What the difference is between Størmer Verlet and regular Verlet method?

Question

I was wondering what the difference is between the Størmer Verlet method and the regular Verlet method, if there is any.

Answer 1

My impression is that the two methods are the same, in both cases the position is updated using $$x_{n+1}=2x_n-x_{n-1}+a_n\Delta t^2$$ with $a_n$ the acceleration.

Usually, however, I hear "Verlet integration" to be about the velocity Verlet method, where the velocity at the half-step is used:

1. Compute $x(t+\Delta t)=v(t)+\frac12a(t)\Delta t^2$
2. Compute $a(t+\Delta t)$ using the updated position
3. Compute $v(t+\Delta t)=v(t)+\frac12\left(a(t)+a(t+\Delta t)\right)\Delta t$

This, of course, assumes the acceleration does not depends on velocity, which would require a slight modification to the algorithm (I discuss this here). The link Qmechanic's added to your post can provide more details to the base method.