Dissipativity of θ-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 @q-methods and linear @q-methods for the underlying systems. It is shown that, for @q@?[12,1], any one-leg @q-method and linear @q-method can inherit the dissipativity of the underlying systems.

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