4/15/2015 ﺑﺎﺳﻤﻪ ﺗﻌﺎﻟﯽ اﻫﺪاف 1

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Advanced Numerical Methods 1

ﯽﻟﺎﻌﺗ ﻪﻤﺳﺎﺑ

فاﺪﻫا نﺮﺗﺮﻓ ﻪﭽﺨﯾرﺎﺗ  نﺮﺗﺮﻓ نﺎﺑز ﯽﻧﺎﺒﻣ 

ﻪﻣﺎﻧﺮﺑ رﺎﺘﺧﺎﺳ تارﻮﺘﺳد ﯽﻓﺮﻌﻣ و ﺎﻫﺮﯿﻔﺘﻣ و هداد ﺲﻨﺟ ﻪﻣﺎﻧﺮﺑ لﺮﺘﻨﮐ سﺎﺳا ﯽﺟوﺮﺧ و يدورو ﺎﻫ لاورﺮﯾز و ﻊﺑاﻮﺗ

لواﺪﺘﻣ تﻼﮑﺸﻣ و ﻞﺋﺎﺴﻣ ﯽﺳرﺮﺑ



ﻪﻧﻮﻤﻧ ﻞﺋﺎﺴﻣ



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ﻪﻫد رد ﻻﺎﺑ ﺢﻄﺳ ﯽﺴﯾﻮﻧ ﻪﻣﺎﻧﺮﺑ نﺎﺑز ﮏﯾ ناﻮﻨﻋ ﻪﺑ نﺮﺗﺮﻓ ﺶﯾاﺪﯿﭘ ياﺪﺘﺑا زا



1950

نﺎﺑز ﻦﯾا

ﺖﺳا ﻪﺘﺷاد يدﺎﯾز ﻪﻌﺳﻮﺗ و تاﺮﯿﯿﻐﺗ .

نﺮﺗﺮﻓ نﺎﺑز يﺎﻫ ﻪﺨﺴﻧ



 FORTRAN 1957

 FORTRAN II

 FORTRAN IV

 FORTRAN 66 (released as ANSI standard in 1966)

 FORTRAN 77 (ANSI standard in 1977)

 FORTRAN 2003 (latest ANSI standard version)

ﺪﻧا هﺪﺷ ﻪﺘﺷﻮﻧ نﺮﺗﺮﻓ ﺎﺑ دﻮﺟﻮﻣ ﯽﺳﺪﻨﻬﻣ يﺎﻫ ﻪﻣﺎﻧﺮﺑ زا يا هﺪﻤﻋ ﺖﻤﺴﻗ



.

ﯽﺴﯾﻮﻧ ﻪﻣﺎﻧﺮﺑ و ﻪﻠﺌﺴﻣ ﻞﺣ نآ ﻞﯿﻠﺤﺗ و ﻪﻠﺌﺴﻣ ﻖﯿﻗد ﻦﯿﯿﻌﺗ 

ﻢﺘﯾرﻮﮕﻟا ﯽﺣاﺮﻃ و ﺎﻫ هداد ﯽﻫﺪﻧﺎﻣزﺎﺳ

 ﺎﻫ هداد ﯽﻫﺪﻧﺎﻣزﺎﺳ

ﻢﺘﯾرﻮﮕﻟا ﯽﺣاﺮﻃ ترﺎﭼﻮﻠﻓ ﻪﯿﻬﺗ و ﻢﺘﯾرﻮﮕﻟا ﻪﺑ مزﻻ تﺎﯿﺋﺰﺟ ندوﺰﻓا

ﻪﻣﺎﻧﺮﺑ ﺪﮐ ﻦﺘﺷﻮﻧ



ﻪﻣﺎﻧﺮﺑ ﺖﺴﺗ و اﺮﺟا



ﻪﻌﺳﻮﺗ و يراﺪﻬﮕﻧ



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Advanced Numerical Methods 5 FORTRAN

Program

FORTRAN Compiler

Libraries Link with

Libraries Executable File

Source Code Object Code Executable Code

نﺮﺗﺮﻓ نﺎﺑز ﯽﻧﺎﺒﻣ ﺎﻫﺮﯿﻐﺘﻣ و ﺎﻫ ﺖﺑﺎﺛ ،هداد ﺲﻨﺟ

نﺮﺗﺮﻓ



5 دراد ﻪﯾﺎﭘ هداد ﺲﻨﺟ عﻮﻧ :

ﺢﯿﺤﺻ راﺪﻘﻣ INTEGER

يرﺎﺸﻋا راﺪﻘﻣ

REAL

ﻂﻠﺘﺨﻣ راﺪﻘﻣ COMPLEX

ﯽﻓﺮﺣ راﺪﻘﻣ CHARACTER

ﯽﻘﻄﻨﻣ راﺪﻘﻣ LOGICAL

يﺎﻫ ﺲﻨﺟ

 INTEGER

و ﺪﻨﻫد ﯽﻣ صﺎﺼﺘﺧا هدﺎﻔﺘﺳا ياﺮﺑ ار ﺎﻫ ﺖﯾﺎﺑ زا ﯽﺼﺨﺸﻣ داﺪﻌﺗ

REAL

.

