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We prove a sharp uniform generalized Gaussian bound for the Green's functionof the Lax-Wendroff and Beam-Warming schemes. Our bound highlights the spatialregion that leads to the well-known (rather weak) instability of these schemesin the maximum norm. We also recover uniform bounds in the maximum norm whenthese schemes are applied to initial data of bounded variation.

The Green's function of the Lax-Wendroff and Beam-Warming schemes