 Solution

Apply the method to the Dahlquist test equation $y^{\prime }=\lambda y$ and set $z=h\lambda$. Its amplification roots satisfyAt $z=0$ the roots are $1$ and $5/11$. A root can leave the unit disk only through $\xi =e^{i\phi }$. Substitution gives the boundary equationDirect separation into real and imaginary parts shows that both branches satisfy $\mathrm{Re}z\ge 0$; equality occurs on the branch through $z=0$. Hence no root crosses the unit circle in $\mathrm{Re}z<0$. Moreover both roots tend to zero as $z\to \infty$ in the left half-plane. Consequently the method is A-stable, and it also strongly damps the infinitely stiff limit.