Solution to Difference Equation

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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 closed-form 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. https:\\people.revoledu.com\kardi\ tutorial\DifferenceEquation\