We develop method of characteristics schemes based on explicit Runge–Kutta and pseudo‐Runge–Kutta third‐ and fourth‐order solvers along the characteristics. Schemes based on Runge–Kutta solvers are found to be strongly unstable for certain physics‐motivated models. In contrast, schemes based on pseudo‐Runge–Kutta solvers are shown to be only weakly unstable for periodic boundary conditions and essentially stable for the more physically relevant nonreflecting boundary conditions. Our implementation of nonreflecting boundary conditions does not rely on interpolation.

中文翻译：

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基于特征方法的具有交叉直线特征的双曲型方程的高阶显式格式

我们根据特征沿显式Runge-Kutta和伪Runge-Kutta三阶和四阶求解器开发特征方案的方法。发现基于Runge-Kutta求解器的方案对于某些物理激励模型非常不稳定。相比之下，基于伪Runge-Kutta求解器的方案仅在周期性边界条件下微弱不稳定，而在与物理相关的非反射边界条件下基本稳定。我们的非反射边界条件的实现不依赖于插值。