Abstract:Based on the classical Magnus series method,This paper proposed a simple and efficient fourthorder integrator for solving the general nonlinear dynamic systems.The method is a kind of geometric integration method and can preserve many main qualitative porperties of the exact solution.The method involves only two or three matrix exponentials and thus avoids a lot of complex commutators involved in the Magnus method.The numerical examples were given to demonstrate the validity and effectiveness of the proposed method.