This may or may not be useful to those having issues: I have an iPhone 6s, and got the dreaded 4013 error. Tried many things--restarting phone, computer, etc., reconnecting cords to different ports, disconnecting them at pivotal moments. The last thing I thought to try was to take the phone out of its battery case (which I got fairly recently). That did it--made all the difference. Update went smoothly after that. This may not be the same thing plaguing others, but it definitely made it work for me.