Numerical difference between Julia and (C, Fortran, Python) for a chaotic damped driven pendulum

[ChrisRackauckas]

@mendeli

I wrote a simple code implementing a midpoint 2nd order Runge-Kutta method for a damped driven pendulum in different languages to compared run times. While the results were exactly the same for C, Fortran and Python (Fortran and C tested up to t = 10⁷) the results for Julia drifted away from these after a rather short time.

Since the problem is chaotic with the given parameters, any slight difference the initial conditions will grow with time; however, all languages tested except for Julia apparently were able to perform exactly the same calculations.

It’s chaotic, so the simplest things can cause this. My guess is that the first 3 use the same standard math library definition of sin and cos, while Julia’s is different in 1ulp or so.