实时RK算法的稳定性分析  

Stability Analysis of Real-time RK Algorithm

作　　者：黄振全[1] 蒋珉[2] 陈志武[1] 

机构地区：[1]桂林空军学院,桂林541003 [2]东南大学自动化研究所,南京210096

出　　处：《系统仿真学报》2008年第5期1143-1145,共3页Journal of System Simulation

基　　金：高等学校博士学科点专项科研基金(2004-0286012)

摘　　要：首先针对一般RK算法与实时RK算法的稳定域进行比较,提出了求解绝对稳定域的方法,分析了绝对稳定域面积与绝对稳定区间大小的区别,采用寻优方法推导出实时三级二阶、四级三阶、五级四阶、六级五阶实时RK算法的最大稳定域,并画出不同阶实时RK算法可能达到的最大稳定域与稳定区间的图形。最后通过对实时RK算法的绝对稳定域面积与稳定区间的比较和仿真实例分析,得出了采用绝对稳定域面积能更好地表征实时RK算法稳定性的结论。而且基于最大稳定域面积的实时RK算法将在实时仿真中得到了广泛的应用。Firstly, a method was put forward to calculate the absolute stability region aiming at comparison between the general RK algorithm stability region and the real-time RK algorithm stability region, and the difference of the absolute stability region area and zone size were analyzed, Adopting optimizing methods, maximum stability region of real-time three-stage two-order, four-stage three-order, five-stage four-order and six-stage five-order Runge-Kutta algorithms were deduced, and also the figures were sketched for different order real-time RK algorithms of which may be achieved the maximum absolute stability region area and zone, Finally, according to comparison of the real-time RK algorithm absolute stability region area and zone and simulation example analysis, it is deduced that a conclusion has used the stability region area to be able to attribute the real-time RK algorithm stability well. Based on maximum stability region, the real-time RK algorithm can be used a wide application in real-time simulation.

关 键 词：实时仿真 龙格-库塔算法 稳定性 稳定域面积 稳定区间 

分 类 号：TP391[自动化与计算机技术—计算机应用技术]