.


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, , :

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.





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