Solve the inhomogeneous recurrence relation

a_{n}=3a_{n-1}+n^{2}-3 with a_{0}=1

Any help please? I tried a few different cases which got me nowhere.

Printable View

- Oct 29th 2012, 08:58 AMTimsBobby2Solve the following inhomogeneous recurrence relation...
Solve the inhomogeneous recurrence relation

a_{n}=3a_{n-1}+n^{2}-3 with a_{0}=1

Any help please? I tried a few different cases which got me nowhere. - Oct 29th 2012, 11:15 AMMarkFLRe: Solve the following inhomogeneous recurrence relation...
You may use the process of symbolic differencing to get a homogeneous recurrence. We are given:

(1)

Now, replace with to get:

(2)

Now, subtract (1) from (2) to get another recurrence. Repeat this process until you have a homogeneous recurrence, from which you may determine the closed form from the characteristic roots, and then determine the parameters from the initial values. - Oct 29th 2012, 11:21 AMjohnsomeoneRe: Solve the following inhomogeneous recurrence relation...
Think of recurrence equations as being like a discrete type of differential equation.

1) Solve the homogeneous case: to get

2) Now use variation of parameters. Try:

You can further simply that.