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1/36

ANALISA NUMERIK

RINDU TRISNA WIDIASTUTI (G1B009029) TRISA ENGGOLA(G1B009075)

METODE NUMERIK, ( AKAR-AKAR PERSAMAAN, Hal. 25)

contoh 1

hitn! "alah "at a#a$ %a$i &'$"aaan &an!#at ti!a t'$"'t.

P'n*'l'"aian +

-

1 -

1./5 .1/100

2

2

5

a). D'n!an 'n!!na#an 'to%' "'t'n!ah int'$al.

NO

1 1. 2. 1.5 -. .

2 1.5 2. 1./5 -1.0/5 .

3 1.5 1./5 1.25 -1.0/5 .1/100

4 1.25 1./5 1.0/5 -.3 .1/100

5 1.0/5 1./5 1./10/5 -.32 .1/100

6 1./10/5 1./5 1./0 -.12/3 .22

7 1./10/5 1./0 1./25 -.12/3 .228 1./25 1./0 1.// -.51/ .22

9 1.// 1./0 1./22 -.13 .51

10 1.// 1./22 1./15 -.13 .51

11 1./15 1./22 1./13 -.5/ .51

12 1./13 1./22 1./210 -.111 .12

13 1./13 1./210 1./2 -.111 -.

). D'n!an 'n!!na#an 'to%' int'$&ola"i lini'$

NO

1 1. 2. 1.5/1 -. .

2 1.5/1 2. 1./51 -1. .

1./51 2. 1./2/00 -.2//5 .

1./2/00 2. 1./1 -.3 .

5 1./1 2. 1./135 -.11 .

1./135 2. 1./2 -.35 .

/ 1./2 2. 1./25 -.15 .

0 1./25 2. E$$+522 -.2 E$$+522

3 1./25 E$$+522 E$$+522 -.2 E$$+5221 1./25 E$$+522 1./2 -.2 -.

4()672--6

i

4(i)

Xi

Xi+1 Xt f(Xi) f(Xi+1)

Xi Xi+1 X* f(Xi) f(Xi+1)


2/36

ANALISA NUMERIK


8). D'n!an 'n!!na#an 'to%' N'9ton-Ra&h"on

NO f'(xi)

1 1. . -. 2. 2.

2 . 2.2 2. 5.000 .

2.2 1.015 5.000 .303 15.32

1.015 1.//0 .303 .55/ 1./0

5 1.//0 1./2/ .55/ .2 3.553

1./2/ 1./25 .2 . 3./

/ 1./25 1./25 . . 3.1

0 1./25 1./25 . . 3.1

Xi

Xi+1 f(Xi) f(Xi+1)


3/36

ANALISA NUMERIK



4/36

ANALISA NUMERIK



5/36

ANALISA NUMERIK



6/36

ANALISA NUMERIK



7/36

ANALISA NUMERIK


Tugas, 15/7/2011

Hitn! "alah "at a#a$ %a$i &'$"aaan '$i#t+

a). D'n!an 'to%' "'t'n!ah int'$al.

'62./10201020

1 -.201/10

1.5 -.1011

2 1.0351

2.5 .023

NO

1 1.5 2.5 2. -.101

2 1.5 2. 1./5 -.101

3 1.5 1./5 1.25 -.101

4 1.5 1.25 1.525 -.101

5 1.5 1.525 1.5125 -.101

-1.0/5 6 1.5 1.5125 1.515 -.101

.1/100 7 1.5 1.515 1.5/01 -.101

-.3 8 1.5/01 1.515 1.511/2 -.

-.32 9 1.511/2 1.515 1.51/ -.

-.12/3 10 1.511/2 1.51/ 1.512/ -.

.22 11 1.511/2 1.512/ 1.51221 -.

-.51/ 12 1.511/2 1.51221 1.5113 -.-.13 13 1.5113 1.51221 1.5120 -.2

.51 14 1.5120 1.51221 1.51215 -.0

-.5/

-.111 ). D'n!an 'to%' int'$&ola"i lini'$

.12 NO

.5 1 1.5 2.5 1.53 -.101

2 1.5 1.53 1.51223 -.101

1.5 1.51223 1.5121 -.101

1.5 1.5121 1.5121 -.101

5 1.5 1.5121 1.5121 -.101

-1.

-.2//5 c). D'n!an 'to%' N'9ton-Ra&h"on

-.3 NO

-.11 1 1.5 1.512 -.101 .

