一类弱非线性振动问题的算法研究  

Algorithm study of a class of weak nonlinear vibration system

作　　者：陈汉军[1] 黄东卫[1] 高琴[1] 

机构地区：[1]天津工业大学理学院,天津300160

出　　处：《天津工业大学学报》2005年第6期54-56,共3页Journal of Tiangong University

基　　金：国家自然科学基金项目(10472077;50375107)天津应用基础研究重点项目(043801911)

摘　　要：分析了龙格库塔法、多尺度法、插值摄动第一法、插值摄动第二法等4种方法在计算一类非线性振动问题时的差异,给出了每一种方法对应的时程图和相位图,编写了每种方法的Matlab程序．研究表明当参数ε很小、离开初值的时间很小时,插值摄动第一法比多尺度法有更好的精度．ε=0．1时插值摄动第二法误差为22．5％．The difference of Runge-Kutta method, the method of multiple scales, the first method of interpolate perturbation, the second method perturbation to calculate a type of nonlinear vibration problems is analyzed, and timedisplacement diagram and phase diagram corresponding every method is provided. The program of every algorithm is written in Matlab. The results show that the first interpolate perturbation method is more exact than the method of multiple scales when ε and the time deviating from the initial value are vety small, and when ε = 0.1, the second interpolate perturbation method error is 22.5%.

关 键 词：龙格库塔法 多尺度法 插值摄动法 MATLAB 

分 类 号：O231.2[理学—运筹学与控制论]