  The dynamics of a viscous accretion disc subject to a slowly varying warp of
large amplitude is considered. Attention is restricted to discs in which
self-gravitation is negligible, and to the generic case in which the resonant
wave propagation found in inviscid Keplerian discs does not occur. The
equations of fluid dynamics are derived in a coordinate system that follows the
principal warping motion of the disc. They are reduced using asymptotic methods
for thin discs, and solved to extract the equation governing the warp. In
general, this is a wave equation of parabolic type with non-linear dispersion
and diffusion, which describes fully non-linear bending waves. This method
generalizes the linear theory of Papaloizou & Pringle (1983) to allow for an
arbitrary rotation law, and extends it into the non-linear domain, where it
connects with a generalized version of the theory of Pringle (1992). The
astrophysical implications of this analysis are discussed briefly.
