 Solution

Apply the numerical method to the test equation $y^{\prime }=\lambda y$ and put $z=h\lambda$. Its linear stability domain is the set of $z$ for which the computed amplification is stable, for a one-step method $|R(z)|\le 1$ with all stage solves well-defined. The method is A-stable if this includes the whole closed left half-plane (or its interior with boundary limits).