新方法计算常微分方程初值问题总体误差

New Method to Calculate Global Error for Initial Value Problem of Ordinary Differential Equations

本文给出了一种简单可靠的计算常微分方程或微分方程组数值解总体误差的方法，并对误差计算的渐进性及其条件作了分析。本文结果表明，当初值误差为零时，用形式简单的梯形公式即可满意地计算各种算法的总体误差。对一些特殊情况，即使初始误差不等于零，也能得到满意的结果。本文还给出了一些数值计算实例，以验证理论推导所得的结果。

This paper presents a simple and reliable method to calculate global error of ordinary differential equations. The results show that, for many algorithm widely used in practice, the global error can be calculated satisfactory when the initial error equals to zero. In this case, a simple trapezoid integral formula for the calculation of global error can give out accurate enough result. In certain special cases, the calculation is also satisfactory even if the initial error is not equal to zero. Several numerical examples were given to verified the conclusion.