变量代换在常微分方程初值问题中的应用

本文在常微分方程初值问题的数值解中，引入了理想变量代换和准理想代换的概念，并给出了几种建立代换的方法。对于方程数量巨大、解曲线形状类似、计算速度又十分重要的场合，只要对数值解中的典型曲线进行分析，即可以建立起适当的变量代换。这样，在求其他解的时候，就可以应用该变量代换，使计算速度有大幅度的提高。

The application of variable transformation in the initial value problem of ordinary differential equations

The concept of ideal variable transformation and quasi ideal variable transformation is introduced in the initial value problem of ordinary differential equations. Some methods to construct the transformation are also proposed. If the number of equations is huge and the shapes of solutions are similar with each other, the speed of calculation can be much faster than that of conventional method using the transformation based on any one of solutions.