中文摘要：

利用已存在的三阶最优化力梯度辛格式以对称组合方法获得两个新的四阶力梯度辛积分器.它们在求解摄动Kepler混沌问题的能量精度和一维定态Schrdinger方程的能量本征值精度方面比Forest-Ruth四阶非力梯度辛积分器要好得多,甚至还要明显优越于已有的四阶最优化力梯度辛积分器。

英文摘要：

This paper provides two new fourth-order force gradient symplectic intrgrators,each of which is obtained from a symmetric product of two identied optimal third-order force gradient symplectic algorithms reported in the literature.They are both greatly superior to the fourth-order non-gradient symplectic method of Forest and Ruth in the accuracy of either energy on chaotic perturbed Kepler problems or the energy eigenvalues for one-dimensional Schrdinger equations.So are they to the known optimalfourth-order force gradient symplectic scheme.