 Default is: INTEGER*4and REAL*4

 DOUBLE PRECISIONis same as REAL*8

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ﺖﺑاﻮﺛ و ﺎﻫﺮﯿﻐﺘﻣ نﻼﻋا



ﯽﺘﻗو



يﺮﯿﻐﺘﻣ رد نﺮﺗﺮﻓ هدﺎﻔﺘﺳا

،دﻮﺷ ﯽﻣ ﺮﻠﯾﺎﭙﻣﺎﮐ ﻪﺑ نآ ﮏﯾ ﻞﺤﻣ ﻪﻈﻓﺎﺣ صﺎﺼﺘﺧا ﺪﻫد ﯽﻣ

. . دﻮﺷ ﯽﻣ هﺮﯿﺧذ ﻪﻈﻓﺎﺣ ﻞﺤﻣ نآ رد ﺖﺳا هﺪﺷ هداد صﺎﺼﺘﺧا ﺮﯿﻐﺘﻣ نآ ﻪﺑ ﻪﮐ يراﺪﻘﻣ ﺲﻨﺟ



ﮏﯾ ﺮﯿﻐﺘﻣ نﺎﯿﺑ هﺪﻨﻨﮐ عﻮﻧ يا هداد ﺖﺳا ﻪﮐ رد ﻞﺤﻣ ﻪﻈﻓﺎﺣ ﯽﺻﺎﺼﺘﺧا نآ

ﺮﯿﻐﺘﻣ

راﺮﻗ . دﺮﮐ نﻼﻋا ﺮﻠﯾﺎﭙﻣﺎﮐ ﻪﺑ ار ﺮﯿﻐﺘﻣ ﺮﻫ ﺲﻨﺟ ﻪﮐ ﺖﺳا مزﻻ ﻦﯾاﺮﺑﺎﻨﺑ . دﻮﺷ ﯽﻣ هداد

INTEGER :: NumValue, Sum REAL :: Velocity, Mass REAL(8) :: Time

CHARACTER(15) :: FirstName REAL DIMENSION(50) :: Vector

ﻞﺒﻗ  زا نﻼﻋا ﮏﯾ

،ﺮﯿﻐﺘﻣ مزﻻ ﺖﺳا ﻪﺑ ﻪﮐ ﻦﯾا نآ ﺮﯿﻐﺘﻣ رد ﻪﻣﺎﻧﺮﺑ ﻪﭼ يراﺪﻘﻣ ار ﺪﻫاﻮﺧ ﺖﺷاد بﻮﺧ

.ﺪﺷﺪﻫاﻮﺧﺎﻄﺧدﺎﺠﯾاﺚﻋﺎﺑﺮﯿﻐﺘﻣﮏﯾﻪﺑنﻮﮕﻤﻫﺎﻧﺮﯾدﺎﻘﻣنداد. دﻮﺷهﺪﯿﺸﯾﺪﻧا

نﺮﺗﺮﻓ نﺎﺑز ﯽﻧﺎﺒﻣ ﺢﯾﺮﺻ و ﯽﻨﻤﺿ يﺎﻫ ن ﻼﻋا 

رد



نﺮﺗﺮﻓ ﻦﯾا نﺎﮑﻣا دﻮﺟو دراد ﻪﮐ يﺮﯿﻐﺘﻣ ار نوﺪﺑ نﻼﻋا ﺲﻨﺟ نآ رد ﻪﻣﺎﻧﺮﺑ هدﺎﻔﺘﺳا دﺮﮐ

. : دﻮﺷ ﯽﻣ ﻦﯿﯿﻌﺗ نآ مﺎﻧ لوا فﺮﺣ ﻪﺑ ﻪﺟﻮﺗ ﺎﺑ ﺮﯿﻐﺘﻣ ﺲﻨﺟ ﺖﻟﺎﺣ ﻦﯾا رد

 I-N defineINTEGERvariable

 A-H, O-Z defineREALvariables

ﺎﺑ



هدﺎﻔﺘﺳا زا رﻮﺘﺳد Implicit ناﻮﺗ ﯽﻣ

ﺎﻫﺮﯿﻐﺘﻣ ار ترﻮﺻ ﻪﺑ ﯽﻨﻤﺿ نﻼﻋا دﺮﮐ :

