将区域[a,b进行分划: x0=a,x=a+九h,=1,2,…,N b=a 称为步长 y(x)=y(x)+」f(x,yx)h x ≈y(x)+hf(,y(5) v(x,)+h2b f(r, +c, h,y( ; +ch)
1 1 ( ) ( ) ( , ( )) ( ) ( , ( )) i i x i i x i y x y x f x y x dx y x hf y + + = + + 1 ( ) ( , ( )) n i j i j i j j y x h b f x c h y x c h = + + + 1 1 n j j b = = 将区域[a,b]进行分划： 0 , , 1,2,..., . x a x a jh j N j b a h N = = + = − = 称为步长
若 k,=f(x,+ch, y(+ch)sf(x, y(x )) k,=f(; +C,h,y(x,+c,h)af(r, y(x)) k,=f(+c,h,(, +c,h)af(x, y( )
若则 1 1 1 2 2 2 ( , ( )) ( , ( )), ( , ( )) ( , ( )), ...... ( , ( )) ( , ( )). i i i i i i i i n i n i n i i k f x c h y x c h f x y x k f x c h y x c h f x y x k f x c h y x c h f x y x = + + = + + = + +