So you changed your mind. You want your stubborn ex boyfriend back. He's gone off and is doing his own thing but you want him back. According to a Tyra Banks Show poll, 50% of men still pine over their ex girlfriends, so depending on your situation there may be hope
Find a new guy to hang out with and occupy your time while you're in the trying to get your ex boyfriend back. You can also bond with a good girlfriend and increase your activities. You don't want to get into a situation where you're alone at home thinking about calling him. Guy's don't like desperate women.
Send your ex boyfriend a quick email out of the blue telling him how you were thinking about him that day because of "__fill in the blank___" Fill in that blank with something memorable from your relationship. Don't write a book, just a few quick lines. If he responds to that email you have hope (he's probably thinking about you too), if not he's not not into it and you should definitely move on. Anything beyond that will be too much like stalking.
Wait a couple of days and then reply to the email again or send him a quick text saying "what's up" to initiate a conversation. When he asks what you've been up to say something constructive like "working hard." You need to appear as if you have occupied your time with other important things while apart if you want your ex boyfriend back.
Invite him out for coffee or something else similar and simple. Keep the visit to about a half an hour and be delightful to remind him of why he was interested in the first place.
Take things slow as you rebuild the relationship with your ex boyfriend -- start off as friends and then work your way up from there.