  The previously developed Flux-Vector-Splitting (FVS) method was formulated
here for the first-order version of Z4 formalism. Then, the characteristics of
this method formulated for Z4 formalism were studied by numerically analyzing
the evolution of two types of black holes (free and stuffed). Finally, these
numerical results from the FVS method were compared with those from the Local
Lax Friedrichs and Modified Local Lax Friedrichs methods to reveal the
dependency of numerical solution by Z4 formalism on the choice of numerical
scheme.
