精细时程积分法的误差分析与精度设计

通过对精细积分法递推过程的误差分析，发现该方法能莸得高精度数值结果的根本原因是：数值计算的相对误差不随递推过程的进行而扩散。数值结果的精度仅仅取决于初始Taylor级数的计算精度和指数矩阵A的最大模特征。同时，提出了一种精度估计和精度设计的方法。

Error analysis and accuracy design for the precise time-integration method

By means of error analysis of recursion process of precise integration, the authors discover the essential reason of obtaining the high precise numerical results of exponential matrix exp(A) in the precise time-integration method , which is that the relative error of numerical computation is not enlarged in a whole recurrent process. The accuracy of numerical results only depends on the computational accuracy of initial Taylor series and maximum modulus eigenvalue of matrix A. Meanwhile, a kind of particular method of accuracy estimating and accuracy designing is also proposed in the present paper.