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

Abstract

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 ∈ [frac(1, 2), 1], any one-leg θ-method and linear θ-method can inherit the dissipativity of the underlying systems. © 2006 Elsevier B.V. All rights reserved.