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Numerical solutions to wave-type PDEs utilizing method-of-lines require theODE solver's stability domain to include a large stretch of the imaginary axissurrounding the origin. We show here that extrapolation based solvers ofGragg-Bulirsch-Stoer (GBS) type can meet this requirement. Extrapolationmethods utilize several independent time stepping sequences, making them highlysuited for parallel execution. Traditional extrapolation schemes use all timestepping sequences to maximize the method's order of accuracy. The presentmethod instead maintains a desired order of accuracy while employing additionaltime stepping sequences to shape the resulting stability domain. We optimizethe extrapolation coefficients to maximize the stability domain's imaginaryaxis coverage. This yields a family of explicit schemes that approaches maximaltime step size for wave propagation problems. On a computer with several coreswe achieve both high order and fast time to solution compared with traditionalODE integrators.

A parallel-in-time approach for wave-type PDEs