§4 Multistep Method 例:设pn=an1+aa1+a22+M(只y十y1+月y2+月y3 确定式中待定系数a,a,a2,A,B,月2,B,使得公式具有4阶 精度。 解:y-=y-hy+是h2y-是y+hy+O(h) Vi-2=y:-2hy'+2h2y-ih'y+2hty(+O(h) yi=y; -hy+2hym-6h'yi+o(h) yi_r=yi-2hy+2h y th'yi+o(h) ′3=y-3hy"+2h2ym-2h3y24)+O(h) y(xm1)=yi+hy+jhy+hv +1h'y()+o(h5)/*y(x )=yi* Ca+a1+a2=1 h(-a1-2a2+B+B1+B2)=h 7个未知数 h2(a1+2a2-B1-2B2-363)=lh h(-a1-a2+1月+2B2+263)=4h 5个方程 h(2a1+3a2-B1-月2-2B3)=是h例：设 ( ) +1 0 1 -1 2 -2 0 1 -1 2 -2 3 -3 = + + + +  +  + i i i i i i i i y a y a y a y h b y b y b y b y 确定式中待定系数a0 , a1 , a2 , b0 , b1 , b2 , b3 , 使得公式具有4阶 精度。 §4 Multistep Method 解： ( ) 4 (4) 5 2 4 3 1 6 2 1 2 1 yi-1 = yi - hy i + h y i - h y i + h yi + O h 2 2 ( ) 4 (4) 5 3 3 2 3 2 4 yi-2 = yi - hy i + h y i - h y i + h yi + O h ( ) 3 (4) 4 6 2 1 2 1 y i-1 = y i - hy i + h y i - h yi + O h 2 2 ( ) 3 (4) 4 3 2 4 y i-2 = y i - hy i + h y i - h yi + O h 3 ( ) 3 (4) 4 2 2 9 2 9 y i-3 = y i - hy i + h y i - h yi + O h ( ) ( ) 4 (4) 5 2 4 3 1 6 2 1 2 1 y xi+1 = yi + hy i + h y i + h y i + h yi + O h /* y(xi ) = yi */ a0 +a1 +a2 = 1 h(-a1 - 2a2 + b 0 + b1 + b 2 ) = h 2 2 1 2 1 2 1 2 3 2 1 h ( a + 2a - b - 2b - 3b ) = h 3 6 1 2 3 9 2 1 2 1 3 2 4 6 1 3 1 h (- a - a + b + 2b + b ) = h 4 2 4 1 2 3 9 3 2 4 6 1 1 3 2 2 2 4 1 4 1 h ( a + a - b - b - b ) = h 个未知数 个方程 7 5