ok this is complicated so im going to dumb it down a bit, no offence lol.
Ok the book that Grandma death wrote is the most important thing in the whole movie, and to fully understand the film you will need to read it. It is available in some libraries and all over the net.
The Philosophy of time travel is a philosophical theory that branches off from traditional christianity. Where ‘God’ controls all of the universe including time. Therefore time is predetermined But because god has given us free will we are able to change our futures (watch the scenes between donnie and the male teacher they discuss all of this). Because we are able to change our futures and break from gods control it creates an inbalance in reality. On the night when the jet falls into Donnies bed in the beginning of the movie he had changed time and thus creating a tangent universe, not controlled by god. BEcause of its lack of godly control it will destroy itself withen 28 days and take the primary universe (the actual universe) along with it.
So donnie (referred to as the living reciever) must close the tangent unviverse before it implodes on itself. He is guided by two ‘angels’ or ‘agents’ sent via the forth dimension (water) this is Frank and Gretchin (and are referred to as manipulated dead) they have died inside the tangent universe, so closing the tangent universe would prevent their deaths.
Everyone else are manipulated living and help drive Donnie to his destiny. They will do anything to make sure their universe is not destroyed.
The only way to close the tangent universe is to die via the jet engine crushing him. Think about it though, if donnie dies then he wouldnt burn the peverts house meaning his mom wouldnt take the early flight back meaning no jet engine would break off.
There are more examples of occurances like this in the book, such as a mayan warrior dieing from a runaway arrow where there was no one around or a medieval knight being struck by a sword he was yet to make.
You cannot clump this entire movie into one simple phrase like, he did it to save his girlfriend or because he was scared of Frank. You cannot do this because Donnie tells us so, in reference to the ‘life’ line: “you cant just clump all of these emotions into two extremes (love and fear) and ignore the rest”
Throughout the entire movie there are many references to religion (namely christianity) almost all manipulated living are christian, he calls the pervert the anti-christ, the movie they watch is ‘christs final temptation’, Donnie: “I could spend my whole life debating over and over again, weighing the pros and cons, and in the end I still wouldn’t have any proof, so I just don’t debate it any more. (laughs) It’s absurd.”
Dr. Thurman: “The search for God is absurd?”
Donnie: “It is if everyone dies alone.”
“Do you mean God’s master plan? Do you now believe in God?”
“If the sky were to suddenly open up, there would be no law, there would be no rule. It would only be you and your memories, the choices you made, and the people you touched. If this world were to end, there would only be you, and him, and no one else.”
So there you go that is the directors intention.