AFAIK, many physics engines like Physx and Havok don't incorporate cylinder as basic shape because it is expensive than sphere, box and capsule. But bullet engine does incorporate cylinder as a basic shape. Do they found any fast algorithm to simulate the cylinder and what is that?
I don´t know about the speed or exact nature of the cylinder shaped collider in bullet, but this paper gives a nice overview about cylinder collision.
If you are only after the implementation of their collision you may want to start here and try to recreate what they are doing with it.