Convergence Analysis of a Krylov Subspace Spectral Method for the 1-D Wave Equation in an Inhomogeneous Medium

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.