Personally I would not have thought there is even any quesion here. You observe the obligations of Purim according to where you are on the 14th and 15th of adar. Being stuck somewhere does not make a difference.

Rav Bransdorfer thinks otherwise. The rabbi quoted the Shulchan Aruch and Mishna Berura who say that because oen is stuck in another place against his will, he should read megilla and fulfill the other obligations according to the appropriate day of his real place where he intended to be, not where he happens to be stuck. 

So, according to that, someone from Yerushalayim stuck abroad, say in New York, because of the war but had intended to be back home for Purim, should celebrate Purim in New York on the 15th of Adar even though he is in New York and everyone else is celebrating on the 14th. Good luck finding a minyan that will read the megilla on the 15th...

And, someone from New York who got "stuck" in Jerusalem because of the war but had originally intended to be back home by Purim should celebrate in Jerusalem on the 14th even though everyone else there is celebrating on the 15th. In this scenario there is an easy solution to go to a different city for Purim, like Bet Shemesh or Bnei Braq or Efrat or wherever and celebrate on the 14th with everyone else. And then maybe go to Jerusalem to celebrate again on the 15th like the way a lot of yeshiva boys do. 

Rav Bransdorfer says the rule for this is that it depends where you intended to be when you traveled form your house to somewhere else - if you intended to be back home, celebrate as if you are home, and if you intended to be away, celebrate as if you are away. 

Rav Bransdrfer does suggest because of it being a machloket, even though he paskens as above, that one could celebrate on both days to fulfill all opinions and obligations

source: Haredim Yerushalayim