时间积分方法的研究进展与挑战

时间积分方法是动力学常微分方程的一种有效数值求解工具，广泛应用于航空航天、土木工程、机械制造等工程领域的动力学分析。介绍了近几十年来时间积分方法的研究进展。回顾了该领域的经典工作，包括级数展开法、Runge-Kutta法和Newmark方法；介绍了为解决经典时间积分方法在精度、效率、耗散和稳定性方面的不足而发展出的先进时间积分方法，主要包括参数方法、高阶无条件稳定方法、保能量方法、线性多步法、复合方法和BN稳定型方法；分析比较了已有方法的性能特点和适用范围，指出了时间积分方法发展中值得关注的若干问题。 

Advances and challenges in time integration methods

Time integration methods are a powerful tool for solving transient responses, which have been widely used to solve dynamic problems in aerospace, civil engineering, machinery manufacturing, and other fields. This paper reviews the advances in time integration methods in the past decades. Firstly, some classical methods, such as the series expansion method, the Runge-Kutta method and the Newmark method, are introduced. To solve the drawbacks involved in the classical methods, several time integration methods with more desirable numerical properties, including accuracy, efficiency, dissipation and stability, have been developed. Moreover, the advanced methods, including parameters methods, higher-order unconditionally stable methods, energy-conserving methods, linear multistep methods, composite methods and BN-stable methods, are introduced in this paper. Finally, the numerical properties and application scope of the existing time integration methods are compared, and some issues worthy of attention are given.