On the stability of continuous quadrature rules for differential equations with several constant delays

The aim of the present paper is to study the stability propertiesof the numerical methods for pure delay differential equations.The methods we consider are based on a quadrature rule and aninterpolant (NCE) to get an approximation of the retarded part(continuous quadrature rule). As a test equation we consider and we give sufficient conditions for the boundedness of thesolutions. The same behaviour is preserved by the continuousquadrature rule under some restriction on the parameters. Asa conclusion we give some examples. This work was supported by CNR and M.U.R.S.T.