四阶杆振动方程的一族高稳定的十字架格式

A Family of Cross Schemes with High Stability for Four-order Rob Vibration Equation

用辛几何的观点得到了四阶杆振动方程的一族十字架辛格式,对于四阶杆振动方程的稳定条件不一定随时间方向的精度的提高而放宽,而随空间方向精度的提高稳定范围缩小。数值例子表明单辛算法具有良好的数值稳定性。

We constructed a femily of cross symplectic schemes for four-order rob vibration equation from the viewpoint of symplectic geometry. The stable conditions of them don't improve with the accuracy bettering of time direction, while decrease in space direction with accuracy bettering. It shows that these schemes are stable during a long time by an example.