Fortran Programs Sai

7/25/2019 Fortran Programs Sai

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Contents

BISECTION ................................................................................................................................... 2

NEWTON RAPHSON METHOD .................................................................................................. 4

INTERPOLATION ......................................................................................................................... 5

MODIFIED EULER METHOD ...................................................................................................... 7

RUNGE KUTTA 4TH ORDER ........................................................................................................ 8

SIMPSON 1/3 ................................................................................................................................. 9

LEAST SQUARE FIT .................................................................................................................. 10

BINARY SEARCH....................................................................................................................... 11

BUBBLE SORT ........................................................................................................................... 12

GAUSS ELIMINATION .............................................................................................................. 13


2/13

2

BISECTION

!PROGRAM TO FIND THE ROOTS OF THE EQUATIONS USING BISECTIONMETHOD!

PROGRAM BISECTION

IMPLICIT NONEREAL, PARAMETER :: e=0.0001INTEGER :: I

REAL :: a,b,Xm,f

WRITE(*,*)' ENTER THE VALUE OF LOWER AND UPPER LIMIT [a,b] OF THE

EQUATION'READ(*,*) a,b

IF (f(a)*f(b)>0) THEN

WRITE(*,*)' INVALID INTERVAL'STOP

ENDIFWRITE(*,*)'_______________________________________________'

WRITE(*,*)' I a b Xm'WRITE(*,*)'-----------------------------------------------------------------------'

I=0

do WHILE (abs(b-a)>e)

Xm = (a+b)*.5IF(F(Xm)==0) GOTO 10

IF(f(a)*f(Xm)


3/13

3

OUTPUT

ENTER THE VALUE OF LOWER AND UPPER LIMIT [a,b] OF THE EQUATION

2

4

_______________________________________________I a b Xm

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

0 2.00000000 3.00000000 3.000000001 2.50000000 3.00000000 2.50000000

2 2.75000000 3.00000000 2.75000000

3 2.87500000 3.00000000 2.87500000

4 2.93750000 3.00000000 2.937500005 2.93750000 2.96875000 2.96875000

6 2.93750000 2.95312500 2.95312500

7 2.93750000 2.94531250 2.945312508 2.94140625 2.94531250 2.94140625

9 2.94140625 2.94335938 2.94335938

10 2.94238281 2.94335938 2.94238281

11 2.94238281 2.94287109 2.9428710912 2.94262695 2.94287109 2.94262695

13 2.94274902 2.94287109 2.94274902

14 2.94281006 2.94287109 2.94281006

ROOT OF THE GIVEN EQUATION IS= 2.94281006

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


4/13

4

NEWTON RAPHSON METHOD

!PROGRAM TO FIND THE ROOT USING NEWTON RAPHSON METHODPROGRAM NR

IMPLICIT NONE

REAL :: x,xo,fx,dfxREAL, PARAMETER:: tol=1e-6integer :: k

WRITE(*,*)'ENTER THE INITIAL VALUE XO'

READ(*,*) xo

WRITE(*,*)'____________________________'WRITE(*,*)'__________I_______XO________'

k=0

10 k=k+1call fun (xo,fx,dfx)

x=xo-fx/dfxif(abs(x-xo)


5/13

5

INTERPOLATION

PROGRAM LAGRANGE_INTERPOLATIONIMPLICIT NONE

INTEGER,PARAMETER :: N=4

INTEGER :: I,JREAL ::P,SREAL,PARAMETER ::K=3.0

REAL,DIMENSION(20):: X(20),Y(20)

DATA (X(I), I=1,4)/3.2,2.7,1,4.8/

DATA (Y(I), I=1,4)/22,17.8,14.2,38.3/S=0

DO I=1,N

P=1DO J=1,N

IF (I==J) GOTO 5P=P*(K-X(J))/(X(I)-X(J))

5 ENDDOS=S+P*Y(I)

ENDDO

WRITE(*,*)'INTERPOLATION OF(',K,')=',S

END PROGRAM LAGRANGE_INTERPOLATION

OUTPUT

INTERPOLATION OF( 3.00000000 )= 20.2119598


6/13

6

DIFFERENTIATION

PROGRAM THREE_POINT_FORMULA_DIFFERENTIATION

IMPLICIT NONEINTEGER, PARAMETER :: NN=20

REAL, DIMENSION(0:NN) :: x,fxINTEGER :: I,N=4

REAL :: fp0,fp1,fp2,h=0.2DO I=0,N

x(I)=I*h

fx(I)=(x(I))**4

WRITE(*,*)I,x(I),fx(I),4*((x(I))**3)END DO

WRITE(*,*)'**************'

