Numerical Stability For Several Classes Of Delay Systems Of Linear Discrete And Distributed Type

Delay differential-algebraic equations arise in a wide variety of scientific and engineering applications, including circuit analysis, computer-aided design and real–time simulation of mechanical systems, chemical process simulation and optimal control. However, because of the complexity of the delay differential-algebraic equations, it becomes quite difficult to obtain the analytic solutions. And it becomes more difficult when the equations include integral argument. Therefore, it is necessary to investigate the numerical methods for delay differential-algebraic equations (DDAEs).In the past years a great deal of progress has been made in the analysis of numerical solutions of differential-algebraic equations, and at the same time much work has been done in the field of numerical solution of Volterra integro-differential equations. At present research on the numerical methods of delay differential-algebraic equations with integral argument hasn't been advanced developed and there is much of creative work to be done.This paper deals with the asymptotic stability of linear neutral Volterra delay-integro-differential equations. When the coefficient matrix of the derivation argument is singular, the equations become delay differential-algebraic systems .The linear multistep methods and Runge-Kutta methods have been applied to them and corresponding results have been made in the light of L.R.Potzold, U.Ascher, J.J.Zhao's research results. In addition, this paper introduces the block implicit methods and deals with the stability block methods for a kind of general linear delay differential-algebraic equations.