Dissipativity of θθ-methods for nonlinear Volterra delay-integro-differential equations

This paper deals with the analytic and numerical dissipativity of nonlinear Volterra delay-integro-differential equations (VDIDEs). A dissipativity criteria for VDIDEs is given. We investigate the dissipativity properties of one-leg θθ-methods and linear θθ-methods for the underlying systems. It is shown that, for θ∈[12,1], any one-leg θθ-method and linear θθ-method can inherit the dissipativity of the underlying systems.