首先将非线性薛定谔方程变形为齐次方程的形式，然后用精细积分法模拟其随时间的演化过程。

First of all, a non-linear Schrodinger equation can be converted into homogeneous equations, and then the precise integration method can be used to solve these problems.

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本论文以动态刚度矩阵和精细时程积分法为基础，分析了内燃机轴系的三维耦合振动形式。

In this thesis, 3-d coupling vibrations of internal combustion engine shafting are presented basing on dynamic stiffness matrix and precise time-integration method.

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