Project ForgeEngineering Mathematics
Calculus
GATE 2021
Hard
The ODE dy/dt = -πy, y(0)=1, is solved numerically using the explicit scheme [y(t_{n+1}) - y(t_n)]/h = -πy(t_n), h = time step. This numerical scheme is stable for all values of h in the interval
- 0 < h < 2/π
- B0 < h < 1
- C0 < h < π/2
- Dfor all h > 0
Explanation
The scheme gives y(t_{n+1}) = (1-hπ)y(t_n), an amplification factor of (1-hπ). Stability (bounded solution) requires |1-hπ| < 1, i.e. 0 < hπ < 2, i.e. 0 < h < 2/π.
Source: GATE ME 2021 Session 1 (ME-1) (2021)
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