1.

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 ______.

A. \(0 < h < \frac{\pi}{2}\)
B. \(0 < h < \frac{2}{\pi}\)
C. 0 < h < 1
D. for all h > 0
Answer» C. 0 < h < 1


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