) 中图学技术大荸学系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS en+=v(n+1)-ynl y(m)yl+hf(n, y(x,))-f(rn,y,)+hII, nr len+hLy(xm)-yn+hTn+ ≤(1+ML)en+h7,T=mx7 <(1+hL(1+hL)e,- +hr)+hT (1+hL)2ln1+(1+hL)+)h7 ≤(1+h)2(1+hL)en2+M)+(+hL)+1 (1+h1)3n2+(1+)2+(+h)+1k7数 学 系 University of Science and Technology of China DEPARTMENT OF MATHEMATICS 1 1 1 ( ) n+ = n+ − n+ e y x y 1 ( ) ( , ( )) ( , )  n − n + n n − n n + hTn+ y x y h f x y x f x y 1 ( )  n + n − n + hTn+ e hL y x y j j  (1+ hL) en + hT , T = max T  (1+ hL)((1+ hL) en−1 + hT)+ hT (1 hL) en 1 ((1 hL) 1)hT 2 = + − + + + (1 hL) ((1 hL) en 2 hT) ((1 hL) 1)hT 2  + + − + + + + (1 hL) en ((1 hL) (1 hL) 1)hT 2 2 3 = + − + + + + + 