How do I kill a swain?

I swear all I ever see this character do is walk around doing damage and healing. I get him low and he drops a zhonyas and heals all of it back up. I try to push my lane but all he does is poke me down in a second. I try to stay away from him and he kills me. I try to play the game and he ruins it. How do I go agaisnt Swain ?