1, 2, 3, 4
220201
2011
: ..
..
..
" ".
4 "" 220201 . , .
- , ( ).
: .. ,
, ( ), 2011
1
. . .
, , , . , . , , , , , . , , , , ,
- , . , , , , .
, y=f(x) 1
|
|
(x 1 1 ).
= 0, , ,
1 .
, . .
, .
, . , . .
, , , . :
?
?
?
?
2.1
. , . .
n,
(1.1)
n +1 . , n +1 , , . , , n +1 (xi , yi) (i= 1,2, , n +1) xi ,≠ xj. , (xi , yi)
(1.2)
n +1 , , xi ,≠ xj i ≠ j
(1.3)
n +1 (xi, yi) , .
, , n + 1 , , ( ) . , , : , , . .
. , , 1 0 . ,
(1.4)
( i ≠ j j ) ; 1, x=xj 0, x=xi, i ≠ j.
yi i -
. ,
|
|
(1.5)
, + 1
(xi, yi). , : + 1 , , , ( ) , , .
2.2
.
( ) . , , , , , .
, . , , . . .
, , x1 = x0+h, x2=x0+2h, xm= x0+mh. h . . , .
f(x) 0, 1 = 0 + h,..., = 0 + nh ( ).
y1 ─ y0 =
y2 ─ y1 = (1.6)
..
Yn ─ yn-1 =
, . , k, k-e
Δkym = Δk-1ym-1─ Δk-1ym (1.7)
xi | yi | Δ1ym | Δ2ym | Δ3ym | Δ4ym | Δ5ym |
x0 | y0 | Δ1y0 | ||||
1 | y1 | Δ1y1 | Δ2y0 | |||
x2 | y2 | Δ1y2 | Δ2y1 | Δ3y0 | ||
x3 | y3 | Δ1y3 | Δ2y2 | Δ3y1 | Δ4y0 | |
x4 | y4 | Δ1y4 | Δ2y3 | Δ3y2 | Δ4y1 | Δ5y0 |
y=f(x ) x0, x1=x0 + h, x2 = x0 +2 h,, xn=x0 + nh. y y0 = f(x0), y1 = f(x1), , yn=f(xn). F () , , F (xk)=yk (k = 0, 1 ,, ). , , , , .
(1.8)
0,1,...,
=x. , =1,
(x1 ̣─ x0)= h
,
=2.
0, 1
, ,
(1.9)
1.8,
(1.10)
-
.
. (4.13) - . (. . ) - . , , . , . , . , .
|
|
(2.16)
. ,
x=x0 + th (1.11)
, (2.16), t
..
(1.10),
(1.12)
. ,
,
.
, , , , .
.
(1.13)
(),
(1.14)
(1.13)
(1.15)
. , , , .
x = xn + th
,
(1.16)
(7.16) .