Analysis of descriptor systems using numerical algorithms
Analysis of descriptor systems using numerical algorithms
复制标题
使用数值算法分析描述符系统
DOI：
10.1109/tac.1981.1102560
复制
发表时间：
1981
影响因子：
6.8
通讯作者：
M. Epton
中科院分区：
文献类型：
--
作者：
R. F. Sincovec;A. Erisman;E. Yip;M. Epton
本文分析了大规模动力系统E y（t）=Ay（t）+g（t），Y（t_{0}）=y_{0}的数值解法，其中E和A是可能奇异的矩阵.这种类型的系统被称为隐式系统，最近被称为广义系统，因为它们是由用物理变量来表示系统方程而产生的。这种系统的特殊情况是代数微分系统。我们讨论了这种提法的数值优势，并确定了一类数值积分算法，具有准确性和稳定性，适合于广义系统，并保持结构，检测不可解系统，解决初始值的一致性问题，并适用于“僵硬”的广义系统。我们还提出了一个算法的控制的局部截断误差的状态变量。
In this paper we analyze numerical methods for the solution of the large scale dynamical system E\dot{y}(t)=Ay(t)+g(t),Y(t_{0})=y_{0} , where E and A are matrices, possibly singular. Systems of this type have been referred to as implicit systems and more recently as descriptor systems since they arise from formulating system equations in physical variables. Special cases of such systems are algebraic-differential systems. We discuss the numerical advantages of this formulation and identify a class of numerical integration algorithms which have accuracy and stability properties appropriate to descriptor systems and which preserve structure, detect nonsolvable systems, resolve initial value consistency problems, and are applicable to "stiff" descriptor systems. We also present an algorithm for the control of the local truncation error on only the state variables.