The discussion revolves around the process of converting inhomogeneous recurrence relations to homogeneous ones, specifically focusing on linear second-order difference equations. Participants express confusion about the conversion process and seek clarification and examples to enhance their understanding.
Participants generally express confusion and seek clarification, indicating that there is no consensus on the conversion process or examples of inhomogeneous recurrence relations.
Participants have not provided specific examples or detailed steps for the conversion process, leaving the discussion open-ended regarding the methodology and application.
andrew said:Hi all,
Could someone please explain to me the process involved in converting an inhomogeneous recurrence to a homogeneous recurrence, I'm completely confused as to how it works.Thanks
chisigma said:For semplicity we suppose that we have linear second order difference equations. A homogeneous difference equation is written as...
$\displaystyle a_{n+2} + c_{1}\ a_{n+1}+ c_{0}\ a_{n} = 0\ (1)$
An inhomogeneous difference equation is written as...
$\displaystyle a_{n+2} + c_{1}\ a_{n+1} + c_{0}\ a_{n} = b_{n}\ (2)$
Kind regards
$\chi$ $\sigma$
andrew said:Could you possibly provide an example, this would help me understand it a bit better.
chisigma said:An example of linear homogeneous second order difference equation is here...
http://mathhelpboards.com/discrete-mathematics-set-theory-logic-15/recursive-sequences-finding-their-expressions-10478.html#post48615
Kind regards
$\chi$ $\sigma$
andrew said:Sorry, I meant an example of an inhomogeneous recurrence relation, I understand how to solve a homogeneous recurrence relation, but converting an inhomogeneous recurrence is where I am struggling.