Asymptotic Stability Of Neutral Delay Differential-Algebraic Equations-and Numerical Methods

Delay differential-algebraic equations (DDAEs), which has both delay and algebraic constraints,arise in a wide variety of engineering, medicine, biology, physics,space and economic fields. And neutral delay-integro-differential-algebraic equation is subclass of the differential-algebraic system.Recently, with the rapid development of delay system technology, many scholars have pay careful attention to the algorithm theory of NDDAEs.However, because of the complexity of DIDAEs, it becomes quite difficult to obtain the analytic solutions. Therefore, it is necessary to investigate the numerical methods for DIDAEs and they have become one of the most important and primary methods to solve DIDAEs.Furthermore,effective and reliable computational methods and the stability of numerical methods are the important problems we have to face in the research of numerical solution.This paper adopts two kinds of method to analyze the numerical stability of neutral delay integro-differential algebraic equations(NDIDAEs) . This thesis is concerned with the asymptotic stability of analytical and numerical solutions of (NDIDAEs).First, it has simply introduced the thesis research situation and some basic knowledge,basic theorems , some common lemma of delay differential equations (DDEs)and the main work of this paper.Based on this, it further discussed the numerical stability of two step Runge-Kutta method to solve the NDIDAEs, and it is proved that A -stable two-step Kutta-Runge methods can preserve the asymptotic stability of the underlying linear systems.At last, we study the numerical stability of the Rosenbrock method and Linear Multistep methods solving NDIDAEs, it is shown that A - stable Rosenbrock method and Linear Multistep methods can keep the asymptotic stability of underlying linear systems.