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Centered three-level wave scheme

For

v_{m}^{n + 1} - 2 ρ v_{m}^{n} + v_{m}^{n - 1} = μ (v_{m + 1}^{n} - 2 v_{m}^{n} + v_{m - 1}^{n}),

the amplification polynomial is

G^{2} + (4 μ sin^{2} (θ /2) - 2 ρ) G + 1 = 0.

All modes have unit-modulus roots only when

ρ = 1

and

0 \leq μ \leq 1

.

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Solution