. , (13) (1)-(2).
, (13) ,
(14)
( ) , , .
(13)
(15)
. . ( ) (15) (8) (14), .. (15) .
.
(15) i+1. , (15) , (14), . ,
i =0,1,..., n, (16)
.
, , ,
, :
(17)
- . (17) ( -). , (15) i+1, , (i+1).
,
(1)
(18)
y(xi-1) y(xi) i-1 i , (18) y(xi+1)
(19)
.
, ( ) , , (19) . (19) . (11) y'(xi) ,
|
|
(19).
(19) : (19) . i+1 i i-1. , , : h. (19) , , , , , (19). ,
(20)
(19).
1. y(0)=1.
, . , , , , .
. (5)
0 =1 = 0,1, 2 :
, e-3x.
, , y1, y2, y3, .
() =0.2 , h = 0.1 (.. ). , y(0.2) = 0.581881..., .
(8) | 0.7 | 0.51 | ≈0.07 |
(14) | ≈0.7846 | ≈0.6343 | ≈-0.05 |
(15) | ≈0.7478 | ≈0.5788 | ≈0.003 |
(16) | 0.755 | ≈0.5895 | ≈-0.008 |
(19)-(20) | 0.755 | 0.587 | ≈-0.005 |
= () (1)-(2) - , xi (.. -i) x= xi+1.
(21)
(21), , (8). , .
= 2 (21)
(22)
xi (1), :
(23)
(1),
:
(24)
) (22), i=0, 1, , n:
(25)
.
|
|
i=0 (23) (24) , y0 =y (x0), (2), (25) , . , , , (25) o(h3), , .