Abstract
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 ( t − τ ) , y ′ ( t − τ ) ) ) . 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 θ-methods and linear θ-methods for the underlying systems are investigated. It is shown that, for 1 2 < θ ⩽ 1 , both one-leg θ-method and linear θ-method are dissipative. Numerical examples illustrate the theoretical results.
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