一种提高增维精细积分法计算精度的方法

提出了一种提高常系数非齐次常微分方程组增维精细积分法计算精度的方法。对于常系数非齐次常微分方程组，一般增维精细积分方法在每一个时间步内把非齐次项当成常数，并取其值为该时间步的初始值。在每一个时间步长内，仍然将非齐次项当成常数，但是该常数的值取为该时间段内不同时刻值的平均值，或者取为中间时刻的值，计算精度得到了很大的改善。数值算例显示了方法的有效性。

A Method to Improve the Calculating Accuracy of Increment-dimensional Precise Integration Method

In this paper, a method to improve the calculating accuracy of increment-dimensional precise integration method is proposed., Generally, for constant coefficient non-homogeneous ordinary differential equations, the inhomogeneous terms was consider as a constant within each time step, and the initial value was chosen as the first value in increment-dimensional precise integration method. At each time step, the inhomogeneous terms was consider as a constant within each time step still, but its value is equal to a average of this time interval, or is equal to the value of intermediate time. So the calculation accuracy has been greatly improved. Numerical example shows the effectiveness of the method.