  We present a model of a viscously evolving accretion disc around a magnetized
neutron star. The model features the varying outer radius of the hot ionized
part of the disc due to cooling and the varying inner radius of the disc due to
interaction with the magnetosphere. It also includes hindering of accretion on
the neutron star because of the centrifugal barrier and irradiation of the
outer disc and companion star by X-rays from the neutron star and disc. When
setting inner boundary conditions, we take into account that processes at the
inner disc occur on a time scale much less than the viscous time scale of the
whole disc. We consider three types of outflow from the disc inner edge: zero
outflow, one based on MHD calculations, and a very efficient propeller
mechanism. The light curves of an X-ray transient after the outburst peak can
be calculated by a corresponding, publicly available code. We compare observed
light curves of the 2013 burst of Aql X-1 in X-ray and optical bands with
modeled ones. We find that the fast drop of the $0.3-10$ keV flux can be solely
explained by a radial shrinking of the hot disc. At the same time, models with
the neutron star magnetic field $>10^8$ G have better fits because the
accretion efficiency behaviour emphasizes the 'knee' on the light curve. We
also find that a plato emission can be produced by a disc-reservoir with
stalled accretion.
