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

翻译：我们提出了一种高效的时间积分方法，用于处理具有时间高频振荡输入项的Klein-Gordon方程。新方法在从缓变到高度振荡的整个范围内均具有高精度。该方法基于针对输入项结构定制的分裂格式，能够均匀地解析系统中所有频率的振荡，且误差常数不随振荡增强而增大。数值实验验证了我们的理论发现，并展示了新方案的有效性。