一类中立型微分方程单步法的稳定性分析

STABILITICAL ANALYSIS OF THE ONE-STEP METHOD FOR A CLASS OF NEUTRAL-TYPED DIFFERENTIAL EQUATIONS

讨论下列形式的中立型微分方程 (组 ) :(A) x′(t) =F(t,x(t) ,x(g(t,x(t) ) ) ,x′(g(t,x(t) ) ) ) ,t∈ [a ,b],(B) x(a) =x0 ,x′(a) =z0 ,其中z0 是隐式方程z=F(a,x0 ,x0 ,z)的一个实根 .首先给出几个引理 ,然后给出了该方程 (组 )的一种单步方法—改进欧拉法的稳定性证明 .

We consider the following group of neutral-typed differential equations (A) x′(t)=F(t,x(t),x(g(t,x(t))),x′(g(t,(x(t)))),t∈[a,b], (B) x(a)=x 0,x′(a)=z 0, where z o is a real root of the algebraic equation z=F(a,x 0,x 0,z).Several lemmas are presented and the stability of the improved Euler's method is proved.