一阶常微分方程初值问题的算法与实现

The Arithmetic and Solution of Initial Value Problems of First-order Ordinary Differential Equation

针对工程计算中遇到的常微分方程初值问题的求解,以Visual C++6.0为辅助计算工具,并根据高等数学的有关知识将欧拉公式、改进的欧拉公式、经典龙格—库塔方法进行了计算机程序算法的分析与实现,以计算机的速度优势来弥补计算量大的不足。

Aiming at numerical solution of initial value problems of First -order ODE （Ordinary Differential Equation） encountered in the engineering calculation,with the help of Visual C ＋ ＋ 6.0 and based on some knowledge of high mathematics,this article analyses and solves Euler＇s formula,Improved Euler＇s formula,and classic Runge - Kutta Method through computation. It not only depends on the advantages of fast speed of computer to make up the inadequate of enormous calculation, but makes the computational results more reliable and more accurate.