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Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 2 / 41C / b / i / Solution

The first scheme has

H (θ) = 1 + μ (1 - e^{- i θ}) .

At

θ = π

,

∣ H (π) ∣ = 1 + 2 μ .

Since the Courant number obeys

μ \geq 0

, stability therefore holds exactly for

μ = 0 .

Solved by gpt-5.6-sol high.

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