Based on the seven point central dispersion relation preserving (DRP) space discretization scheme, and combined with five kinds of Runge-Kutta time integration scheme, the dissipation and dispersion errors induced by time and global discretization schemes, the effective wave number ranges, the error propagation of long distance, the accumulated error of low, middle and high frequency wave were analyzed by using traditional Von Neumann method and a new correct error propagation method from three aspects, i.e., error component, error propagation, and error accumulation. In addition, the advantage and disadvantage of all the combined schemes were compared by analyzing their stability and accuracy. The accuracy of ORK6 time integration scheme combined with seven point central space discretization scheme was the highest among these combination schemes. Finally, a few numerical tests were presented to show the accuracy of these schemes in simulation of one dimensional scalar and vector wave motion.