From the HCN observations of dense molecular cloud L694-2, Lee et al.(2007) determined internal distributions of density and velocity for the cloud. The density profile collaborates roughly with the Bonnor- Ebert gas sphere, but the velocity field departs significantly from the result of numerical simulations that are started from the BE sphere. Taking L694-2 as an example of collapsing clouds, we have performed a series of collapse simulations and determined initial configurations for the cloud in such a way that the resulting density and velocity profiles both match with the empirically deduced ones. Among many trial configurations the cloud which is initially uniform in density and bound by an expanding envelop depicts most closely the empirically obtained profiles of both density and velocity.

The Fokker-Planck (FP) model is one of the commonly used methods for studies of the dynamical evolution of dense spherical stellar systems such as globular clusters and galactic nuclei. The FP model is numerically stable in most cases, but we find that it encounters numerical difficulties rather often when the effects of tidal shocks are included in two-dimensional (energy and angular momentum space) version of the FP model or when the initial condition is extreme (e.g., a very large cluster mass and a small cluster radius). To avoid such a problem, we have developed a new integration scheme for a two-dimensional FP equation by adopting an Alternating Direction Implicit (ADI) method given in the Douglas-Rachford split form. We find that our ADI method reduces the computing time by a factor of ~2 compared to the fully implicit method, and resolves problems of numerical instability.