Dissipativity of θ-methods for nonlinear delay differential equations of neutral type

This paper is concerned with the analytic and numerical dissipativity of nonlinear neutral delay differential equations (NDDEs) of the form y^'(t)=F(y(t),G(y([email protected]),y^'([email protected]))). The basic idea is to reformulate the original problem eliminating the dependence on the derivative of the solution in the past values. A dissipativity criteria for nonlinear NDDEs is given. Dissipativity properties of one-leg @q-methods and linear @q-methods for the underlying systems are investigated. It is shown that, for 12<@q=<1, both one-leg @q-method and linear @q-method are dissipative. Numerical examples illustrate the theoretical results.

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