能量的局部误差估计和直接积分法的时步自适应算法

本文研究了直接积分法中时间离散引起的位移和速度局部误差，区分了动力系统的能量，能量的局部误差和位移、速度局部误差的能量三者的关系。提出将系统能量的局部误差作为后验误差估计指标。该误差估计指标的物理意义明确，不仅考虑了位移局部误差而且还考虑了速度局部误差对能量局部误差的影响。本文还给出了相应的时间步长自适应调节算法，并在算例中实现了时间步长的自适调节计算，同时验证了本文误差估计的精确性和可靠性

Local Error Estimator of Energy and Adaptive Time-Stepping Procedure for Direct Integration Method

In this paper,the local errors of displacement and velocity induced by temporal discrete in directintegration are studied.Then,the difference among the system energy,local error of energy as well as the energyfor local errors of displacement and velocity are distinguished,The local error of energy is presented as a posteriorierror estimator which has clear physical meaning. In the estimator not only the local errors of displacement but alsothe local errors of velocity are taken into account.An adaptive time-stepping procedure is presented. The numericalcomputation is also performed,and the presented estimator is proved to be of high accuracy and reliability.