-.35 2 1.512 1.5121 . .

-.15 1.5121 1.5121 . .

-.2

E$$+522

E$$+522.1

4()6'-

i

4(i)

Xi

Xi+1 Xt f(Xi)

f(xt)

Xi

Xi+1 X* f(Xi)

f(x*)

Xi

Xi+1 f(Xi) f(Xi+1)


8/36

ANALISA NUMERIK


Hitn! "alah "at a#a$ %a$i &'$"aaan t'$"'t.

P'n*'l'"aian+

a. D'n!an 'n!!na#an 'to%' "'t'n!ah int'$al

No

1 1 -1

2 2 1

1 1

5 5 31

NO

1 1. 2. 1.5 -1. 1.

2 1.5 2. 1./5 -.0/5 1.

1./5 2. 1.0/5 -.21 1.

1./5 1.0/5 1.0125 -.21 .21/

5 1./5 1.0125 1./0125 -.21 .13

1./0125 1.0125 1./300 -.0/1 .13

/ 1./300 1.0125 1.03 -.20 .13

0 1./300 1.03 1.0/0 -.20 .111

3 1.0/0 1.03 1.02/ -./0 .111

1 1.0/0 1.02/ 1.01/ -./0 .

11 1.01/ 1.02/ 1.0225 -./ .

12 1.01/ 1.0225 1.02 -./ .120

1 1.01/ 1.02 1.0100 -./ .2/

1 1.0100 1.02 1.013 -.2 .2/

f(x)=x3x22x+1=0

i

4(i)

Xi

Xi+1 Xt f(Xi) f(Xi+1)


9/36

ANALISA NUMERIK


. D'n!an 'n!!na#an 'to%' int'$&ola"i lini'$

No

1 1 -1

2 2 1

1

1

5 5 31

NO1 1. 2. 1.5 -1. 1.

2 2. 2. :DI;


10/36

ANALISA NUMERIK


c. D'n!an 'n!!na#an 'to%' n'9ton-$a&h"on

No 4>()

1 1 -12 2

13

0

5 5

NO f'(xi)

1 1. 1. -1. -1. -1.

2 1. . -1. 1. -1.

. .5 1. -.125 -2.

.5 . -.125 .1/ -2.25

5 . .5 .1/ . -2.23

%. D'n!an 'n!!na#an 'to%' S'cant

No1 1 -1

2 2 1

1

1

5 5 31

NO

1 . 1. .5 1. -1.

2 1. .5 .205/ -1. -.125 .5 .205/ .513 -.125 ./3

.205/ .513 .5 ./3 -.

4()6-2-2716

4>()62-2-26

i

Xi

Xi+1 f(Xi) f(Xi+1)

i

4(i)

Xi1 Xi Xi+1 f(Xi1) f(Xi)


11/36

ANALISA NUMERIK


5 .513 .5 .5 -. .

'. D'n!an 'n!!na#an 'to%' It'$a"i

No

1 1 -1

2 2 1

1

1

5 5 31

N!

1 1. 1.25332 2.2335

2 1.25332 1.532 1.50//

1.532 1.53/ 0./5

1.53/ 1./01 5.31

5 1./01 1./2351 2.35

1./2351 1./530 1./2

/ 1./530 1.///5/ .33///

0 1.///5/ 1./0/0/ .5/1

3 1./0/0/ 1./30 .21/

1 1./30 1./3/2/ .131

11 1./3/2/ 1./3325 .1115

12 1./3325 1.03 .3

1 1.03 1.015 .0

1 1.015 1.01 .233

15 1.01 1.01 .12/

1 1.01 1.01// .35

1/ 1.01// 1.010 .

10 1.010 1.0100 .2

13 1.0100 1.0131 .12

2 1.0131 1.0132 ./

21 1.0132 1.013 .

4() 6 -2-2716

6 (272-1)1


12/36

ANALISA NUMERIK


22 1.013 1.013 .25

2 1.013 1.013 .1

2 1.013 1.013 .0

25 1.013 1.013 .5


13/36

ANALISA NUMERIK


.023 1.03

1.03 .5

.5 .22

.22 .02

.02 .2

.2 .53

.53 -.

.53 -.

