非线性动力方程的增维精细积分法

对线性定常结构的动力系统提出的精细积分法，能得到在数值上逼近于精确解的结果。但是对于非齐次动力方程却涉及到矩阵求逆的困难，而且通常与时间有关的非齐次项不能进入精细积分的细化过程。采用增维的方法，将非齐次动力方程化为齐次方程，在实施精细积分的过程中不必进行矩阵求逆。这种处理方法对于程序实现和提高数值计算的稳定性十分有利，而且在大型问题中可明显提高计算效率，数值算例显示本文方法是有效的。

Increment-dimensional precise integration method for nonlinear dynam icequation

The precise integration method proposed for linear-invari ant dynamic system can give precise numerical results approaching to the exa ct solution at the integration points. However, it is more or less difficult wh en the algorithm is used to the non homogeneous dynamic system due to the in verse matrix calculations, and the non homogeneous vector with relation to tim e variable do not be considered in the process of division of the precise integ ration. In this paper, the original non homogeneous equation is converted into homogeneous equation by means of increment dimensional method. Then, precise i ntegration method can be used and the inverse matrix need not be computed in th e integration. The present method is not only benefit to both programming impl ementation and improving the numerical stability, but also more efficient t o the large scale problem. The numerical examples show the validity and effici ency of the method in this paper.