I was given an example
$R_n = R_{n-1} + R_{n-2} $
This equation is given as an second-order equation.
Why is it so?
I was given an example
$R_n = R_{n-1} + R_{n-2} $
This equation is given as an second-order equation.
Why is it so?
The fact that it is second-order refers to the fact that the largest difference in indices is $2$. For example,
$ R_{n+4}=3R_{n+1}^2+R_n $
is a fourth-order difference equation and
$ R_{n+3}=2R_{n+2}\cdot R_{n+1} $
is a second order difference equation.
If you're familiar with ODEs, the terminology is analogous.
One explanation is that one solves (see Recurrence relation, Wikipedia, under "Solving") the following homogeneous difference equation (or recurrence relation) with constant coefficients
$a_{n}+Aa_{n-1}+Ba_{n-2}=0,$
by means of the second degree characteristic equation
$r^2+Ar+B=0,$
pretty much as one woud solve a homogeneous second-order linear ordinary differential equation with constant coefficients.