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Abstract
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 θ-methods and linear θ-methods for the underlying system is investigated. It is shown that, for ½<θ≤1, both the one-leg θ-methods and linear θ-methods are dissipative. Numerical example illustrates the theoretical results.
Acknowledgements
We acknowledge three anonymous reviewers for their constructive criticism of our paper. This work is supported by the NNSF of Shandong Province (No. ZR2010AQ021), the Key Project of Science and Technology of Weihai (No. 2010-3-96), the NSFC under grant No.11026189 and the Natural Scientific Research Innovation Foundation in Harbin Institute of Technology (No. HIT.NSRIF.201016 and HIT.NSRIF.201014).