Dissipativity of -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 θ -methods and linear θ -methods for the underlying systems. It is shown that, for θ ∈ [ 1 2 , 1 ] , any one-leg θ -method and linear θ -method can inherit the dissipativity of the underlying systems.