Abstract: The alternating group iterative method for the dispersive equation with periodic boundary condition is presented. A twolevel implicit difference scheme is designed, and an alternating group iterative method is suggested which is capable of parallelism on parallel computer. In addition, unconditional stability of the difference scheme and convergence of the iterative process are proved. The alternating group iterative method is used to solve the implicit scheme and the Crank-Nicolson scheme of the dispersive equation. The results show that this method has good accuracy and practicability.

Key words: parallel computation , unconditionally stable, alternating group iterative method, dispersive equation