanisms by which the eccentricity
growth eventually saturates into a non-linear regime.
