, , :
h= 1.0.
h = 1.0
:
:
,
h = 0.5 h = 0.25, , , , , . 1.
1
h | IT | Ε | |
1,0 | 2,3484 | 0,0441 | |
0,5 | 2,3813 | 0,0112 | |
0,25 | 2,3898 | 0,0027 | |
h | IS | Ε | |
1,0 | 2,3743 | 0,0182 | |
0,5 | 2,3923 | 0,0002 | |
0,25 | 2,3926 | 0,0001 | |
IG | Ε | ||
2,0536 | 0,3389 | ||
2,4471 | 0,0546 | ||
2,3859 | 0,0066 | ||
2,3931 | 0,0006 | ||
2,3925 | 0,0000 |
, - , , .
1. n , 2n .
2. n , 2 .
, , .
3. , , .
4. , .
, , , , . , e-0.5, e-0.16667. .
. , , , . (. 14).
, ; . , . , . , , . , .
|
|
9 8:
, .
( ) .
/2,
. , . , 4*10-5 7*10-5 . ,
.
, .
, , . 100, ,
, EFF , TEMPI 2 TMPINC. A B, . N, . , N .
- . 6. , , : H - , 1. . . , SUM4, , 4; , SUM2, 2. X + ( SUM4) ( SUM2), X .
. X . , X , . . , X , . -, 4 , 2. , , . -, X A + H 2, X B 3.
|
|
I. I 1. ( I, .) , , , . ,
. 6. - . ( 8).
I X . , EFF. SUM 4 , 4, , . SUM 2 , 2. , . , EFF , , , 4 2, /3 64.77/4.
TEMPING TEMP 2. TEMP 2, . . , . , .
. 7. , , , -.
. 6.7. . ( 8).
(. . 6), , . -,
, . 3a - , .
. (18) ,
, , , N = 10, N = 20, . , , N .
= 3500 . 10 , 14.512723%, 20 14.512664%. , .
. 6.8. () ( 8).
, , , . 6.8. , , 2000 C, (3600 ) 15% 7000 . . , , , , , , , , .
|
|
1. , h = 1.0 h = 1.0. f(x) :
2. : <=x<=b f"(x)>0, , , , . (, f(x) .)
3. . , h = 1 , .
4. . , , h = 0.5, ( 1/3000). , .
5. 4, . , , . .
N | h | IS | |
0.45 | 3.3500 | -1.0474 | |
0.225 | 2.4079 | -0.1053 | |
0.1125 | 2.3206 | -0.0180 |
6. , . . (18) , . ?
7.
K(30), . 1.6858. (85), . 3.832. (85) , (30) ?
8. [4]
. , h . h=0.25, 0.1, 0.05, 0.02 0.01. h. (, , , , .)
9.*
:
. 6 ;
. 10 ;
. 10 ;
. 18 10 . . : 0 10 10 0? ?
|
|
10.* 9.
11. 10 , a, b n h.
12. 11 , n . n . (: ; N , (N/2)*2 N.)
13. , . 7, , , . .
14. , , . 7, , . , SUM4 SUM2, , , 2. , . , , , N, ; . , , .
15. , a0, a1, a2, a3, a4, a5 a6 a, b n, . n .
16. , . 7, , , , . , EFF (T1) < EFF (T2) > EFF (T3), . , .
17. , x = -h, 0 h = 0, y1 y2. =+b+2 , b . a, b c, h h ,
.
18. n . , f(x) (. ).
19. , , 18, .
20. , , 18, , 19, .
.
21. 20
. , .
22. , , , :
23. , n=3m, . . 3. , A, , k=3h.
. , , .
. - ?
24. , n = 4m. , h k = 2h.
|
|
( , ).
25. , f(x) . , φ(x) 3, I
. , 0 x1 .
, , (. 6).
26. , f(x) 3,
(: , . 25)
27. , f(x) . , φ() 3, .
. , , φ, . .
: , .
28.
. , (, ).
29*. . ,
;
;
.
.
30. , , y () x.
x | y | x | y |
1.0 | 1.00 | 2.2 | 5.12 |
1.2 | 1.82 | 2.4 | 6.38 |
1.4 | 2.08 | 2.6 | 6.98 |
1.6 | 3.18 | 2.8 | 8.22 |
1.8 | 3.52 | 3.0 | 9.00 |
2.0 | 4.70 |
, :
. ,
. ,
. 1.0 1.2 2.8 3.0 1.2 2.8.
x , , ? 31. , y () .
x | y | X | Y |
0.21 | 0.43 | ||
0.30 | 0.37 | ||
0.37 | 0.33 | ||
0.45 | 0.29 | ||
0.49 | 0.25 | ||
0.50 | 0.19 | ||
0.49 | 0.13 | ||
0.47 | 0.08 | ||
0.45 | 0.04 |
, .
[1] Alt F., Electronic digital computers, Academic Press, New York, 1958, p. 203205; pa1 Z., Numerical Analysis, Wiley, New York, 1961, p. 370386.
[2] Richardson L. F.,Gaunt J. A., The deferred approach to the limit, Trans. Roy. Soc. London, 226 A, 300 (1927).
[3] ., . 3 : ildebnd F. ., Introduction to numerical analysis, McGraw-Hill, 1956
[4] Scarborough J. ., Numerical mathematical analysis, The Johns Hopkins Press, 1950.