  We develop a simplified model for studying the long-term evolution of giant
planets in protoplanetary discs. The model accounts for the eccentricity
evolution of the planets and the dynamics of eccentric discs under the
influences of secular planet-disc interactions and internal disc pressure,
self-gravity and viscosity. Adopting the ansatz that the disc precesses
coherently with aligned apsides, the eccentricity evolution equations of the
planet-disc system reduce to a set of linearized ODEs, which allows for fast
computation of the evolution of planet-disc eccentricities over long
timescales. Applying our model to "giant planet + external disc" systems, we
are able to reproduce and explain the secular behaviours found in previously
published hydrodynamical simulations. We re-examine the possibility of
eccentricity excitation (due to secular resonance) of multiple planets embedded
in a dispersing disc, and find that taking into account the dynamics of
eccentric discs can significantly affect the evolution of the planets'
eccentricities.
