  A method for following fragmentation simulations further in time using
smoothed particle hydrodynamics (SPH) is presented. In a normal SPH simulation
of the collapse and fragmentation of a molecular cloud, high-density regions of
gas that form protostars are represented by many particles with small
separations. These high-density regions require small time steps, limiting the
time for which the simulation can be followed. Thus, the end result of the
fragmentation can never be definitively ascertained, and comparisons between
cloud fragmentation calculations and the observed characteristics of stellar
systems cannot be made. In this paper, each high-density region is replaced by
a single, non-gaseous particle, with appropriate boundary conditions, which
contains all the mass in the region and accretes any infalling mass. This
enables the evolution of the cloud and the resulting protostars to be followed
for many orbits or until most of the original cloud mass has been accreted.