DO I=1,(N-1)

fp0=(1/(2*h))*(-3*fx(I-1)+4*fx(I)-fx(I+1))fp1=(1/(2*h))*(-fx(I-1)+fx(I+1))

fp2=(1/(2*h))*(fx(I-1)-4*fx(I)+3*fx(I+1))

WRITE(*,*)I,fp0,fp1,fp2END DO

END PROGRAM THREE_POINT_FORMULA_DIFFERENTIATION

output

0 0.00000000 0.00000000 0.00000000

1 0.200000003 1.60000008E-03 3.20000015E-022 0.400000006 2.56000012E-02 0.256000012

3 0.600000024 0.129600018 0.864000082

4 0.800000012 0.409600019 2.04800010

**************

1 -4.80000004E-02 6.40000030E-02 0.175999999

2 -8.00000355E-02 0.320000052 0.7200000883 8.00001249E-02 0.960000038 1.83999991


7/13

7

MODIFIED EULER METHOD

! to find the value of ode by modified euler method

PROGRAM PCM

IMPLICIT NONEINTEGER, PARAMETER :: MM=10

INTEGER :: n,I

REAL, DIMENSION(0:MM) :: xn=0,yn=0

REAL :: yp,h=0.1,k1,k2,py

WRITE(*,*)'ENTER THE VALUE OF N'

READ(*,*)n

DO I=1,n

xn(I)=xn(I-1)+h

END DO

WRITE(*,*)'__________n_________xn____________yn_________'WRITE(*,*)0,xn(0),yn(0)

DO I=1,nk1=h*yp(xn(I-1),yn(I-1))

py=yn(I-1)+k1

k2=h*yp(xn(I),py)

yn(I)=yn(I-1)+0.5*(k1+k2)

WRITE(*,*)I,xn(I),yn(I)

END DO

WRITE(*,*)'_____________________________________________'

END PROGRAM PCM

REAL FUNCTION yp(xn,yn)

IMPLICIT NONEREAL :: xn,yn

yp=1-yn

RETURN

END FUNCTION yp

output

ENTER THE VALUE OF N

3__________n_________xn____________yn_________

0 0.00000000 0.000000001 0.100000001 9.49999988E-022 0.200000003 0.180974990

3 0.300000012 0.258782357_____________________________________________


8/13

8

RUNGE KUTTA 4THORDER

PROGRAM RUNGE_KUTTA_Fourth_Order

IMPLICIT NONE

INTEGER, PARAMETER :: NN=20INTEGER :: I,n

REAL, DIMENSION(0:NN) :: x,y

REAL :: h,fx,k1,k2,k3,k4

h=0.1

x(0)=0

y(0)=1

WRITE(*,*)x(0),y(0)

READ(*,*)n

DO I=1,n

k1=h*fx(x(I-1),y(I-1))k2=h*fx(x(I-1)+0.5*h,y(I-1)+0.5*k1)

k3=h*fx(x(I-1)+0.5*h,y(I-1)+0.5*k2)k4=h*fx(x(I-1)+h,y(I-1)+k3)

x(I)=x(I-1)+h

y(I)=y(I-1)+(1/6.)*(k1+2*k2+2*k3+k4)

WRITE(*,*)k1,k2,k3,k4,y(I)

END DO

STOP

END PROGRAM RUNGE_KUTTA_Fourth_Order

REAL FUNCTION fx(x,y)IMPLICIT NONE

REAL :: x,y

fx=x+yRETURN

END FUNCTION fx

output

0.00000000 1.000000006

0.100000001 0.109999992 0.110499993 0.121050000 1.110341670.121034168 0.132085875 0.132638454 0.144298017 1.24280512

0.144280523 0.156494543 0.157105252 0.169991046 1.399716970.169971704 0.183470294 0.184145212 0.198386222 1.583648440.198364839 0.213283092 0.214028999 0.229767755 1.79744124

0.229744121 0.246231347 0.247055694 0.264449686 2.04423594


9/13

9

SIMPSON 1/3

program simpson_123

implicit noneINTEGER, PARAMETER :: NN=20

REAL, DIMENSION(0:NN) :: fx

REAL :: a,b,h,sf

INTEGER :: I,m

m=10

a=0

b=1

IF ((m/2)*2/=m) THEN

WRITE(*,*)'number of intervals not even'

STOPENDIF

h=(b-a)/mDO I=0,m

fx(I)=exp(-(a+I*h)*(a+I*h))

WRITE(*,*)I,fx(I)

END DO

sf=fx(0)+fx(m)

DO I=1,(m-1)

IF ((I/2)*2==I) THEN

sf=sf+2*fx(I)ELSE

sf=sf+4*fx(I)

ENDIFEND DO

sf=sf*(h/3.)

