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 ( 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.