### BISECTION3

!Program name: BISECTION3

!Function: x^3-9

!Initial x value is 1.0

!Tolerance 1E-06

!initial Interval dx=0.5

!The number of bisections is 100

!Root is 2.08008382

module finding_roots

implicit none

Real :: xl, xr

contains

subroutine init()

!Root between x=0 and x=3

xl=0.

xr=3.

write (*,5) "iter", "x", "y(x)", "fl", "fl*y(x)"

5  format (a5X,a10X,a20X,a20X,a15X)

end subroutine init

function func(x) result(y)

implicit none

Real :: x

Real :: y !dummy argument

y=x**3-9

end function func

subroutine bisect(xl,xr,x,func,f)

implicit none

integer :: i

real :: xl, xr, x, func, toly

real :: fl, fr, f       !dummy arguments

call init()

fl=func(xl)

fr=func(xr)

toly=1.E-06

do i=1,100

x=0.5*(xl+xr)

f=func(x)

if (f*fl .lt. 0) then

xr=x

fr=f

else

xl=x

fl=f

end if

Write (*,*) i, x, f, fl, f*fl

if (abs(f) .lt. toly) exit

end do

end subroutine bisect

end module finding_roots

use finding_roots

call bisect(xl,xr,x,func,f)

print *, x, func(x)

stop

end

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