.53 .2/

.2/ .0

.0 .11

.11 -.2.11 -.0

.11 .2

.023 1.3310

-.1251 1.5/3

.2 1.53

. 1.5

. 1.5

f'(xi)

1.013

1.5/2

1.5

f(Xi+1)

f(xt)

f(Xi+1)

f(x*)


14/36

ANALISA NUMERIK


Hitn! "alah "at a#a$ %a$i &'$"aaan t'$"'

P'n*'l'"aian+

a. D'n!an 'n!!na#an 'to%' "'t'n!ah i

No

1 1 -2

2 2 2

32 22

5 5

NO

-.0/5 1 1. 2. 1.5

-.21 2 1. 1.5 1.25

.21/ 1. 1.25 1.125

.13 1.125 1.25 1.10/5

-.0/1 5 1.125 1.10/5 1.1525

-.20 1.1525 1.10/5 1.1/100

.111 / 1.1/100 1.10/5 1.1/33

-./0 0 1.1/100 1.1/33 1.1/5/0

.

-./

.120

.2/

-.2

.1

3x3+4x28x1=0

i

4(i)

f(xt) X

i X

i+1 Xt


15/36

ANALISA NUMERIK


. D'n!an 'n!!na#an 'to%' int'$&ola"i

No

1 1 -2

2 2 2

32

22

5 5

NO-.0/5 1 1. 2. 1.0

:DI;


16/36

ANALISA NUMERIK


c. D'n!an 'n!!na#an 'to%' n'9ton-$a

No

1 -02 1 3

2

3/

5 10

NO

1 . -.125 -1.

2 -.125 -.1101 .5

-.1101 -.11053 .12

-.11053 -.11053 .

%. D'n!an 'n!!na#an 'to%' S'cant

No1 1 -2

2 2 2

32

22

5 5

NO

-.125 1 . 1. -1.

./3 2 1. -1. .-. -1. . .323

. . .323 -.00

f(x) = 3x3+4x28x1=0

f'(x) = 9x2+8x8 = 0

i

4>(i)

Xi

Xi+1 f(Xi)

i

4(i)

f(Xi+1)

Xi1 Xi Xi+1


17/36

ANALISA NUMERIK


. 5 .323 -.00 -.1

-.00 -.1 -.11//

/ -.1 -.11// -.110

0 -.11// -.110 -.11053

'. D'n!an 'n!!na#an 'to%' It'$a"i

No

1 1 -2

2 2 2

32

22

5 5

N!

1 1. 1.105 .155/

2 1.105 1.1/ .3

1.1/ 1.1/531 .10

1.1/531 1.1/5// .12

5 1.1/5// 1.1/5/0 .1

f(x) = 3x3+4x28x1=0

x = (8/3x4/3x2+1/3)1/3

i

4(i)

Xi Xi+1 ?a @


18/36

ANALISA NUMERIK



19/36

ANALISA NUMERIK



20/36

ANALISA NUMERIK


t.

t'$al

-2. 2. .125

-2. .125 1.130

-2. 1.130 -.2

-.2 1.130 .11

-.2 .11 -.232

-.232 .11 -.50

-.50 .11 .5

-.50 .5 .1

f(Xi)

f(Xi+1)

f(xt)


21/36

ANALISA NUMERIK


lini'$

-2. 2. -1.1352

-1.1352 2. -.5

-.5 2. -.32

-.32 2. -.10

-.10 2. -.32

-.32 2. -.

-. 2. -.25/

-.25/ 2. -.1103

-.1103 2. -.

-. 2. -.2-.2 2. -.152

-.152 2. -.//

-.// 2. -.3

-.3 2. -.13

-.13 2. -.1

-.1 2. -.5

f(Xi) f(Xi+1) f(x*)


22/36

ANALISA NUMERIK


h"on

f'(xi)

.5 -0.

.12 -0.0530

. -0.02225

. -0.0221/

-1. -2. 0.

-2. 0. -./120. -./12 -1./25

-./12 -1./25 2.302

f(Xi+1)

f(Xi1) f(Xi) f(Xi+1)


23/36

ANALISA NUMERIK


-1./25 2.302 -.120

2.302 -.120 -./52

-.120 -./52 .

-./52 . .


24/36

ANALISA NUMERIK



25/36

ANALISA NUMERIK



26/36

ANALISA NUMERIK



27/36

ANALISA NUMERIK



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ANALISA NUMERIK



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ANALISA NUMERIK



31/36

ANALISA NUMERIK



32/36

ANALISA NUMERIK



33/36

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ANALISA NUMERIK



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ANALISA NUMERIK



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