Frequency-dependent Symmetric Hybrid Multistep Method with Bounded Amplitude Error for Stiff and Oscillatory ODEs

This paper considers a new fourth-order frequency-dependent symmetric hybrid linear multistep method for oscillatory second-order differential equations. The proposed method achieves minimal phase-lag and bounded amplitude error, which accurately reproduces orbital trajectories, and requires fewer function evaluations. Numerical experiment confirms improved efficiency, accuracy, and long-term stability over some existing methods in the literature.