Asymptotic behavior of nonlinear delay differential–algebraic equations and implicit Euler methods

This paper is concerned with the theory of asymptotic behavior of a class of nonlinear delay differential–algebraic equations and implicit Euler methods. Sufficient conditions for the theory of stability and asymptotic stability of the equations are given. An example shows these conditions can be applied conveniently to nonlinear equations. It is also showed that the implicit Euler methods are stable and asymptotically stable.