Asymptotic Stability Of Generalized Neutral Delay Differential-Algebraic Equations

Delay differential-algebraic equations (DDAEs), which has both delay and algebraic constraints, arise in a wide variety of scientific and engineering applications, such as circuit analysis,optimal control, real-time simulation. Neutral delay differential-algebraic equations (NDDAEs) is more complicated than (DDAEs) since it not only has delay terms but also has the derivatives of delay terms. Generalized neutral delay differential-algebraic equations (GNDDAEs) which have different delays in the entries of the vector valued unknown functions, which is more complicated than (NDDAEs).The results for (GNDDAEs) are more general than those already reported , almost all of the conclusions from (GNDDAEs) can be applied to (NDDAEs) and DDAEs.Because of these equations are complicated, the analytic solution of (GNDDAEs) is difficult to obtain, the discussion of the asymptotic stability of (GNDDAEs) is necessary, then we can analysis the numerical solutions.This thesis is concerned with the asymptotic stability of analytical and numerical solutions of generalized neutral delay differential-algebraic equations(GNDDAEs).First, we considered the roots of characteristic equation of the (GNDDAEs), we get a new sufficient condition under the conditon that all the coefficient matrices can be transformed to upper triangular by nonsingular constant matrices. This assumption is true for the Hessenberg form . Then we discuss the asymptotic stability of $\theta$-methods, linear multistep methods, and two-step Runge-Kutta methods, when they are applied to the (GNDDAEs). Finally, some numerical experiments are carried out to demonstrate our conclusions, we will compare these methods, which method is asymptotic stable quickly.