Solution to Difference Equation

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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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