一种新的三阶非力梯度辛积分算法

基于分部的Runge-Kutta离散形式,引入了相位误差最小的思想,给出了一种新的三级三阶非力梯度辛积分算法,并通过数值试验与经典的Ruth、McLachlan&Atela以及Iwatsu的三级三阶非力梯度辛算法从稳定性、长时程、保结构性等方面进行了对比.结果显示新推导的三级三阶非力梯度辛算法稳定性较好、长时程运算误差小,表明该算法具有好的保结构性和较强的长时程跟踪能力.进一步通过数值试验与力梯度辛算法比较,也显示出该算法的有效性和具有较高的精度.

A New Solution to the Third-Order Non-Gradient Symplectic Integration Algorithm

In this paper,a new solution to the three-stage third-order non-gradient symplectic integration algorithm is given based on the minimum phase error principle and the partitioned Runge-Kutta form.Several other non-gradient methods,such as Ruth’s,McLachlan&Atela’s and Iwatsu’s symplectic integration algorithm of three-stage third-order,are employed to compare the performance with the present algorithm by numerical experiments.The numerical results show that the present algorithm is good at stability,and much superior to the other methods in the features of long-time computing ability.The further numerical experiments is used to compare the algorithm with above non-gradient symplectic methods and some force-gradient symplectic methods,the results also show that the algorithm is effective with high accuracy.These appealing features of the algorithm would make it effective to have the ability of structure-preserving and long-time tracing.