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

摘要

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∈[12,1], any one-leg θ-method and linear θ-method can inherit the dissipativity of the underlying systems.