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FORTRAN 90+: PROGRAM EXAMPLE

It is recommended to look at the numerical methods codes where programming is demonstrated. An additional example is included here.
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
!  Uses bisection method to find square root
!
!   x*x - c  = 0
!   over the interval [a,b]
!
!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
PROGRAM sqrt 
  IMPLICIT NONE
  INTEGER :: nmax, n
  REAL :: tol, d
  REAL :: a, b, c
  REAL :: fa, fc
​
  WRITE(*,*) ’ Input Constant d (x^2-d=0) ’
  READ(*,*) d
  WRITE(*,*) ’ Input Lower and Upper Limits’
  READ(*,*) a, b
​
  tol = 0.000001
  nmax = 100
​
  fa = f(a,d)
  c = (a + b ) /2.
  fc = f(c,d)
  n = 1 
​
  DO WHILE (n <= nmax)
     IF((b-a)/2.0 < tol) THEN
       WRITE(*,*) ’Root’,c,’gives’,fc,’after’,n,’iterations’
       EXIT
     ENDIF
     IF(fa*fc > 0.0) THEN
        a = c
     ELSE
        b = c
     ENDIF  
     c = (a + b ) /2.
     fc = f(c,d)
     n = n + 1
  ENDDO
  
CONTAINS
   REAL  FUNCTION F(x,n)
   REAL :: x
   REAL :: n 
   f = x*x - n 
   END FUNCTION F
END PROGRAM