预备知识： y'(x)=f(xy.) ++) yx)+以=+时fy) k =hf(xy) Ox ay dx Ox ay k,=hf(x +h,y +k) 预报一校正公式截断误差分析 假设y(x,)=y,k=hf(x,y)=hf(x,(x,)》=hy'(x,) k =hf (x,+h,y +k)=hf(x,+h,y(x)+k) ay =x)+h+h+o) Ox ay dx hly'(x,)+hy"(x,)+(h) 预报—校正公式截断误差分析        = + + = + = + + ( , ) ( , ) ( ) 2 1 2 1 1 1 1 2 k hf x h y k k hf x y y y k k n n n n n n ( ) ( , ) ( ) ( , ) n n n n n n f x y y f x f dx dy y f x f y x y x f x y   +   =   +    =  = 预备知识： ( , ) ( , ( )) ( ) 1 n n n n n 假设y(x n ) = yn k = hf x y = hf x y x = hy x  ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( , ( )) ( , ) ( , ( ) ) 2 2 2 1 2 1 1 h y x hy x O h O h dx dy y f h x f h y x h y x O h y f h x f h y x h y f k x f h f x y x h k hf x h y k hf x h y x k n n n n n n n n n n n =  +  +       +   +   =  +        +   +   =  +       +   +   = + = + + = + + 