  In this paper we investigate the asymptotic behavior of the cosmological
model based on phantom scalar field on the ground of qualitative analysis of
the system of the cosmological model's differential equations and show that as
opposed to models with classical scalar field, such models have stable
asymptotic solutions with constant value of the potential both in infinite past
and infinite future. We also develop numerical models of the cosmological
evolution models with phantom scalar field in this paper.
  {\bf keywords}: cosmological model, phantom scalar field, quality analysis,
asymptotic behavior, numerical simulation, numerical gravitation.\\ {\bf PACS}:
04.20.Cv, 98.80.Cq, 96.50.S 52.27.Ny
