Analyzing high-frequency systems in mechanics and structural dynamics is a challenging problem that can be difficult to handle by conventional methods. This research addresses this problem, by developing an efficient numerical approach. The fundamentals of the new method are developed on the single-degree-of-freedom structural systems subjected to seismic excitation. The basic idea is to effectively couple the numerical integrators with the specific forms of interpolators to extend an efficient algorithm for nonlinear time-history analysis of structural systems. The integrators consist of the original Newton–Cotes 5-Point formula and its higher-order pair which are formulated in this study. Moreover, new forms of Hermite interpolators are introduced and developed in this work for new applications of seismic analysis. These are the key issues of the new formulation. Accordingly, the presented method is called Improved Newton–Cotes-Hermite 5-Point (I-NCH-5P). It efficiently manages high-frequency linear systems and nonlinear systems under any form of excitations, including earthquake records. Notably, both damped and undamped (conservative) systems are covered. High precision and remarkable simplicity in computer coding are the distinctive characteristics of I-NCH-5P. Numerical experiments clearly show that the superiority of I-NCH-5P over conventional methods like Duhamel integral, Newmark-β, and Wilson-θ methods.
