A solution of a difference equation is an expression (or formula) that makes the difference equation true for all values of the integer variable k. The nature of a difference equation allows the solution to be calculated recursively. It is easier to see the solution of the difference equation through algebraic equation.
We have difference equation with initial value .
Then we can determine set the
k = 0: initial value
k = 1:
k = 2:
k = 3:
k = 4:
k = n:
However, the series has a closed-form of
Thus the solution of the difference equation with initial value is
See: Numerical Example
Preferable reference for this tutorial is
Teknomo, Kardi (2015) Difference Equation Tutorial. https:\\people.revoledu.com\kardi\ tutorial\DifferenceEquation\