龙格-库塔方法
MATLAB语言
插值(计算机图形学)
基质(化学分析)
变量(数学)
块(置换群论)
控制理论(社会学)
计算机科学
功能(生物学)
数学
数学优化
算法
微分方程
数学分析
计算机图形学(图像)
几何学
操作系统
人工智能
复合材料
生物
进化生物学
材料科学
动画
控制(管理)
作者
Xiaofeng Li,Xiaoxue Liu,Xiangwei Li,He Wang,Hanfei Guo
出处
期刊:Engineering Computations
[Emerald (MCB UP)]
日期:2022-10-03
卷期号:39 (9): 3232-3254
被引量:2
标识
DOI:10.1108/ec-08-2021-0500
摘要
Purpose The purpose of this paper is to propose an improved method which can shorten the calculation time and improve the calculation efficiency under the premise of ensuring the calculation accuracy for calculating the response of dynamic systems with periodic time-varying characteristics. Design/methodology/approach An improved method is proposed based on Runge–Kutta method according to the composition characteristics of the state space matrix and the external load vector formed by the reduction of the dynamic equation of the periodic time-varying system. The recursive scheme of the holistic matrix of the system using the Runge–Kutta method is improved to be the sub-block matrix that is divided into the upper and lower parts to reduce the calculation steps and the occupied computer memory. Findings The calculation time consumption is reduced to a certain extent about 10–35% by changing the synthesis method of the time-varying matrix of the dynamics system, and the method proposed of paper consumes 43–75% less calculation time in total than the original Runge–Kutta method without affecting the calculation accuracy. When the ode45 command that implements the Runge–Kutta method in the MATLAB software used to solve the system dynamics equation include the time variable which cannot provide its specific analytic function form, so the time variable value corresponding to the solution time needs to be determined by the interpolation method, which causes the calculation efficiency of the ode45 command to be substantially reduced. Originality/value The proposed method can be applied to solve dynamic systems with periodic time-varying characteristics, and can consume less calculation time than the original Runge–Kutta method without affecting the calculation accuracy, especially the superiority of the improved method of this paper can be better demonstrated when the degree of freedom of the periodic time-varying dynamics system is greater.
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