TVD of a Model Problem Analyze whether the upwind scheme (6.22), the Lax–Friedrichs scheme (6.25)

and the Lax–Wendroff scheme (6.30) applied to the scalar partial differential equation ut + aux, a> 0, t ≥ 0, x ∈ IR satisfy the TVD property.

Hint: Apply Lemma 6.3.