I am working on different methods to solve Recurrence Relations. I am using Iteration method and substitution method, which involves Induction, but I feel that sometimes Induction method creates a bit confusion, so I want to know that which of these two methods is more reliable?
I don't know what exactly you mean by the iteration method, but I think that this question has no definitive answer no matter what you mean by that.
The best method is the one that works, and that depends on the recurrence relation. After solving many of them you will get a sense of what can work in different cases. But you will still come across problems where you pretty much have to test all the methods you know to find one that works (and sometimes even that is not enough and you either get stuck or have to learn/figure out a new technique or new twist on a technique you already know).