Metode Numerik Handout (Unsada) By Ridwan

8/17/2019 Metode Numerik Handout (Unsada) By Ridwan

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METODE NUMERIK

Eko Budi Wahyono


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FLOW - CHARD

• Pemuka !"o#"am

•

Penu$u! !"o#"am

• In!u$ % ou$!u$

&TAR T

&TOP


3/34

FLOW - CHARD

• Pe"nya$aan da$a' hi$un#an

•

Pe"nya$aan (o"

• Pe"nya$aan i(

)A

TIDAK

)A

*+-,.Beda.,

&i#n/(012


4/34

P"o#"am !3o$ #"a4k (un#5i

• F3o6-7ha"$

&TAR T

*+-,.28.,

)+9:;-<

P3o$/9'y0

&TO

P


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P"o#"am #"a4k (un#5i !o3inom

!an#ka$ dua

• =PRO>RAM MEN>>AMBAR FUN>&I KWADRAT

• 9+-,.2;.,? =in!u$ @a"iae3 ea5 9 da"i -, 5am!ai , den#an 5!a5i2;

• y+9:;-


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HA&IL OUTPUT >RAFIK

-5 -4 -3 -2 -1 0 1 2 3 4 5-10

-8

-6

-4

-2

0

2

4

6

8

10

Grafik Fungsi Y vs Variabel bebas x

Varabel Bebas(x)

F u n g s i Y


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In$"uk5i

Ke$ik !"o#"am dia$a5 dan ek5eku5i!"o#"am $e"5eu$ 5e$e3ah ada ha5i3nya$unGukkan ke!ada do5en un$uk dini3ai'

5e"$a !e3aGa"i komen-komennya a#a"nan$i a!ai3a di$anyakan da3am uGian5auda"a 5udah 5ia!


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P"o#"am $au3a5i (un#5i

• F3o6 - 7ha"d&TAR T

9 (/90$anda---------------------i+8?eda+28?

9+-

,2.eda.,2

8

;


9/34

o6-7ha"d $au3a5i (un#5i a#ian

;

• F3o6-7ha"d

(+9:;-<

8

5i#n/(01

2

*'('$anda/i0

5i#n/(0J

2

$anda/i0

+2


10/34


• F3o6-7ha"d

i+i8

;

i+8

9+-,2.eda.,2

,


11/34


• F3o6-7ha"d

$anda/i0++2

iJ8

Aka"nya ada3ah+9

Aka"nya adadi in$e"@a3a'

i+i8

&TOP

,

a+9-eda' +9


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P"o#"am $au3a5i-a#ian 8

• (!"in$(/9 (/90 $andan0? = Menu3i5 3ae3ko3om $ae3

• (!"in$(/---------------------n0? = Memua$ #a"i5 a6a3$ae3

• i+8?eda+28? = Menen$ukan ni3ai a6a3 i danni3ai 5!a5i

• (o" 9+-,2.eda.,2 = Pe"nya$aan (o" $idakdiakhi"i $i$ik koma

• (+9:;-


13/34

P"o#"am $au3a5i-a#ian ;

• i( 5i#n/(0J2 = Pe"nya$aan i( $idak diakhi"i den#an $i$ik koma

• $anda/i0+? = menen$ukan ou$!u$ $anda

• (!"in$(/ =5n'$anda/i00? = Pe"in$ah menu3i5 ou$!u$ $anda

• e35e = Pe"nya$aan e35e $idak diakhi"i $i$ik koma

• $anda/i0+2? = menen$ukan ou$!u$ $anda

• (!"in$(/ =5n'$anda/i00? = Pe"in$ah menu3i5 ou$!u$$anda

• end?

• end?

• i+i8? = in7"emen$ i• end?

•


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P"o#"am $au3a5i-a#ian • i+8? = ini5ia3i5a5i ni3ai i

• (o" 9+-,2.eda.,2 = !e"nya$aan (o" $idak diakhi"i den#an $i$ikkoma

• i( $anda/i0++2 = !e"nya$aan i( $idak diakhi"i den#an $i$ikkoma

• (!"in$(/Aka"nya ada3ah + =(n'90? = Pe"nya$aan ou$!u$ 9

•

e35e= Pe"nya$aan e35e $idak diakhi"i $i$ik koma• i( iJ8

• i( $anda/i0+$anda/i-80

• a+9-eda?

• +9?

•

(!"in$(/Aka"nya ada di in$e"@a3 =8('=8(n'a'0?• end?

• end?

• end?

• i+i8?= in7"emen$ i

•

end?


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OUTPUT PRO>RAM TABULA&I

9 (/90 $anda------------------------------2 8222 -;< -282 --; -8;2 -

-; -;;2 --;; -82 --;2 -222 --8< -Q2 --8 -,2 --8 -22 -

-8; -,2 -

8; -,2 -8 -22 -8 -,2 -

8< -Q2 -;2 -222 -;; -82 -; -;;2 -; -8;2 -;< -282 -

2 8222 aka" ada di in$e"@a3 -2'-;


16/34

In$"uk5i

• Ke$ik !"o#"am dia$a5 da3am Gende3aedi$o" ma$3a dan ek5eku5i !"o#"am$e"5eu$' 5e3anGu$nya $unGukkan

ha5i3nya !ada do5en

• Ha(a3kan komen$a" yan# ada da3am!"o#"am a#a" anda 5ia! da3am uGian


17/34

BI&ECTION• Pen7a"ian aka" !e"5amaan den#an

!endeka$an mema#i 5e#menmenGadi dua

• *"+/939u0%;

939u

*u+9"

93

9u

*3+9"

9"

Aka"

y

9

&E>ME

N

&E>MENATA&

&E>MENBAWAH


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• Pen#uGian 5e#men aka".

