一类2-指标变延迟微分代数方程BDF方法的收敛性  

Convergence of Backward Differentiation Formulas for Index-2 Differential-algebraic Equations with Variable Delay

作　　者：刘红良[1] 肖爱国[1] 

机构地区：[1]湘潭大学数学与计算科学学院,科学工程计算与数值仿真湖南省重点实验室,湘潭411105

出　　处：《工程数学学报》2011年第3期335-342,共8页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10971175);教育部高校博士点基金(20094301110001);湖南省自然科学基金(09JJ3002);湘潭大学博士科研启动项目(11QDZ01)~~

摘　　要：延迟微分代数方程经常出现在自动控制、电力和电路分析、多体动力学等许多实际应用问题中.目前对延迟微分代数方程数值分析研究主要集中于线性问题和1-指标问题;对高指标非线性延迟微分代数方程数值分析的研究较困难,国内外仅有少量工作且大多为常延迟.本文将向后微分公式(BDF)应用于求解2-指标非线性变延迟微分代数方程,获得了相应的收敛性结果,并通过数值试验进行了验证.Delay differential-algebraic equations often arise in automatic control,power and circuit analysis,multi-body dynamics,etc.The current researches on numerical analysis for delay-differential-algebraic equations are mainly focused on linear problems and 1-index problems.It is di？cult to do numerical analysis for high-index nonlinear delay-differential-algebraic equations,and there are only a few results for this kind of problems,furthermore,most of them are about constant-delay problems.The backward differentiation formulas are applied in this paper to index-2 nonlinear differential-algebraic equations with variable delay.The corresponding convergence results are obtained and confirmed by some numerical examples.

关 键 词：2-指标微分代数方程 向后微分公式 收敛性 变延迟 

分 类 号：O221.4[理学—运筹学与控制论]