program newton
!
! Solves f(x) = 0 by Newton’s method
!
implicit none
integer :: its = 0 ! iteration counter
integer :: maxits = 20 ! maximum iterations
integer :: converged = 0 ! convergence flag
real :: eps = 1.0e-6 ! maximum error
real :: x = 2 ! starting guess
! introduce a new form of the do loop
do while (converged == 0 .and. its < maxits)
x = x - f(x) / df(x)
write(*,*) x, f(x)
its = its + 1
if (abs(f(x)) <= eps) converged = 1
end do
if (converged == 1) then
write(*,*) ’Newton converged’
else
write(*,*) ’Newton did not converge’
end if
contains
function f(x)
real :: f, x
f = x**3 + x - 3.0
end function f
function df(x)
! first derivative of f(x)
real :: df, x
df = 3 * x**2 + 1
end function df
end program newton