The ordinary differential equation \(\frac{dy}{dt}=-\pi y\) subject to an initial condition y(0) = 1 is solved numerically using the following scheme:
\(\frac{y(t_{n+1})-y(t_n)}{h}=-\pi y(t_n)\)
where h is the time step, tn = nh, and n = 0, 1, 2, .... This numerical scheme is stable for all values of h in the interval ______.
1
\(0 < h < \frac{\pi}{2}\)
2
\(0 < h < \frac{2}{\pi}\)
3
0 < h < 1
4
for all h > 0