Consider the explicit midpoint method, i.e $$y_{n+1}-y_{n-1} = 2hf(y_n).$$
I'm asked to apply this method to the linear test equation, $f(y_n) = \lambda y_n,$ in order to find the method's stability region.
So I have $$y_{n+1}-y_{n-1} = 2h\lambda y_n.$$
In the problems I've done before I wouldn't have the $y_{n-1}$ term so I could just easily write $y_{n+1} = R(z)y_n.$ How would I solve this?