IMPLICIT REAL (A-Z) IMPLICIT CHARACTER*2 (W) IMPLICIT DOUBLE PRECISION (D)

نﻼﻋا



ﺢﯾﺮﺻ ﯽﻣﺎﻤﺗ ﺎﻫﺮﯿﻐﺘﻣ : IMPLICIT NONE

ﺪﻫد ﯽﻣ ﺮﮐﺬﺗ ار نآ ﯽﯾﺎﻄﺧ مﺎﻐﯿﭘ ﺎﺑ ﺪﺷﺎﺑ هﺪﺸﻧ نﻼﻋا يﺮﯿﻐﺘﻣ ﺮﮔا ترﻮﺻ ﻦﯾا رد

.

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ﺎﻫﺮﯿﻐﺘﻣ ﻪﺑ ﻪﯿﻟوا ﯽﻫد راﺪﻘﻣ

 REAL :: Velocity=20.5, Mass=2.0, Weight=19.62

يﺎﻫ ﺖﺑﺎﺛ



ﺎﺑ

مﺎﻧ : ﺖﯿﻠﺑﺎﻗ

PARAMETER

REAL, PARAMETER :: Pi=3.1415927, TwoPi=2.0*Pi, Pio2=Pi/2 ﻦﯾا ﺖﺑاﻮﺛ ﻞﺑﺎﻗ ﺮﯿﯿﻐﺗ ﺪﻨﺘﺴﯿﻧ .

ﯽﺿﺎﯾر تﺎﯿﻠﻤﻋ



ﺖﻣﻼﻋ ﻊﺑﺎﺗ

**

ناﻮﺗ

*

بﺮﺿ

/

ﻢﯿﺴﻘﺗ

+

ﻊﻤﺟ

-

ﻖﯾﺮﻔﺗ

نﺮﺗﺮﻓ نﺎﺑز ﯽﻧﺎﺒﻣ ﯽﺿﺎﯾر تﺎﯿﻠﻤﻋ 

B**2-4.0*A*C 9.0/4.0  2.25 9/4  2

تﺎﯿﻠﻤﻋ مﺪﻘﺗ ﺪﻋاﻮﻗ

 ﺖﺴﺨﻧ  ﻞﻤﻋ ﻪﺑ ناﻮﺗ مﺎﺠﻧا ﯽﻣ دﻮﺷ . ﻪﭽﻧﺎﻨﭼ ﺶﯿﺑ زا ﮏﯾ ناﻮﺗ ﺖﺸﭘ ﻢﻫﺮﺳ راﺮﻗ ﺪﻧﺮﯿﮔ ﻞﻤﻋ

ﻪﺑ .دﻮﺷﯽﻣمﺎﺠﻧاﭗﭼﻪﺑﺖﺳارزانﺪﻧﺎﺳرناﻮﺗ

ﺲﭘ  زا

،ناﻮﺗ مﺪﻘﺗ تﺎﯿﻠﻤﻋ ﺎﺑ بﺮﺿ و ﻢﯿﺴﻘﺗ ﺖﺳا . رد ﻞﻤﻋ يﺎﻫ بﺮﺿ و ﻢﯿﺴﻘﺗ ﯽﻟاﻮﺘﻣ

ﻞﻤﻋ .دﻮﺷ ﯽﻣمﺎﭽﻧاﺖﺳارﻪﺑﭗﭼزاﻢﯿﺴﻘﺗﺎﯾ وبﺮﺿ

ﻞﻤﻋ  ﻊﻤﺟ و ﻢﯿﺴﻘﺗ رد ﺮﺧآ ﺮﺳ مﺎﺠﻧا دﻮﺷ ﯽﻣ . ﺐﯿﺗﺮﺗ يﺎﻫ ﻞﻤﻋ ﻊﻤﺟ و ﺎﯾ ﻖﯾﺮﻔﺗ ﺰﯿﻧ زا ﭗﭼ

ﻪﺑ .ﺖﺳاﺖﺳار

ﺎﺑ  هدﺎﻔﺘﺳا زا ﺰﺘﻧاﺮﭘ ناﻮﺗ ﯽﻣ مﺪﻘﺗ يدﺎﻋ تﺎﯿﻠﻤﻋ ار ﺮﯿﯿﻐﺗ داد .

