For a numerical method for solving $y^{\prime}=f(t, y)$, define the linear stability domain, and state when such a method is A-stable.

Determine all values of the real parameter $a$ for which the Runge-Kutta method

$$\begin{aligned} k_{1} &=f\left(t_{n}+\left(\frac{1}{2}-a\right) h, y_{n}+\left(\frac{1}{4} h k_{1}+\left(\frac{1}{4}-a\right) h k_{2}\right)\right) \\ k_{2} &=f\left(t_{n}+\left(\frac{1}{2}+a\right) h, y_{n}+\left(\left(\frac{1}{4}+a\right) h k_{1}+\frac{1}{4} h k_{2}\right)\right) \\ y_{n+1} &=y_{n}+\frac{1}{2} h\left(k_{1}+k_{2}\right) \end{aligned}$$

is A-stable.