An improved explicit time integration method is proposed for linear and nonlinear dynamics. Its calculation procedure is obtained with cubic B-spline interpolation approximation and weighted residual method. In the formulation, a momentum corrector is used to improve actual computation accuracy, especially for some special discontinuous loads. Analytical solutions of the local truncation errors, algorithmic damping and period elongation have been deduced to obtain the influence of algorithmic parameters on these basis algorithmic properties. The proposed method possesses at least second-order accuracy and can achieve at most third-order accuracy for no physical damping case. With free algorithmic parameters, the proposed method has controllable stability and numerical dissipation. Some demonstrative numerical examples are tested to confirm high efficiency of the proposed method for a variety of dynamic problems such as, dynamic response analysis of linear systems under various representative applied loads, finite element analysis (FEA) for dynamic response of engineering structures, and nonlinear dynamic analysis for strong nonlinear system.

针对线性和非线性动力学提出了一种改进的显式时间积分方法。其计算过程采用三次B样条插值逼近和加权残差法得到。在公式中，使用动量校正器来提高实际计算精度，特别是对于一些特殊的不连续载荷。推导出局部截断误差、算法阻尼和周期伸长的解析解，得到算法参数对这些基础算法性质的影响。所提出的方法至少具有二阶精度，并且在没有物理阻尼的情况下最多可以达到三阶精度。该方法算法参数自由，稳定性和数值耗散可控。