  We perform simulations in a gravitational collapsing model using the Einstein
equations. In this paper, we review the equations for constructing the initial
values and the evolution form of the Einstein equations called the BSSN
formulation. In addition, since we treat a nonvacuum case, we review the
evolution equations of the matter fields of a perfect fluid. To make the
simulations stable, we propose a modified system, which decreases numerical
errors in analysis, and we actually perform stable simulations with decreased
numerical errors.

General Relativity and Quantum Cosmology