I saw a really moving animated short that used this as part of its plot, but I forget the name (japanese) and haven't been able to google it since.
A couple of high school sweethearts promise they'll love each other forever, but there's a war on and the boy quickly gets recruited to fight at the edge of the solar system (I remember a scene where they stand at some railroad tracks and watch a monumental silver space craft fly overhead, one of the battle cruisers), but before he gets there the boy and girl continue their relationship as pen pals, at first sending messages back and forth from mars base (45 minute delay, but not aging any faster), but as the boy travels closer to the front of the war, his velocity increases and he ages less than the girl waiting for him back on earth, and of course more time passes by between messages.
Eventually it's the boys 20something birthday and he still has love for the girl, while the girl has already grown up and moved on with her life.
It's probably the Makoto Shinkai film the other guy posted but another book that uses time dilation is The Forever War. And there's the classic Childhood's End.
A couple of high school sweethearts promise they'll love each other forever, but there's a war on and the boy quickly gets recruited to fight at the edge of the solar system (I remember a scene where they stand at some railroad tracks and watch a monumental silver space craft fly overhead, one of the battle cruisers), but before he gets there the boy and girl continue their relationship as pen pals, at first sending messages back and forth from mars base (45 minute delay, but not aging any faster), but as the boy travels closer to the front of the war, his velocity increases and he ages less than the girl waiting for him back on earth, and of course more time passes by between messages.
Eventually it's the boys 20something birthday and he still has love for the girl, while the girl has already grown up and moved on with her life.