The completion ('initiation' de facto) of the KASI Orbit Propagator and Estimator (KASIOPEA) has been delayed for several reasons unfortunately. Due to the lack of working staffs and the Division priority rearrangement, the initial plan was dismantled and ignored for many years. However, fundamental researches regarding the essential parts of KASIOPEA has been done by author. The numerical integration module of the KASIOPEA is the most sensitive part in the precision of the final output in general. There is no silver bullet in the numerical integration in an orbit propagation as a non-stiff ODE case. Many numerical integration method like single-step methods, multi-step method, and extrapolation methods have been used in overly populated orbit propagator or estimator. In this study, several popular methods from single-step, multi-step, and extrapolation methods have been tested in numerical accuracy and stability.