Flux-Vector-Splitting (FVS) method for Z4 formalism and its numerical   analysis
  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. 
Ryosuke Yano, Kojiro Suzuki, Hisayasu Kuroda