数值特征方法在一类守恒系统中的稳定性分析。第一部分：周期边界条件
Stability analysis of the numerical Method of characteristics applied to a class of energy-preserving systems. Part I: Periodic boundary conditions
AI总结：
本文研究了特征方法在非耗散双曲偏微分方程周期边界条件下的数值稳定性，比较了三种求解器的稳定性差异。
摘要：
我们研究了特征方法（MoC）应用于非耗散双曲偏微分方程（PDEs）系统时的数值（不）稳定性。我们考虑了三种不同的特征求解器：简单的欧拉（SE）、修改欧拉（ME）和 leap-frog（LF）。前两种求解器在非耗散常微分方程（ODEs）中表现出轻微但无条件的数值不稳定性。当应用于非耗散 PDEs 时，它们的不稳定性相似（或更强，对于 MoC-ME）。另一方面，LF 求解器在非耗散 ODEs 中已知是稳定的。然而，当在 MoC 框架下应用于非耗散 PDEs 时，它在三种求解器中表现出最强的不稳定性。我们还评论了在 MoC 框架下使用四阶龙格-库塔求解器的使用。
英文摘要：
We study numerical (in)stability of the Method of characteristics (MoC) applied to a system of non-dissipative hyperbolic partial differential equations (PDEs) with periodic boundary conditions. We consider three different solvers along the characteristics: simple Euler (SE), modified Euler (ME), and Leap-frog (LF). The two former solvers are well known to exhibit a mild, but unconditional, numerical instability for non-dissipative ordinary differential equations (ODEs). They are found to have a similar (or stronger, for the MoC-ME) instability when applied to non-dissipative PDEs. On the other hand, the LF solver is known to be stable when applied to non-dissipative ODEs. However, when applied to non-dissipative PDEs within the MoC framework, it was found to have by far the strongest instability among all three solvers. We also comment on the use of the fourth-order Runge--Kutta solver within the MoC framework.
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