A flexible leaping-point scheme and a time-splitting method are introduced to the new generation of IAP (Institute of Atmospheric Physics, Chinese Academy of Sciences) atmospheric general circulation model (IAP AGCM-4), and the model's dynamical framework is tested by Rossby-Haurwitz (R-H) wave and by Held-Suarez proposal. The results show that the flexible leaping-point scheme can also conserve the available energy without computational chaos, and it can enlarge the time step especially in the model without filter. A time-splitting method is adopted to compute adjustment process and advection process respectively, and a nonlinear iterative time integration scheme with 3 times iteration is applied to both the processes. The time-splitting method can economize CPU time by 10.7% (N=5) and 19.9% (N=10), respectively. As R-H-type pattern of wave number 4 is taken as the initial condition, in the first 80 days of integration, the dynamical framework can preserve the wave pattern well, and the total available energy only reduce 0.1%. From the 80th day, the wave pattern of zonal wind becomes deformed and then breaks, while the corresponding kinetic energy and total available energy begin to decrease sharply. By the 365th day, the fields of zonal wind and geopotential height become parallel to the longitudinal direction, and the total available energy has decreased 8%. The analysis shows that it is due to the rotational adaption and the dissipation of advection term. The test by Held-Suarez proposal also shows the reliability of the dynamical framework of IAP AGCM-4.