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

GATE Mechanical Engineering (ME) 2021 Shift 1 Solved Paper

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The ordinary differential equation

\;{dy}/{dt} = −π y

subject to an initial condition y(0) = 1 is solved numerically using the following scheme:

\;{y(t_{n\;+\;1})−y(t_{n})}/{h} = −π y(t_{n})

where h is the time step, t_n = nh, and n = 0, 1, 2, .... This numerical scheme is stable for all values of h in the interval ______.

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