Inhomogeneous recurrence relation

[andrew1]

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]

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

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

$\chi$ $\sigma$

 

[andrew1]

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

$\chi$ $\sigma$

Could you possibly provide an example, this would help me understand it a bit better.

 

[chisigma]

Could you possibly provide an example, this would help me understand it a bit better.

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

$\chi$ $\sigma$

 

[andrew1]

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

$\chi$ $\sigma$

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.

 

[chisigma]

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.

A general procedure to attack inhomogeneous difference equation is illustrated here...

http://mathhelpboards.com/discrete-mathematics-set-theory-logic-15/difference-equation-tutorial-draft-part-ii-860.html#post4671

Kind regards

$\chi$ $\sigma$