Hi, I'm really struggling to get the answer with these boundary locus methods. If anyone could help that would be great. The linear multistep method is
y[n+2] - 4/3 y[n+1] +1/3 y[n] = 2/3 hf[n+2]
I get the stability polynomial to be,
pi(r,h) = r^2 - 4/3 r + 1/3 - 2/3 hr^2
Then sub in r=e^(i*theta) and set the stability polynomial = 0, then find the endpoints of the interval such that Im(h(theta)) = 0 and end up with
theta = 0 and theta = 9
However after this I get really stuck, the answer is
h is a member of (-infinity, 0) union (4, infinity)
and I can't work out how to get the 4 at all.
Thanks again for any help!