Newton Raphson Method on Fortran90

[jhosamelly]

Here's what I need to do:

"Compare the effectiveness of the bisection method and Newton’s method for the
equation x^3−2x−2 = 0 which has a single root between x=−4 and x = 2."So far I've done

ok. this is working but of course I need to do iteration which I don't know how. Can someone teach me please? I'm trying the Newton-Raphson Method first.

Thanks for the help in advance.EDITED: Sorry, I posted the wrong pic earlier. Here's the correct one.

 

[gsal]

program nr
real:: x, xnew, err

write(*,*) "starting x?:"
read(*,*) x

do
    xnew = x - ( (x**3 - (2*x) - 2) / ( ( 3*(x**2) )-2) )
    err = 100*abs( (xnew-x)/x )
    x = xnew
    write(*,*) "x = ", xnew, "  error = ", err
    if (err < 0.000001) exit
end do

end program nr

 

[jhosamelly]

thanks ) Is that the iteration already?

 

[gsal]

Yes.

Isn't it? Run it and verify the solution

 

[LudusRex]

I would suggest that you utilize the resources available to you, such as textbooks or online tutorials, to learn how to implement the iteration process for the Newton-Raphson method. This process involves repeatedly updating the initial guess for the root until a desired level of accuracy is achieved. Once you have implemented this process, you can compare the effectiveness of the bisection method and Newton's method by analyzing the number of iterations required for each method to converge to the root and the accuracy of the root approximation. Additionally, it would be beneficial to also consider the computational complexity and stability of each method. By comparing these factors, you can determine which method is more effective for solving the given equation.