The analytic and discretized dissipativity of nonlinear infinite-delay systems of the form x＇（t） = g（x（t）,x（qt））（q∈ （0, 1）, t 〉 0） is investigated. A sufficient condition is presented to ensure that the above nonlinear system is dissipative. It is proved the backward Euler method inherits the dissipativity of the underlying system. Numerical examples are given to confirm the theoretical results.
The sufficient conditions for the stability and asymptotic stability of Runge-Kutta methods for nonlinear neutral delay integro-differential equations are derived. A numerical test that confirms the theoretical results is given in the end.
