Thread: Difference Equations

I have been reading the recent difference equation post and a question occurred to me. (Please forgive me I know many techniques but little theory for linear algebra.)

I know how to solve something like


But what about

for example. Is there a general method to attack something like this?

(I don't know if this even has a "nice" solution, I'm just using it as a sample equation where one or more of the coefficients depends on n.)

-Dan

Particular cases are often easier than general ones. The example you listed in fact has a straightforward solution.

. If you work relation for small n, you find the general formula for a as where and are arbitrary.

Originally Posted by topsquark

(I don't know if this even has a "nice" solution, I'm just using it as a sample equation where one or more of the coefficients depends on n.)

I am moving this to Discrete Math.

Think of Difference Equations as Differencial equations.

Does a general differencial equation have a "nice" solutions? I wish!

However, there is a method to finding them. A very powerful method is known as generating functions.

You can learn more about them here.