  This paper presents a convergence analysis of a Krylov subspace spectral
(KSS) method applied to a 1-D wave equation in an inhomogeneous medium. It will
be shown that for sufficiently regular initial data, this KSS method yields
unconditional stability, spectral accuracy in space, and second-order accuracy
in time, in the case of constant wave speed and a bandlimited reaction term
coefficient. Numerical experiments that corroborate the established theory are
included, along with an investigation of generalizations, such as to higher
space dimensions and nonlinear PDEs, that features performance comparisons with
other Krylov subspace-based time-stepping methods. This paper also includes the
first stability analysis of a KSS method that does not assume a bandlimited
reaction term coefficient.
