Dissipativity of one-leg methods for dynamical systems with delays Original Research Article

This paper is concerned with the numerical solution of dissipative initial value problems with delays by one-leg methods. We focus on the dissipativity of numerical methods. Some general results are given. Specially, an irreducible one-leg method is dissipative for finite-dimensional dynamical systems with delays if and only if it is A-stable and it is dissipative for infinite-dimensional systems if and only if it is strongly A-stable.