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ﯽﺿﺎﯾر ﻊﺑاﻮﺗ



ﻊﺑﺎﺗ مﺎﻧ ﻊﺑﺎﺗ رﺎﮐ حﺮﺷ

ABS(x)

^{ﻖﻠﻄﻣ رﺪﻗ}

COS(x), SIN(x),Tan(x)

(نﺎﯾدار ﺐﺴﺣ ﺮﺑx) ﯽﺗﺎﺜﻠﺜﻣ ﻊﺑاﻮﺗ

INT(x)

x ﯽﻘﯿﻘﺣ ﺖﻤﺴﻗ

FLOOR(x)

X يوﺎﺴﻣ ﺎﯾ ﺮﺘﮑﭼﻮﮐ ﺢﯿﺤﺻ دﺪﻋ ﻦﯾﺮﺘﮔرﺰﺑ

MOD(x,y)

^y^ﺮﺑ^x^ﺢﯿﺤﺻ

EXP(x)

^{ناﻮﺗ ﻊﺑﺎﺗ}

LOG(x)

ﯽﻌﯿﺒﻃ ﻢﺘﯾرﺎﮕﻟ

SQRT(x)

^رﺬﺟ

MAX or MIN(x1,…,x2)

ﻢﻤﯿﻨﯿﻣ و ﻢﻤﯾﺰﮐﺎﻣ

نﺮﺗﺮﻓ نﺎﺑز ﯽﻧﺎﺒﻣ يا ﻪﻄﺑار تارﺎﺒﻋ  )

Relational Expressions (

يا ﻪﻄﺑار ﻢﺋﻼﻋ ﻪﻄﺑار

.LT. or <

زا ﺖﺳاﺮﺗ ﮏﭼﻮﮐ

.LE. or <=

زا ﺖﺳا يوﺎﺴﻣ ﺎﯾﺮﺗ ﮏﭼﻮﮐ

.EQ. or ==

ﺎﺑ ﺖﺳا يوﺎﺴﻣ

.NE. or /=

ﺎﺑ ﺖﺳا يوﺎﺴﻣ ﺎﻧ

.GT. or >

زا ﺖﺳاﺮﺗ گرﺰﺑ

.GE. or >=

زا ﺖﺳا يوﺎﺴﻣ ﺎﯾﺮﺗ گرﺰﺑ

 ﺪﻨﺘﺴﻫ ﻪﺴﯾﺎﻘﻣ ﻞﺑﺎﻗ ﺰﯿﻧ ﯽﻓﺮﺣ يﺎﻫ ﻪﺘﺷر .

 ود ترﺎﺒﻋ يدﺪﻋ ﺎﯾ ﺮﯿﻏ يدﺪﻋ ﺎﺑ ﺮﮕﯾﺪﮑﯾ ﻪﺴﯾﺎﻘﻣ هﺪﺷ ﺎﺗ مﻮﻠﻌﻣ دﻮﺷ

ﻪﮐ . ﻂﻠﻏ ﺎﯾ ﺖﺳا ﺢﯿﺤﺻ ﯽﺑﺎﺨﺘﻧا ﻪﻄﺑار

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ﯽﻘﻄﻨﻣ تارﺎﺒﻋ



)

Logical Expressions (



،ﺮﯾدﺎﻘﻣ

.TRUE.

ﺎﯾ

.FALSE.

ﺪﻨﻫاﻮﺧ دﻮﺑ .

ﯽﻘﻄﻨﻣ ﺖﻣﻼﻋ لﺎﺜﻣ مﻮﻬﻔﻣ

.AND. A .AND. B ﯽﻘﻄﻨﻣ ﯽﻔﻄﻋ ﺐﯿﮐﺮﺗ

.OR. A .OR. B ﯽﻘﻄﻨﻣ ﯽﻠﺼﻓ ﺐﯿﮐﺮﺗ

.NEQV. A .NEQV. B ﯽﻘﻄﻨﻣ يزرا ﻢﻫ مﺪﻋ

.EQV. A .EQV. B ﯽﻘﻄﻨﻣ يزرا ﻢﻫ

.NOT. .NOT. A ﯽﻘﻄﻨﻣ ﯽﻔﻧ

نﺮﺗﺮﻓ نﺎﺑز ﯽﻧﺎﺒﻣ بﺎﺴﺘﻧا ﻪﻠﻤﺟ  )

Assignments Statement (

دور ﯽﻣ رﺎﮐ ﻪﺑ ﺪﺷﺎﺑ مزﻻ ﻪﮐ ﺎﺟﺮﻫ رد ﺎﻫﺮﯿﻐﺘﻣ ﻪﺑ يﺮﯾدﺎﻘﻣ بﺎﺴﺘﻧا ياﺮﺑ بﺎﺴﺘﻧا ﻪﻠﻤﺟ  .

