Stability Analysis Of A Class Of Systems Of Nonlinear Delay Algebraic Equations And Second Order BDF Methods

Delay differential-algebraic equations(DDAEs)arises in a wide variety of scientific and engineering applications.In present,many research on linear delay differential-algebraic equations,but the research results of nonlinear delay differential-algebraic equations are rare in the literature.In this paper,a class of nonlinear delay differential-algebraic equations(DDAEs)is considered.Sufficient conditions for the theory of stability and asymptotic stability of the equations are given.Then,the paper discusses numerical treatments of DDAEs and finds some conditions under which the two-step BDF methods are stable and asymptotically stable.Last,some numerical experiments are easy to check.