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We present a basic althought little known numerical stability condition: for convection equations, the von Neumann stability constraint ∥ ∥ ≤ (1 +    Δ) ∥ ∥ drives to the stability condition Δ ≤ Δ with $\mathit{\alpha }\mathrm{=}\frac{\mathit{p}\mathrm{(}\mathrm{2}\mathit{q}\mathrm{-}\mathrm{1}\mathrm{)}}{\mathit{q}\mathrm{(}\mathrm{2}\mathit{p}\mathrm{-}\mathrm{1}\mathrm{)}}$ where is an integer linked to the stability domain of the time scheme and  ≥  an integer linked to the upwind property of the space discretization (in the...