一阶常微分方程泰勒级数解法的计算机实现

The Computer Realization of Solution With Taylor Series for First-Order Ordinary Differential Equations

本文在微分运算精确解算法的基础上提出的计算公式和算法,使一阶常微分方程的泰勒级数解法得以在计算机上实现,为求解一阶常微分方程提供了一种新的比较可靠的数值方法。文中还给出了几个例子,把泰勒级数解法与龙格-库塔法的解题结果进行了比较。

In this paper a set of formulae and an algorithm are proposed on the basisof the algorithm of precise solution to differentiating operation. They makepossible that the computer realization of solution with Taylor series for first-order ordinary differential equations, providing a new and relatively reliablenumerical method for the solution of equations. Examples are also presented,and the results of the Runge-Kutta method as compared with the Taylor seriesmethod.