非线性(时滞)动力学问题的一种新暂态时程积分解法  

An Innovative Transient Time-integration Method for Nonlinear Dynamic Problems with or without Time-delay

作　　者：颜廷浩 任传波[1] 周继磊[1] 吴凯伟 曹军帅 孙志钏 YAN Ting-hao;REN Chuan-bo;ZHOU Ji-lei;WU Kai-wei;CAO Jun-shuai;SUN Zhi-chuan(School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255000, China)

机构地区：[1]山东理工大学交通与车辆工程学院,淄博255000

出　　处：《科学技术与工程》2020年第32期13099-13106,共8页Science Technology and Engineering

基　　金：国家自然科学基金(51275280)。

摘　　要：非线性微分方程很难求得精确解析解,数值方法是求解非线性问题的一种有效手段。针对非线性微分方程,提出一种新的暂态时程积分方法。在暂态时程积分过程中,将非线性项看作非齐次项,在瞬态区间起始时刻处进行Taylor展开,并结合Romberg数值积分进行计算。Taylor展开时,将系统状态方程连续引入到非线性项导数的求解过程中,可简单有效地计算高阶导数。在此基础上,对含有时滞的非线性微分方程数值解法进行了研究,将时滞项同样看作非齐次项,利用线性插值处理后,结合Romberg积分进行计算。实例计算结果表明,该方法对有无时滞的非线性微分方程均可求得较高精度的数值解。It is difficult to obtain an exact analytical solution for nonlinear differential equations.Numerical methods are an effective way to solve nonlinear problems.Therefore,an innovative transient time-integration method was proposed for nonlinear differential equations.In the transient time-integration process,the nonlinear term was regarded as a non-homogeneous term.Taylor expansion was performed at the beginning of the transient interval.Romberg numerical integration was used for calculation.The system state equation was continuously introduced into the nonlinear term derivative,then the high-order derivative could be calculated simply and efficiently.On this basis,the numerical solution of nonlinear differential equations with time-delay was studied.The time-delay term was also treated as a non-homogeneous term.Linear interpolation and Romberg integral were used for calculation.The example results show that the method can obtain a higher precision numerical solution for nonlinear differential equations with or without time delay.

关 键 词：非线性微分方程 时滞 暂态时程积分法 Romberg积分 TAYLOR级数 线性插值 

分 类 号：O302[理学—力学]