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We propose an efficient approach for time integration of Klein-Gordonequations with highly oscillatory in time input terms. The new methods arehighly accurate in the entire range, from slowly varying up to highlyoscillatory regimes. Our approach is based on splitting methods tailored to thestructure of the input term which allows us to resolve the oscillations in thesystem uniformly in all frequencies, while the error constant does not grow asthe oscillations increase. Numerical experiments highlight our theoreticalfindings and demonstrate the efficiency of the new schemes.

Effective highly accurate time integrators for linear Klein-Gordon equations across the scales