Solution Lecture a7

! Implementation of Newton's method for exp x + x = 5
! with a stopping condition
implicit none
real x, F, Fprime, d, p, q
integer k

! Enter the starting x0
read *, x

do k = 1, 100 
    F = exp(x) + x - 5
    Fprime = exp(x) + 1
    d = F / Fprime
    x = x - d
    if (abs(d) < 1e-3) then
        print *, k, 'iterations needed'
        exit
    endif
enddo

end

! Implementation of Newton's method for x^3 + p x + q = 0
! with a stopping condition
implicit none
real x, F, Fprime, d, p, q
integer k

read *, p, q, x
print *, x

do k = 1, 100 
    F = x**3 + p * x + q
    Fprime = 3 * x**2 + p
    if (abs(Fprime) < 1e-6) then
        print *, 'Error: the derivative is too close to zero'
        stop
    endif
    d = F / Fprime
    x = x - d
    ! We stop the iteration if x does not change more than a certain value
    if (abs(d) < 1e-3) then
        print *, 'x =', x
        print *, k, 'iterations needed'
        ! stop the loop
        stop
    endif
    print *, x
enddo

print *, 'Method does not converge'

end

! Implementation of Newton's method for x^3 + p x + q = 0
! with a stopping condition
implicit none
real x, F, Fprime, d, p, q
integer k, i, r

read *, r

do i = -r, r
    x = i

    p = -2.
    q = 2.

    do k = 1, 100 
        F = x**3 + p * x + q
        Fprime = 3 * x**2 + p
        if (abs(Fprime) < 1e-6) then
            print *, 'Error: the derivative is too close to zero'
            stop
        endif
        d = F / Fprime
        x = x - d
        ! We stop the iteration if x does not change more than a certain value
        if (abs(d) < 1e-3) then
            print *, i, k
            ! stop the loop
            exit
        endif
    enddo
enddo

end