【摘要】 本文利用一维双曲型偏微分方程组初边值问题数值稳定性的ＧＫＳ定理的物理解释和推广．分析了多次透射公式在数值实现中可能出现的一种高频失稳机制。即在多维离散网格中，沿某一空间方向的外行简谐波，由于与其他空间方向节点运动的耦合效应可以使能量传播方向反向。文中通过数值试验对这一失稳机制作了初步验证。更多还原

【Abstract】 The GKS13’ stability theorem for one-dimensional model of hyperbolic initial and boundary value problem and its explanation and extension based on the concept of group velocity are generalized firstly. Another possible high-frequency instability mechanism in numerical realization of multi-transmitting formula (MTF) is pointed out based on that explanation and extension, namely. coupling effect of outgoing harmonic wave along one direction and node motion in other directions can reverse the energy propagation in multi-dimensional discrete grids. This instability mechanism is preliminarily verified through numerical experiments.更多还原