INTEGER :: Number, Term

REAL :: Xcoordinate,Ycoordinate CHARACTER (5)::String

! Assignments Statement Xcoordinate = 5.23

Ycoordinate = sqrt(25.0) Number=17

Term = Number / 3 + 2

Xcoordinate = 2.0 * Xcoordinate String = ”alpha”

(8)

يدورو



/ ﯽﺟوﺮﺧ )

List-Directed I/O (

هدﺎﺳ  ﺖﺳا ﺮﯾز ﻞﮑﺷ ﻪﺑ ﯽﺟوﺮﺧ ﻪﺑ ﺎﻫ هداد لﺎﺳرا ﺖﻟﺎﺣ ﻦﯾﺮﺗ :

PRINT*, “Enter a float and an integer:”

READ*, x, j

PRINT*, “float = “, x, “ integer = “, j

WRITE (*,*) “Enter a float and an integer:”

READ (*,*) x, j

WRITE (*,*), “float = “, x, “ integer = “, j

 ﯽﻟﺎﺧ ﯽﺟوﺮﺧ ﻂﺧ ﮏﯾ دﺎﺠﯾا ياﺮﺑ :

WRITE (,) PRINT*

نﺮﺗﺮﻓ نﺎﺑز ﯽﻧﺎﺒﻣ ﻪﻣﺎﻧﺮﺑ ﻞﮑﺷ و ﺐﯿﮐﺮﺗ 

ﻪﻣﺎﻧﺮﺑ ﺮﺘﯿﺗ



)

Heading (

ﺎﻫ ﻒﯾﺮﻌﺗ و تﺎﻧﻼﻋا ﺖﻤﺴﻗ



)

Specification part (

ﻪﻣﺎﻧﺮﺑ ﯽﯾاﺮﺟا ﺖﻤﺴﻗ



)

Subprogram part (

ﻪﻣﺎﻧﺮﺑ ﯽﻧﺎﯾﺎﭘ ﻪﻠﻤﺟ



)

END PROGRAM statement

(

(9)

ﻪﻣﺎﻧﺮﺑ ﻞﮑﺷ و ﺐﯿﮐﺮﺗ

 PROGRAM name !heading

!

!specification part IMPLICIT NONE

REAL :: Xcoordinate,Ycoordinate, Hight, Velocity,&

Time

INTEGER :: Number, Term CHARACTER (5)::String

!

!execution part Xcoordinate = 5.23

Ycoordinate = sqrt(25.0)

Number=17; Term = Number / 3 + 2 Xcoordinate = 2.0 * Xcoordinate String = ”alpha”

END PROGRAM name !end of program

نﺮﺗﺮﻓ نﺎﺑز ﯽﻧﺎﺒﻣ ﻪﻣﺎﻧﺮﺑ ﻞﮑﺷ و ﺐﯿﮐﺮﺗ 

PROGRAM circle_area IMPLICIT NONE

!reads a value representing the radius of a circle,

!then calculates and writes out the area of the circle.

REAL :: radius, area

REAL, PARAMETER :: pi=3.141592 READ (5,*) radius

area = pi*radius*radius !calculate area WRITE (6,*) area

END PROGRAM circle_area

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ﻪﻣﺎﻧﺮﺑ ﻞﮑﺷ و ﺐﯿﮐﺮﺗ



PROGRAM circle_area IMPLICIT NONE

!reads a value representing the radius of a circle,

!then calculates and writes out the area of the circle.

REAL :: radius, area

REAL, PARAMETER :: pi=3.141592 READ (5,*) radius

area = pi*radius*radius !calculate area WRITE (6,*) area

END PROGRAM circle_area

ﯽﻟﺮﺘﻨﮐ ﻦﯿﻣاﺮﻓ ﯽﻃﺮﺷ يﺎﻫرﺎﺘﺧﺎﺳ  )

IF, IF-ELSE, … (

CASE



ﻪﻘﻠﺣ



) يﺎﻫرﺎﺘﺧﺎﺳ DO, DO WHILE

(

CONTINUE



يا ﻪﺧﺎﺷ تارﺎﺒﻋ



GOTO

PAUSE



STOP



CALL



RETURN



END



(11)

ﯽﻃﺮﺷ يﺎﻫرﺎﺘﺧﺎﺳ



رﺎﺘﺧﺎﺳ



هدﺎﺳ IF

Syntax: IF (logical_expression) statement

ﻦﮐ رﻮﺒﻋ طﺮﺷ وﺮﯿﭘ ﻪﻠﻤﺟ زا ﻪﻧ ﺮﮔا و ﻦﮐ اﺮﺟا ار طﺮﺷ وﺮﯿﭘ ﻪﻠﻤﺟ ،دﻮﺑ راﺮﻗﺮﺑ ﯽﻘﻄﻨﻣ طﺮﺷ ﺮﮔا .

