Dissipativity of Runge-Kutta methods for dynamical systems with delays

This paper is concerned with the numerical solution of dissipative initial value problems with delays by Runge-Kutta methods. A sufficient condition f or the dissipativity of the systems is given. The concepts of D(l)-dissipat ivity and GD(l)-dissipativity are introduced. We investigate the dissipativ ity properties of (k, l)-algebraically stable Runge-Kutta methods with piec ewise constant or linear interpolation procedures for finite-dimensional an d infinite-dimensional dynamical systems with delays.