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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 Difference Equation Tutorial: Solution with initial value Difference Equation Tutorial: Solution .

Then we can determine set the

k = 0: Difference Equation Tutorial: Solution initial value

k = 1: Difference Equation Tutorial: Solution

k = 2: Difference Equation Tutorial: Solution

k = 3: Difference Equation Tutorial: Solution

Difference Equation Tutorial: Solution

k = 4: Difference Equation Tutorial: Solution

k = n: Difference Equation Tutorial: Solution

However, the series Difference Equation Tutorial: Solution has a closed-form of

Difference Equation Tutorial: Solution

Thus the solution of the difference equation Difference Equation Tutorial: Solution with initial value Difference Equation Tutorial: Solution is

Difference Equation Tutorial: Solution

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\