Krylov subspace spectral (KSS) methods are high-order accurate, explicit time-stepping methods for partial differential equations (PDEs) that possess stability characteristic of implicit methods. KSS methods compute each Fourier coefficient of the solution from an individualized approximation of the solution operator of the PDE. As a result, KSS methods scale effectively to higher spatial resolution. This paper will present a convergence analysis of a second-order KSS method applied to a 1-D wave equation in an inhomogeneous medium. Numerical experiments that corroborate the established theory are included, along with a discussion of generalizations, such as to higher space dimensions.

翻译：Krylov 子空间光谱(KSS) 方法对于具有隐含方法稳定性特征的局部差价方程(PDEs)来说是高度精确、明确的时间跨度方法。 Kylov 子空间光谱(KSS) 方法从PDE 的解决方案操作员的单个近似度计算出溶液的每个Fourier系数。因此, Kylov 子空间光谱(KSS) 方法有效到更高的空间分辨率。本文件将提出对在不相容介质介质中适用于1-D波方程的第二阶级KSS 方法的趋同分析。 包含与既定理论相匹配的数值实验,同时讨论一般化,例如更高的空间维度。