Symplectic precise integration method for duffing equation

The symplectic precise integration method owns the advantages of the symplectic method and the precise integration method. In the implementation procedure of which, matrix inversion is a time-consuming step. Aiming at this problem, we homogenize the inhomogeneous equation approximately before the design of the symplectic precise integration method in this paper. The homogenizing process makes the matrix inversion time-independent and reduces the calculated quantity of the matrix inversion process, which is used in the symplectic precise integration method of the non-damping Duffing equation in this paper. From the numerical results, we can conclude that: The symplectic precise integration method is superior to the classic Runge-Kutta method in the numerical precision, the energy-preserving property and time-consuming; Comparing with the symplectic method, the energy can be preserved in the numerical simulation of the symplectic precise integration method.