Example: IF (Key.LT.0) x=0

Syntax: IF (logical_expression) THEN statement-sequence

END IF

Key < 0 no

yes x=0

ﻪﻣﺎﻧﺮﺑ ﯽﺑﺎﺨﺘﻧا ياﺮﺟا ﯽﻃﺮﺷ يﺎﻫرﺎﺘﺧﺎﺳ 

رﺎﺘﺧﺎﺳ



IF THEN ELSE

Syntax: IF (logical_expression) THEN statement1(s)

ELSE

statement2(s) ENDIF

Example: IF (Key.EQ.0) THEN X=X+1

ELSE X=X+2 ENDIF

Key = 0 no

yes x=x+1

x=x+2

(12)

رﺎﺘﺧﺎﺳ



IF ELSE IF

Syntax: IF (logical_expr1) THEN statement1(s)

ELSE IF (logical_expr2) THEN statement2(s)

ELSE

statement3(s) ENDIF

Example:

10 IF (KSTAT.EQ.1) THEN CLASS=‘FRESHMAN’

ELSE IF (KSTAT.EQ.2) THEN CLASS=‘SOPHOMORE’

ELSE IF (KSTAT.EQ.3) THEN CLASS=‘JUNIOR’

ELSE IF (KSTAT.EQ.4) THEN CLASS=‘SENIOR’

ELSE

CLASS=‘UNKNOWN’

ENDIF

KEY= 1 no

yes X=X+1

X=X+2 KEY= 2

KEY= N no

…

X=X+N yes

yes

no X=-1

ﻪﻣﺎﻧﺮﺑ رد راﺮﮑﺗ تﺎﯿﻠﻤﻋ ﻦﯿﻌﻣ داﺪﻌﺗ ﻪﺑ راﺮﮑﺗ 

) ( DO

ﻪﺑ ﻪﻘﻠﺣ ﻪﻧﺪﺑ و دﻮﺷ ﯽﻣ ﻪﺘﺧﺎﺳ ﻪﻘﻠﺣ هﺪﻧرﺎﻤﺷ ﮏﯾ زا هدﺎﻔﺘﺳا ﺎﺑ ﻪﻘﻠﺣ ،راﺮﮑﺗ عﻮﻧ ﻦﯾا رد  ددﺮﮔ ﯽﻣ راﺮﮑﺗ ،دﻮﺷ ﯽﻣ لﺮﺘﻨﮐ هﺪﻧرﺎﻤﺷ راﺪﻘﻣ ﺎﺑ ﻪﮐ تﺎﻌﻓد داﺪﻌﺗ .

ﯽﻘﻄﻨﻣ ﻂﯾاﺮﺷ نﺪﺷ ﻖﻘﺤﻣ ترﻮﺻ رد راﺮﮑﺗ



)

WHILE DO (

دﻮﺸﯿﻣ دﺎﺠﯾا ،راﺮﮑﺗ طﺮﺷ ﺎﯾ ،ﯽﻘﻄﻨﻣ ترﺎﺒﻋ ﮏﯾ زا هدﺎﻔﺘﺳا ﺎﺑ ﻪﻘﻠﺣ ،راﺮﮑﺗ ﻦﯾا رد  .

رد .ﺖﺳا ﻪﻘﻠﺣ ﻪﻧﺪﺑ تﻼﻤﺟ ياﺮﺟا هﺪﻨﻨﮐ ﻦﯿﯿﻌﺗ ﯽﻘﻄﻨﻣ ترﺎﺒﻋ نآ ترﻮﺻ ﻦﯾا

(13)

ﻦﯿﻌﻣ داﺪﻌﺗ ﻪﺑ راﺮﮑﺗ



)

( DO

Syntax: DO control-variable=initial-value,limit,stepsize statement-sequence

END DO

DO 100 K=2,10,2 PRINT*,A(K) 100 END DO

DO 100 K=2,10,2 PRINT*,A(K) 100 CONTINUE

SUM=0

READ *, Number DO I=1,Number

Sum=Sum+I END DO

ﻪﻣﺎﻧﺮﺑ رد راﺮﮑﺗ تﺎﯿﻠﻤﻋ ﻮﺗ رد ﻮﺗ راﺮﮑﺗ 

INTEGER:: I,J,K

DO I=1,3

DO J=1, 3 DO K=1, 3

PRINT *, I+J+K END DO

END DO

(14)

ﯽﻘﻄﻨﻣ ﻂﯾاﺮﺷ نﺪﺷ ﻖﻘﺤﻣ ترﻮﺻ رد راﺮﮑﺗ



)

WHILE DO (

Syntax: WHILE (logical_expression) DO statement-sequence

END WHILE

READ*,R

WHILE (R.GE.0) DO VOL=2*PI*R**2*CLEN READ*,R

END WHILE

ﺮﮕﯾد هﻮﯿﺷ  )

دﻮﺷ ﯽﻣ اﺮﺟا ﺮﮕﯾد رﺎﺑ ﮏﯾ ﻞﻗاﺪﺣ ﻪﻘﻠﺣ ﻪﻧﺪﺑ (.

