Dissipativity of -methods for a class of nonlinear neutral delay integro-differential equations

This paper is focused on the analytic and numerical dissipativity of nonlinear neutral delay integro-differential equations of the form The dissipativity criteria of the theoretical solutions are obtained by applying the generalization of the Halanay inequality. Furthermore, the dissipativity of one-leg -methods and linear -methods for the underlying system is investigated. It is shown that, for <1, both the one-leg -methods and linear -methods are dissipative. Numerical example illustrates the theoretical results.