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求解运动方程的一种高精度时间步进格式

发表时间:2011-08-15  浏览量:1240  下载量:592
全部作者: 刘忠波
作者单位: 大连海事大学交通运输装备与海洋工程学院
摘 要: 为有效求解力学中常见的运动方程,将运动方程分裂成2个偏微分方程组成的联立方程组。针对该联立方程组,建立三阶Adams�Bashforth格式预报和四阶Adams�Moulton格式校正的有限差分数值模型,在求解中采用迭代法。为证明该算法的优越性,针对单自由度无阻尼质量弹簧振动问题进行数值模拟,同时采用预报校正的Crank�Nicolson格式算法进行比较,在不同时间步长的情况下,将该算法的计算结果、Crank�Nicolson格式算法的计算结果与解析解进行比较。结果表明:该算法的数值结果与解析解结果吻合程度更高,且绝对误差很小,说明高精度时间步进格式可有效求解力学中的运动方程,而预报校正的Crank�Nicolson格式并不适合这种问题。
关 键 词: 物理力学;运动方程;数值计算;预报校正;Adams�Bashforth�Moulton格式
Title: High accuracy time marching scheme to solve motion equations
Author: LIU Zhongbo
Organization: College of Transportation Equipment and Ocean Engineering, Dalian Maritime University
Abstract: To effectively solve motion equations in mechanical problem, the equation was split to two equations. Based on these equations, a composite third order Adams�Bashforth predict and fourth order Adams�Moulton correct was applied and a finite difference method numerical model was established, and iterative method was used in the solution process. To prove the presented algorithm, numerical simulations were carried out upon a one�degree�freedom spring vibration without damping problem, and the Crank�Nicolson scheme was also applied to solve the equations to make a comparison. The computed results of the presented method and those of Crank�Nicolson method were compared against analytical solution with different time steps. The presented could give better results and the agreement is quite good, which shows the presented high accuracy time marching method can be effectively applied to solve the motion equations and Crank�Nicolson scheme is not applicable for this problem.
Key words: physical mechanics; motion equation; numerical model; predict�correct; Adams�Bashforth�Moulton scheme
发表期数: 2011年8月第15期
引用格式: 刘忠波. 求解运动方程的一种高精度时间步进格式[J]. 中国科技论文在线精品论文,2011,4(15):1425-1429.
 
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