非线性动力方程的一种改进精细积分单步方法  

An improved precise integration single-step method for nonlinear dynamic equations

作　　者：刘冬兵 王永 李博文 奕仲飞 张磊[4] 黎慧 LIU Dongbing;WANG Yong;LI Bowen;YI Zhongfei;ZHANG Lei;LI Hui(College of Mathematics and Computer,Panzhihua University,Panzhihua 617000,China;UHV Converter Station Branch of State Grid Shanghai Municipal Electric Power Company,Shanghai 201413,China;Neijiang Power Supply Company of State Grid Sichuan Electric Power Company,Neijiang 641000,China;College of Electrical Engineering&New Energy,China Three Gorges University,Yichang 443002,China)

机构地区：[1]攀枝花学院数学与计算机学院,四川攀枝花617000 [2]国网上海市电力公司特高压换流站分公司,上海201413 [3]国网四川省电力公司内江供电公司,四川内江641000 [4]三峡大学电气与新能源学院,湖北宜昌443002

出　　处：《振动与冲击》2022年第5期182-188,共7页Journal of Vibration and Shock

基　　金：四川省科技厅应用基础项目(2019YJ0683)。

摘　　要：微分求积法和单步块方法都是单步多级数值方法,但是直接应用于求解非线性动力方程时的计算量比较巨大,为此提出了一种基于单步块方法的改进精细积分单步方法。结合精细积分法,该方法采用s级的单步块方法的第s个方程对Duhamel积分项进行数值积分。具体采用四阶Runge-Kutta法获得待求变量的预估值,并采用新四点积分公式计算Duhamel积分项。相对于现有的单步方法,该改进算法在数值精度和稳定性上更优。通过非线性动力方程的典型算例验证了该算法的优势。Differential quadrature method and single-step block method are single-step multistage numerical methods, but the amount of calculation is huger when they are directly applied to solve nonlinear dynamic equations. Here, an improved precise integration single-step method based on the single-step block method was proposed. Combined with the precise integration method, this method adopted the s;equation of the s-level single-step block method to numerically integrate Duhamel integral term. Specifically, the fourth-order Runge-Kutta method was used to obtain the predicted value of the variable to be solved, and the new 4-point integral formula was used to calculate Duhamel integral term. It was shown that compared with the existing single-step method, the proposed improved algorithm has better numerical accuracy and stability;its advantages are verified with typical examples of nonlinear dynamic equations.

关 键 词：非线性 精细积分法 单步块方法 PADÉ逼近 预估-校正 

分 类 号：O322[理学—一般力学与力学基础]