辛算法应用于Duffing方程的保结构性

Structure-Preserving Properties of Symplectic Algorithms for Duffing Equation

讨论了不受外力的Duffing方程在辛算法和非辛算法作用下，相轨线被保持和破坏的性质。证明了当时间步长充分小时，辛算法可以保持原系统的大部分不变闭曲线，而非辛算法却做不到这一点。

In this paper, we discuss the properties of the phase orbits of Duffing equation that are preserved or destroyed under symplectic and non-symplectic discretizations. We prove that symplectic algo- rithms may keep most of the invariant curves of Duffing equation when the time-step is small enough but non-symplectic algorithms cannot.