  We present an efficient new computational method for calculating the binding
energies of the bound states of ultracold alkali-metal dimers in the presence
of magnetic fields. The method is based on propagation of coupled differential
equations and does not use a basis set for the interatomic distance coordinate.
It is much more efficient than the previous method based on a radial basis set
and allows many more spin channels to be included. This is particularly
important in the vicinity of avoided crossings between bound states. We
characterize a number of different avoided crossings in Cs_2 and compare our
converged calculations with experimental results. Small but significant
discrepancies are observed in both crossing strengths and level positions,
especially for levels with l symmetry (rotational angular momentum L=8). The
discrepancies should allow the development of improved potential models in the
future.