Syntax: DO

statement-sequence

IF (logical_expression) EXIT (CYCLE) END DO

ﺎﻫ لاورﺮﯾز و ﻊﺑاﻮﺗ زا هدﺎﻔﺘﺳا ﺎﺑ ﯽﺴﯾﻮﻧ ﻪﻣﺎﻧﺮﺑ ﻊﺑﺎﺗ 

) Function (

ﺪﻧادﺮﮔ ﯽﻣ زﺎﺑ ﺖﺳا هﺪﻧاﻮﺧاﺮﻓ ار نآ ﻪﮐ يا ﻪﻣﺎﻧﺮﺑ ﻪﺑ ار راﺪﻘﻣ ﮏﯾ  .

ﺪﻧادﺮﮔ ﯽﻣ زﺎﺑ ﻊﺑﺎﺗ مﺎﻧ ﻖﯾﺮﻃ زا ار دﻮﺧ راﺪﻘﻣ ﻊﺑﺎﺗ  .

دﻮﺷ ﯽﻣ هﺪﻧاﻮﺧاﺮﻓ ترﺎﺒﻋ ﮏﯾ رد نآ مﺎﻧ زا هدﺎﻔﺘﺳا ﺎﺑ ﻊﺑﺎﺗ  .

لاورﺮﯾز



)

Subroutine (

ﺪﻧادﺮﮔ ﯽﻣ ﺮﺑ ار راﺪﻘﻣ ﮏﯾ زا ﺶﯿﺑ ﺐﻠﻏا  .

ﻖﯾﺮﻃ زا ﺖﺳا هﺪﻧاﻮﺧاﺮﻓ ار لاورﺮﯾز ﻪﮐ يا ﻪﻣﺎﻧﺮﺑ ﻪﺑ هﺪﺷ هﺪﻧادﺮﮔزﺎﺑ ﺮﯾدﺎﻘﻣ  ددﺮﮔ ﯽﻣ لدﺎﺒﺗ لاور ﺮﯾز رد ﻪﺘﻓر رﺎﮑﺑ يﺎﻫﺮﺘﻣارﺎﭘ .

رﻮﺘﺳد ﻖﯾﺮﻃ زا لاور ﺮﯾز  دﻮﺷ ﯽﻣ ﯽﻧاﻮﺧﺮﻓCALL

.

(15)

ﻊﺑﺎﺗ رﺎﺘﺧﺎﺳ



)

Function (

Syntax: [type] FUNCTION fname(p1,p2, … pN)

EXAMPLE:

REAL FUNCTION fahrenheit (c) REAL:: c

fahrenheit = (9.0/5.0)*c + 32.0 ! Convert Celsius to fahrenheit END FUNCTION fahrenheit

USE: f = fahrenheit (0.0)

دﻮﺷ نﻼﻋا ﺪﯾﺎﺑ ﺖﺳا هﺪﻧاﻮﺧاﺮﻓ ار ﻊﺑﺎﺗ ﻪﮐ يا ﻪﻣﺎﻧﺮﺑ رد ﻊﺑﺎﺗ مﺎﻧ  .

REAL :: fahrenheit

ﺎﻫ لاورﺮﯾز و ﻊﺑاﻮﺗ زا هدﺎﻔﺘﺳا ﺎﺑ ﯽﺴﯾﻮﻧ ﻪﻣﺎﻧﺮﺑ ﻊﺑﺎﺗ رﺎﺘﺧﺎﺳ 

) Function (

يا ﻪﻠﻤﺟ ﮏﺗ ﻊﺑاﻮﺗ ﻒﯾﺮﻌﺗ ياﺮﺑ هﺎﺗﻮﮐ و ﻊﯾﺮﺳ شور



PROGRAM MAIN REAL A,B,C

FUNC(X)=A*X**2-B*X+C ...program...

ANS=FUNC(4.2)+1.2 ...

