一类非线性滞时微分代数方程及BDF方法的稳定性分析

发布时间：2018-05-30 00:17

本文选题：稳定 + 非线性滞时微分代数方程　；参考：《上海师范大学》2015年硕士论文

【摘要】：滞时微分代数方程(DDAEs)是具有时滞影响和代数约束的微分方程,为计算机辅助设计、化学反应模拟、线路分析、最优控制、实时仿真以及管理系统等科学与工程应用问题提供了有效的数学模型.目前,关于线性滞时微分代数方程的稳定性与数值算法的研究较多,但对于非线性滞时微分代数方程的研究很少,本文主要研究一类非线性滞时微分代数方程及其数值算法的稳定性与渐近稳定性.首先,根据稳定与渐近稳定的定义,我们给出了方程稳定和渐近稳定的充分条件,其次,讨论了用2阶BDF算法求解这类滞时微分代数方程所得数值解的稳定性与渐近稳定性,最后,给出了一些数值实验来验证本文理论的正确性.
[Abstract]:Delay differential algebraic equation (DDAEs) is a differential equation with time-delay effect and algebraic constraint. It is used for computer-aided design, chemical reaction simulation, circuit analysis, optimal control, etc. Real-time simulation and management systems provide an effective mathematical model for scientific and engineering applications. At present, there are many researches on the stability and numerical algorithms of linear delay differential algebraic equations, but few on nonlinear delay differential algebraic equations. In this paper, the stability and asymptotic stability of a class of nonlinear delay differential algebraic equations and their numerical algorithms are studied. Firstly, according to the definitions of stability and asymptotic stability, we give the sufficient conditions for the stability and asymptotic stability of the equations. Secondly, we discuss the stability and asymptotic stability of the numerical solutions obtained by using the second-order BDF algorithm to solve this kind of delay differential algebraic equations. Finally, some numerical experiments are given to verify the correctness of the theory.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O241.8

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