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Solution
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.
Example
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 closedform of
_{ }
Thus the solution of the difference equation _{ } with initial value _{ } is
_{ }
See: Numerical Example
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Preferable reference for this tutorial is
Teknomo, Kardi (2015) Difference Equation Tutorial. http:\\people.revoledu.com\kardi\ tutorial\DifferenceEquation\