In order to establish a dynamical explicit method with higher accuracy and better stability, explicit method of double time steps and corrected explicit method of double time steps are proposed through integration under the assumption of linear acceleration in two time steps. The stability, accuracy and truncation error analysis are performed on the two new methods. At last, a numerical example is utilized for the comparison of the two new methods, the central difference method and the analytical solution. The results show that explicit method of double time steps is unstable under undamped condition, however，corrected explicit method of double time steps has the same stability condition of central difference method. The amplitude error of explicit method of double time steps is bigger than the corrected explicit method of double time steps and the central difference method when the time step is long. The corrected explicit method of double time steps possesses excellent comprehensive properties with less damping ratio error and periodic error than the central difference method in case of short time step.
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