The Finite difference scheme:

\begin{equation} y_{n+3}-y_{n+1}= \frac {h}{3}(f_{n}-2f_{n+1}+7f_{n+2})

\end{equation}

Deduce that the scheme is convergent and find its interval of absolute stability(if any)

=> the first characteristic polynomial is then

\begin{equation} ρ(r)= r^3 -r \end{equation}

\begin{equation} r^3 -r =0 \end{equation}

\begin{equation} r(r^2-1) =0 \end{equation}

\begin{equation} r=0,-1,1 \end{equation}

These have magnitude less than or equal to 1 and there are no repeated zero with magnitude equal to 1, $|r|<1$. So the method is zero-stable and is convergent.

For its interval of absolute stability, i was thinking to substitute $$y'=λy$$ into finite scheme but because of $y_{n+3}$involve, its not good idea to do so. Can anyone help how to calculate the interval of absolute stability?