• 8 (/930(/9"012 maka ada aka" 9u+9"

• ; (/930(/9"0J2 maka $ak ada aka"93+9"

• (/930(/9"0+2 maka 9"+aka"

• Ke5a3ahan ea+a5//9"3-9"0%9"0822

• Bia5anya di$e$a!kan ke5a3ahanku"an# da"i 8 = 9"+aka"


19/34

P"o#"am Pendeka$an Aka" -

Bi5e7$ion

• F3o6-7ha"d &TAR T

i+8? eda+8? 93+;?9u+2?

9"3+/939u0%;

i 93 9u 9" ea------------------------------------

i+8.eda.82

8


20/34

F3o6-7ha"d Bi5e7$ion -a#ian ;

• F3o6-7ha"d8

9"+/939u0%;? (93+93:;-


21/34

F3o6-7ha"d Bi5e7$ion -a#ian

• F3o6-7ha"d;

9"3+9"?

i+i8?

ea 182

------------------------------------

I$e"a5i 5e3e5ai Aka"nya ada3ah +9"Aka" di!i3ih !ada ea ku"an# da"i 5a$u!e"5en

&TOP


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• =P"o#"am Me$ode Bi5e7$ion

• =In!u$ . i' eda' 93/5e#men a6ah0' 9u/5e#men a$a50

• =Ou$!u$ . Tae3 i' eda' 93' 9u' ea' dan Ni3ai Aka" $ia!5e#men

• i+8? eda+8? 93+;? 9u+2?

• 9"3+/939u0%;?

• (!"in$(/i 93 9u 9" ean0?

• (!"in$(/------------------------------------n0?

• (o" i+8.eda.82

• 9"+/939u0%;?

• (93+93:;-


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• (!"in$(/=;2( =;( =;( =;( =(n'i'93'9u'9"'ea0?

• i( (93(9" 1 2

• 9u+9"?

• e35e

• i( (93(9" J 2

• 93+9"?

• end?

• end?

• 9"3+9"?

• i+i8?

• end?

•

i( ea 1 82• (!"in$(/------------------------------------n0?

• (!"in$(/ I$e"a5i 5e3e5ai Aka"nya ada3ah + =;(n'9"0?

• (!"in$(/ Aka" di!i3ih !ada ea ku"an# da"i 5a$u !e"5enn0?

• end?

P"o#"am !endeka$an aka" Bi5e7$ion a#ian ;


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OUTPUT PRO>RMBI&ECTION

i 93 9u 9" ea

------------------------------------

8 ;22 22 ;,2 22222

; ;,2 22 ;Q, S2S2S

;Q, 22 ;


25/34

INTRUK&I


ha5i3nya !ada do5en

• Ha(a3kan komen$a" yan# ada da3am!"o#"am a#a" anda 5ia! da3am uGian


26/34

Pen7a"ian aka" den#an !endeka$an

Fa35e Po5i$ion

Teo"i

• Fa35e !o5i$ion me"u!akan me$ode!enen$uan aka" !e"5amaan yan#3eih aik aka" 3eih 7e!a$dida!a$kan $e"3iha$ Gum3ah i$e"a5iyan# 3eih 5ediki$' den#an

mem!e"#unakan 5e#i$i#a!e"!o$on#an den#an 5umu 95ehin##a dida!a$kan e5$ima5i

5ea#ai e"iku$


27/34

• )an# 5e3anGu$nya da!a$ di!e"#unakanun$uk men7a"i 9"' 5ea#ai (o"mu3a

(a35e !o5i$ion• *"+9u-/(/9u0/93-9u00%/(/930-(/9u00

• >ama"an 5e7a"a #"a45 me$ode (a35e

!o5i$ion

Aka"9"93

9u

F/9u0

F/930

y

9


28/34

• F3o6-7ha"d

i 93 9u 9"ea------------------------------------

9"3+2

i+8.eda.8

2

i+8? eda+8? 93+;?9u+2?

&TART

8


29/34

• F3o6-7ha"d

;

8

(93+93:;-


30/34

------------------------------------

I$e"a5i 5e3e5ai Aka"nya ada3ah +9"Aka" di!i3ih !ada ea ku"an# da"i 5a$u!e"5en

&TOP

Ea 1 8=

9"3+9"? i+i8?

;


31/34

• =P"o#am Fo35e Po5i$ion

• =In!u$ . i' eda' 93/5e#men a6ah0' 9u/5e#men a$a50• =Ou$!u$ . Tae3 i' eda' 93' 9u' ea' dan Ni3ai Aka" $ia! 5e#men

• i+8? eda+82? 93+;2? 9u+2?

• 9"3+2?

• (!"in$(/i 93 9u 9" ean0?

• (!"in$(/------------------------------------n0?• (o" i+8.eda.82

• (93+93:;-


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• i( (93(9" 1 2

• 9u+9"?

• e35e

• i( (93(9" J 2

• 93+9"?

• end?

• end?

• 9"3+9"?• i+i8?

• end?

• (!"in$(/------------------------------------n0?

• i( ea 1 82

• (!"in$(/ I$e"a5i 5e3e5ai Aka"nya ada3ah + =;(n'9"0?

• (!"in$(/ Aka" di!i3ih !ada ea ku"an# da"i 5a$u !e"5enn0?

• end?


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OUTPUT PRO>RAM FAL&E PO&ITION

i 93 9u 9" ea

------------------------------------

8 ;22 22 ;


34/34

INTRUK&I


ha5i3nya !ada do5en• Ha(a3kan komen$a" yan# ada da3am

!"o#"am a#a" anda 5ia! da3am uGian

Documents

Metode Numerik Handout (Unsada) By Ridwan