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

Alternating Direction Implicit Method for Two-Dimensional Fokker-Planck Equation of Dense Spherical Stellar Systems