解常微分方程的稳定的显式单步法

A stable explicit one-step method for solving ordinary differential equation

应用函数P(x)=1A+Bx+C来近似初值问题dydx=f(x,y),y(x0)=y烅烄烆0的解,应用积分,得到了一个0烆0求解微分方程的一个新方法,它是求解常微分方程的一个显式方法,是一个单步法,最重要的是它dydx=λy,y(0)=y0,(λ<0)是稳定的,数值试验表明该方法简单有效。

In this paper,function P（x）=1A＋Bx＋C is the approximation solution of the ordinary differential equation dydx=f（x,y）,y（x0）=y0. With the integral applied,a new numerical method of ordinary differential equation is proposed.It is a stable explicit one-step method for soving ordinary differential equation.The most impotant thing is that it is stable when the method is applied to the test eqution dydx=λy, y（0）=y0（λ0）.The numerical experiments show that the method is effective.