Difference equations are frequently covered in courses on algorithms due to the relationship to recursion. Believe it or not, I first learned the basics of difference equations from George Boole's book (of Boolean algebra fame). This is freely available either as a download or to read online.
The methods that are the most useful for solving linear difference equations are use of the

characteristic equation or applying the

Z-transform. These are the discrete analogues of the

characteristic equation and

Laplace transform in differential equations.

**References:**
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