END PROGRAM MAIN

(16)

لاورﺮﯾز رﺎﺘﺧﺎﺳ



)

Subroutine (

Syntax: SUBROUTINE fname(p1,p2, … pN)

EXAMPLE:

SUBROUTINE temp_conversion(celsius, fahrenheit) REAL:: celsius, fahrenheit

fahrenheit = (9.0/5.0)*celsius + 32.0 END SUBROUTINE temp_conversion USE: CALL temp_conversion(c, f)

ﺖﺴﯿﻧ ﯽﻘﯿﻘﺣ يﺎﻫﺮﺘﻣارﺎﭘ و ﯽﮕﺘﺧﺎﺳ يﺎﻫﺮﺘﻣارﺎﭘ مﺎﻧ ندﻮﺑ ﯽﮑﯾ ﻪﺑ يزﺎﯿﻧ  .

ﺎﻫ لاورﺮﯾز و ﻊﺑاﻮﺗ زا هدﺎﻔﺘﺳا ﺎﺑ ﯽﺴﯾﻮﻧ ﻪﻣﺎﻧﺮﺑ ﺎﻫ لاورﺮﯾز و ﻊﺑاﻮﺗ يﺮﯿﮔ راﺮﻗ نﺎﮑﻣ 

PROGRAM MAIN

...program body...

END

REAL FUNCTION AVG3(A,B,C) ...function body...

END

SUBROUTINE AVG3S(A,B,C,AV) ...subroutine body...

END

(17)

Advanced Numerical Methods 33 PROGRAMConsole1

IMPLICIT NONE

REAL:: xl, xu, es, xr, ea, Bisection INTEGER:: imax, iter

es=1.e-6; imax=100

! Initial Guess xl=0.0; xu=3.0

!xr=xl;ea=100.0

! Call Function Bisection

xr=Bisection(xl,xu,es,imax,xr,iter,ea) WRITE(*,*), "The root of equation is = ", xr PAUSE

END PROGRAM Console1

!

FUNCTIONBisection(xl, xu, es, imax, xr, iter, ea) IMPLICIT NONE

REAL:: xl, xu, es, xr, ea, Func, Bisection, x, xrold, test INTEGER:: imax, iter

iter=0 DO xrold=xr

xr=(xl+xu)/2.0 iter=iter+1

لﺎﺜﻣ : ندﺮﮐ ﻒﺼﻧ شور ﻂﺳﻮﺗ ﯽﺑﺎﯾ ﻪﺸﯾر

IF(xr/= 0.0) THEN

ea=ABS((xr-xrold)/xr)*100 END IF

test=Func(xl)*Func(xr) IF(test < 0.0) THEN

xu=xr

ELSE IF (test > 0.0) THEN xl=xr

ELSE ea=0.0 END IF

IF(ea<es .OR. iter>=imax) EXIT END DO

Bisection=xr

WRITE(*,*), "The number of iteration is = ", iter WRITE(*,*), "The percent of relative error is = ", ea END FUNCTIONBisection

!

REAL FUNCTION Func(x) IMPLICIT NONE

4/15/2015 ﺑﺎﺳﻤﻪ ﺗﻌﺎﻟﯽ اﻫﺪاف 1

 FORTRAN 1957

INTEGER :: NumValue, Sum REAL :: Velocity, Mass REAL(8) :: Time

هدﺎﻔﺘﺳا زا رﻮﺘﺳد Implicit ناﻮﺗ ﯽﻣ

Logical Expressions (

.AND. A .AND. B ﯽﻘﻄﻨﻣ ﯽﻔﻄﻋ ﺐﯿﮐﺮﺗ

Assignments Statement (

INTEGER :: Number, Term

List-Directed I/O (

PRINT*, “Enter a float and an integer:”

WRITE (*,*) PRINT*

!specification part IMPLICIT NONE

!then calculates and writes out the area of the circle.

REAL :: radius, area

IF, IF-ELSE, … (

Syntax: IF (logical_expression) statement

END IF

Key < 0 no

IF THEN ELSE

Syntax: IF (logical_expression) THEN statement1(s)

ELSE X=X+2 ENDIF

Key = 0 no

IF ELSE IF

Syntax: IF (logical_expr1) THEN statement1(s)

WHILE DO (

Syntax: DO control-variable=initial-value,limit,stepsize statement-sequence

END DO

READ *, Number DO I=1,Number

INTEGER:: I,J,K

Syntax: DO

) Function (

رﻮﺘﺳد ﻖﯾﺮﻃ زا لاور ﺮﯾز  دﻮﺷ ﯽﻣ ﯽﻧاﻮﺧﺮﻓCALL

Function (

EXAMPLE:

REAL:: xl, xu, es, xr, ea, Bisection INTEGER:: imax, iter

WRITE (,) PRINT*