常微分方程初值问题的一种改进单步方法

AN IMPROVED SINGLE STEP SCHEME OF ORDINARY DIFFERENTIAL EQUATION IN INITIAL VALUE PROBLEM

针对一类常微分方程初值问题 u′=a( t) u+f ( t) ,u( 0 =α,用 Hermite插值积分 ,获得了一种改进的 4阶单步方法 ,并证明了该格式的稳定性和收敛性 ,数值实验表明 ,与 4阶 Runge- Kutta方法、4阶 Gear方法相比 ,时间步长较大时 。

An improved single step scheme of fourth order,for a class of ordinary differential equation in initial valueu′ a(t)u+f(t),u(0)=α ,is proposed with a Y Hermite interpolation integral.This paper proves the convergence and stability of this method.Numerical experiment show that this method also has a better precision with larger steplength,compare with the forth order Runge-Kutta scheme and forth order Gear scheme.