III 5
5
: .
- (6) , , .
x | x 1=0. | x 2=2. | x 3=3. | x 4=5. | x5 =7. | |
f (x) | 1. | 0. | 2. | 3. | 5. |
- (4) , , .
x | x 1=0.5 | x 2=0.6 | x 3=0.8 | x 4=1. | |
f (x) | 0.378 | 0.225 | 0.103 | 0.460 |
- (4) 10-3:
- (6) . .
- (4) , 10-5.
- (6) , , , . .
x | x 1=0. | x 2=0.125 | x 3=0.25 | x 4=0.375 | x 5=0.5 | x 6=0.625 | x 7=0.75 | x 8=0.875 | x 9=1. |
f (x) | 0.000000 | 0.124670 | 0.247234 | 0.364902 | 0.473112 | 0.563209 | 0.616193 | 0.579699 | 0.000000 |
- (5) 10-4.
8 *. (5) A = A T>0, . , α α >0.
9 *. (6) , ε=10-2 , . .
10 *. (6) .
1
1.
2. x =1.850.
3. . Max
6. , I h=1.603144, I 2h=1.596321, I R=1.605418, I S=1.605418
9. . , , . : , :
2
1.
2. x =0.213.
3. . Max
6. , I h=0.3669885, I 2h=0.371737, I R=0.365406, I S=0.365406
9. . , , . (1000 ): 0.856, :
3
1.
2. x =0.243.
3. . Max
6. , I h=1.519006, I 2h= 1.5429765, I R= I S=1.511016
9. . , , . : , : 9/5=1.8
|
|
4
1.
2.x=0.1054
3. . Max
6. , I h=1.575095, I 2h=1.572338, I R=1.576014, I S=1.576014
9. . , , . (1000 ): 0.923, :
5
1.
2. x =0.7311
3. . Max
6. , I h=0.371127, I 2h=0.334135, I R=0.383458, I S=0.383458
9. . , , . : , :
:
x | x 1=0. | x 2=0.125 | x 3=0.25 | x 4=0.375 | x 5=0.5 | x 6=0.625 | x 7=0.75 | x 8=0.875 | x 9=1. |
f (x) | 0.909091 | 1.007266 | 1.139113 | 1.278655 | 1.443376 | 1.643421 | 1.889822 | 2.151657 | 0.000000 |
, , . I h=1.375982, I 2h=1.231714, I S= I R=1.424071. , .
- ( h 2) .
:
h 2 | I | Δ1 | Δ2 |
(0.5)2=0.25 | 0.948961 | ||
-1.508016 | |||
(0.25)2=0.0625 | 1.231714 | 6.697392 | |
-3.0777173 | |||
(0.125)2=0.015625 | 1.375982 |
I =1.430612, (3,67%).
:
h 2 | I | Δ1 | Δ2 |
(0.5)2=0.25 | 1.113765833 | ||
-1.131730222 | |||
(0.25)2=0.0625 | 1.32596525 | 4.1011788 | |
-2.092944 | |||
(0.125)2=0.015625 | 1.424072 |
I =1.460779, (1,64%), .
, :
h 2 | I | Δ1 | Δ2 | Δ3 |
(0.25)2=0.0625 | 1.32596525 | |||
-2.092944 | -79.845679 | |||
(0.125)2=0.015625 | 1.424072 | 23.7507015 | ||
-3.484586666 | ||||
(0.0625)2=0.00390625 | 1.464907 |
I =1.479968, 0,35%.
I =1.480273, 0,33%. , : 1.36%.
, :
|
|
h 2 | I | Δ1 | Δ2 |
(0.1)2=0.01 | 1.442913 | ||
-3.7344000 | |||
(0.05)2=0.0025 | 1.470921 | 137.78488888 | |
-5.02613333 | |||
(0.025)2=0.000625 | 1.480345 |
I =1.483702, (0,096%).
.
- .
- , , ?
- A = A T>0, . , α α>0.
- A x =f c
- x=x 0 x=x 0, x=x 1= x 0+ h, x=x 2= x 0+2 h ; 1) 2) .
10.* f(x)
x 0= 0. | x 1=1. | x 2=2. | x 3=3. | x 4=4. |
1.00000 | 0.86603 | 0.50000 | 0.00000 | 0.50000 |
) , , x=x 0 x=x 4. x *=1.5.
)
1 - x=1.5
x 0= 0. | x 1=1. | x 2=2. | x 3=3. | x 4=4. |
0.00000 | 0.50000 | 0.86603 | 1.00000 | 0.86603 |
2 - x=0.8
x 0= 0.1 | x 1=0.5 | x 2=0.9 | x 3=1.3 | x 4=1.7 |
2.3026 | 0.69315 | 0.10536 | 0.26236 | 0.53063 |
3 - x=3.0
x 0= 0. | x 1=1.7 | x 2=3.4 | x 3=5.1 | x 4=6.8 |
0.00000 | 1.3038 | 1.8439 | 2.2583 | 2.6077 |
4 - x=0.1
x 0=--0.4 | x 1=--0.1 | x 2=0.2 | x 3=0.5 | x 4=0.8 |
1.9823 | 1.6710 | 1.3694 | 1.0472 | 0.64350 |
5 - x=1.5
x 0= 0. | x 1=1. | x 2=2.0 | x 3=3.0 | x 4=4.0 |
1.00000 | 1.5403 | 1.5839 | 2.0100 | 3.3464 |
1. [1,2] a=0.5 b=0.451808 c=0.0722874 d=0. 134956 f(x)=0.706145
2. [0.5,0.9] a=0.693147 b=2.72502 c=4.86964 d=4.32685 f(x)= 0.197082
3. [1.7,3.4] a=1.30384 b=0.535474 c=0.204257 d=0.0447927 f(x)=1.75317
4. [0.1,0.2] a=1.67096 b=1.02012 c=0885522 d=0.128102 f(x)=1.46946
5. [1.,2.] a=1.54030 b=0.252035 c=0.432401 d=0.223917 f(x)=1.58621