Recursive integral time extrapolation methods for scalar waves

We derive and compare a variety of algorithms for recursive time extrapolation of scalar waves using approximate operators derived from integral solutions of a wave equation. These methods fall into two categories: those based on combining or interpolating homogeneous solutions, and those based on series expansions of heterogeneous operators. The former suffer from oscillatory noise at large velocity discontinuities unless the time step is small, whereas the latter allow accurate extrapolation at large time steps, but are more costly.