WRITE(*,*)sf

end program simpson_123

output...

0 1.00000000

1 0.9900498392 0.960789442

3 0.9139311914 0.8521437645 0.778800786

6 0.6976763017 0.612626374

8 0.527292371

9 0.444858074

10 0.367879450

0.746824980


10/13

10

LEAST SQUARE FIT

!PROGRAM FOR LEAST SQUARE FIT

PROGRAM LEAST

IMPLICIT NONEINTEGER :: I,N

INTEGER,PARAMETER :: NOP=20

REAL :: SX=0,SY=0,SX2=0,SY2=0,SXY=0

REAL :: M,C,rn

REAL, DIMENSION(NOP) :: X,Y

OPEN(UNIT=1,FILE='LEAST',STATUS='OLD',ACTION='READ')

READ(1,*)N

rn= REAL(N)

DO I=1,N

READ(1,*)X(I),Y(I)SX=SX+X(I)

SY=SY+Y(I)SX2=SX2+X(I)*X(I)

SY2=SY2+Y(I)*Y(I)

SXY=SXY+X(I)*Y(I)

ENDDO

M=((SXY)-SX*(SY/rn))/((SX2)-SX*(SX/rn))

C=(SY/rn)-M*(SX/rn)

WRITE(*,*) M,C

END PROGRAM LEAST

output

0.699999988 2.59999990


11/13

11

BINARY SEARCH

PROGRAM binary_search

IMPLICIT NONE

INTEGER, PARAMETER :: MM=20INTEGER, DIMENSION(1:MM) :: AA

INTEGER :: N,I,J,x,iu,il,im

WRITE(*,*)'No of elements in the array'

READ(*,*) N

WRITE(*,*)'Type in the list'

DO I=1,N

READ(*,*)AA(I)

END DO

WRITE(*,*)'Search for'

READ(*,*)xiu=1

il=Nim=(iu+il)/2

DO

IF (ilx) THEN

il=im-1

ELSE

iu=im+1

ENDIF

END DO

END PROGRAM binary_search

output...

No of elements in the array5

Type in the list2

6

8

15

9

Search for

8

8 is found in the list at 3


12/13

12

BUBBLE SORT

PROGRAM bubble_sort

IMPLICIT NONE

INTEGER, PARAMETER :: MM=20INTEGER, DIMENSION(1:MM) :: AA

INTEGER :: N,I,J,K,x,y

WRITE(*,*)'type in the number of elements'

READ(*,*)N

WRITE(*,*)'read in the list to be sorted'

DO I=1,N

READ(*,*)AA(I)

END DO

DO I=1,N-1

K=IDO J=I+1,N-1

IF (AA(J)>AA(K)) THENK=J

ENDIF

END DO

IF (K/=I) THEN

x=AA(I)

AA(I)=AA(K)

AA(K)=x

ENDIFEND DO

WRITE(*,*)(AA(I),I=1,N)

END PROGRAM bubble_sort

outpu..

type in the number of elements

5

read in the list to be sorted12

49

540

54 12 9 4 0


13/13

13

GAUSS ELIMINATIONPROGRAM ELMN

IMPLICIT NONE

real,allocatable,dimension(:,:) :: a

real,allocatable,dimension(:) :: xreal :: temp1,temp2,sum

integer ::n,k,i,j

write(*,*) 'no. of eqn'

read (*,*) n

allocate (a(1:n,1:n+1))

allocate (x(1:n))

write(*,*)'enter coeff'

do i=1,n

read(*,*)(a(i,j),j=1,n+1)

enddodo k=1,n-1

temp1= a(k,k)if(temp1==0)then

write(*,*)' 0 division'

stop

do i= k+1,n

temp2= a(i,k)/temp1

do j=k ,n+1

a(i,j)=a(i,j)-temp2*(a(k,j))

enddoenddo

endif

enddox(n) = a(n,n+1)/a(n,n)

do i=n-1,1,-1

sum=0.0

do j=i+1,n

sum= sum+a(i,j)*x(j)

enddo

x(i) = (a(i,n+1)-sum)/a(i,i)end do

write(*,*)'soln'do i=1,n

write(*,*)i,x(i)enddoEND PROGRAM ELMN

output ..........................................................................no. of eqn

3

enter coeff

10 -1 -2 4

1 10 -1 3

2 3 20 7

soln

1 0.5034999852 0.335000008

3 0.349999994

Fortran Programs Sai

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