連續流車流模式屬雙曲線型偏微分方程式，求解不易，因此，一般多 藉由有限差分法加以近似求解。本研究以均勻到達車流碰上停等車隊產生 向上游回溯衝擊波，以及停等車隊起動向下游疏解等兩個嚴苛的交通狀況 為例，進行多種有限差分方法在不同階等連續流模式的適用性評比。結果 發現， Lax-F 有限差分法無論是針對一階準線性連續流模式（即LWR 模式） 或高階連續流模式，均能獲致與解析解最為相近的近似解，而且安定性與 收斂性亦佳，適用性最佳。此與以往國內外研究略有不同，主要係因以往 研究所研析的交通案例均侷限於非窒塞交通狀態及Payne 模式本身缺陷所 致一。

Beeαuse continuum trαiffic flow models αre described by hyperbolic pαrtiαl differential equαtions and the exact solutions to the models αre difficult to derive αnalytically，finite difference methods αre commonly used to αpproximate the solutions. In this paper, the finess of several finite difference methods under different continuum flow models is assessed in two extreme trαffic conditions, a bαckward shock wαve formed by α uniform arrival flow encountering α stopped flow and a forward shock wαve formed by α discharging flow. The results show that the Lαx-F method can obtain good α'Pproximαtions for both the first-order quasi-lineαr continuum model (i.e., the LWR model） αnd the high-order continuum flow model with good stα·bility αnd convergence. This finding is different from previous domestic αnd foreign studies primarily because pαst studies ααmined only traffic cαses with uncongested traffic conditions αnd because of the drα1wbαcks of the Pαyne model itself