, , . , () i = 0 + ih (i=0,1,..., ) [ x0, b ]
yi = () (1)-(2) i.
. , 0 (0) = 0 ( (2)), '(x)=f(x0, y0) ( (1)), y= () (0;y0):
(6)
h
(7)
, (6) (1) () (1)-(2). , (1, 1) (6) x=x1 .
=() (1,(1)). =2(=1 + h), , = 2, (2)
.. ,
i = 0,1,..., (8)
, = () (1)-(2) , (. 1), (8) .
. 1.
. . ,
= 1
(9)
(9),
, ( (7)),
(10)
ξi (x0, x1).
(10) (, , ) , .. , . , , .. (8), . , .. b, . ( h) , , . , , (10), 0(h), .. .
. (1) x0 (2)
(9), 1 (7) (10). , (8) (6.16)
|
|
(11)
y(xi) yi.
, (1)-(2) (1).
. (1)-(2) (3). =1
(12)
(12) ()
, , (7) 1. (8)
(13)
, i- (x0,y0) (xi, yi). (13) , , .
. , (1)-(2).