We prove a sharp uniform generalized Gaussian bound for the Green's function of the Lax-Wendroff and Beam-Warming schemes. Our bound highlights the spatial region that leads to the well-known (rather weak) instability of these schemes in the maximum norm. We also recover uniform bounds in the maximum norm when these schemes are applied to initial data of bounded variation.
翻译:我们证明,我们为绿党的Lax-Wendroff和Baam-Warming计划的职能而严格统一地统一地将高斯河系连接起来。我们的连接突出了空间区域,在最大规范中导致这些计划中众所周知的(而不是相对薄弱的)不稳定。 当这些计划应用于受约束变化的初始数据时,我们也在最高规范中恢复了统一的界限。