An improved time integration scheme is proposed for linear and nonlinear dynamics. The proposed scheme has two free parameters which control numerical dissipation and accuracy effectively. Basic properties including spectral stability, algorithmic accuracy, algorithmic damping, period elongation and overshooting behavior are investigated. The influences of algorithmic parameters on these properties are quantified. The effectiveness of the proposed scheme for linear and nonlinear dynamics is evaluated through some numerical examples. Analytical and numerical results demonstrate that the proposed scheme has the following significant characteristics: (1) desirable accuracy can be obtained for various linear and nonlinear problems, when compared with other effective schemes; (2) for nonlinear problems, new scheme also shows good performance; (3) the proposed scheme has simple formulation and good compatibility for various dynamic problems, and thus, is a promising candidate for practical analysis.

中文翻译：

---

一种改进的子步复合时间积分公式，具有增强的线性和非线性动力学性能

针对线性和非线性动力学提出了一种改进的时间积分方案。所提出的方案有两个自由参数，可有效控制数值耗散和精度。研究了包括光谱稳定性、算法精度、算法阻尼、周期延长和过冲行为在内的基本特性。量化算法参数对这些属性的影响。通过一些数值例子评估了所提出的线性和非线性动力学方案的有效性。分析和数值结果表明，该方案具有以下显着特点： (1) 与其他有效方案相比，对各种线性和非线性问题都能获得理想的精度；(2) 对于非线性问题，新方案也表现出良好的性能；