Dissipativity of Runge–Kutta methods for neutral delay differential equations with piecewise constant delay

The numerical approximation of neutral dissipative initial value problems with piecewise constant delay by fixed time stepping Runge–Kutta methods is considered and two sufficient conditions for the dissipativity of the system are given. The concept of (weak) E(λ)E(λ)-dissipativity is introduced. It is shown that under some assumptions a DJ-irreducible, algebraically stable Runge–Kutta method is (weakly) E(λ)E(λ)-dissipative.