  We study the stability of disc accretion in the recurrent nova RS Ophiuchi.
We construct a one-dimensional time-dependent model of the binary-disc system,
which includes viscous heating and radiative cooling and a self-consistent
treatment of the binary potential. We find that the extended accretion disc in
this system is always unstable to the thermal-viscous instability, and
undergoes repeated disc outbursts on ~10-20yr time-scales. This is similar to
the recurrence time-scale of observed outbursts in the RS Oph system, but we
show that the disc's accretion luminosity during outburst is insufficient to
explain the observed outbursts. We explore a range of models, and find that in
most cases the accretion rate during outbursts reaches or exceeds the critical
accretion rate for stable nuclear burning on the white dwarf surface.
Consequently we suggest that a surface nuclear burning triggered by disc
instability may be responsible for the observed outbursts. This allows the
white dwarf mass to grow over time, and we suggest that disc instability in RS
Oph and similar systems may represent a path to Type Ia supernovae.
