非线性动力学系统的精细逐块积分求解方法

针对非线性动力学系统提出了一种精细逐块求解的积分方法。应用此方法，原始的非线性微分方程转换为逐块的代数方程。由于这种隐式积分格式的高精度和稳定性，相比于四阶Runge-Kutta方法和Newmark方法，此方法可以对非线性动力系统应用较大的步长。此外，此方法对具有奇异或接近奇异的系统矩阵的动力学系统仍然有效。数值算例验证了此方法的有效性。

A Precise Block-by-Block Integration Method for Nonlinear Dynamic Systems

This paper proposes a precise block-by-block integration method for nonlinear dynamic systems. By applying the proposed method, the original nonlinear differential equations are converted into algebraic equations within each block. Due to the high accuracy and stability of this implicit integration scheme, a large step size can be utilized for nonlinear dynamic systems, compared with those of the fourth order Runge-Kutta method and the Newmark method. In addition, the proposed method is also effective for dynamic systems with a singular or close to singular system matrix. Numerical examples are given to verify the proposed method.