Abstract: In this paper the calculation accuracy of precise symplectic integration method is discussed. At first, the two and four degree accuracy algorithms are analyzed and the relation of the error to the value of the precise integration number is obtained.Then, the accuracy of any degree precise symplectic algorithm is also discussed and the obtained result is the same and simple. The total error of the method can be approximately written in the calculation error of one time step multiplied by the integration number. Finally, the appropriate integration number is estimated at the control accuracy. It can be found that by this method the accuracy of precise symplectic integration will no longer be controlled by the value of the time step.

Key words: Symplectic algorithm, Precise integration method, Accuracy analysis