The discussion focuses on the conversion of inhomogeneous recurrence relations to homogeneous forms, specifically within the context of linear second-order difference equations. A homogeneous difference equation is represented as an+2 + c1 an+1 + c0 an = 0, while an inhomogeneous equation is expressed as an+2 + c1 an+1 + c0 an = bn. Participants requested examples to clarify the conversion process, emphasizing the need for practical illustrations to enhance understanding.
PREREQUISITESMathematicians, students of discrete mathematics, and anyone interested in understanding and solving recurrence relations, particularly in the context of difference equations.
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.