Asymptotic behavior of multistep runge-kutta methods for systems of delay differential equations

This paper deals with the asymptotic behavior of multistep Runge-Kutta methods for systems of delay differential equations (DDEs). With the help of K.J.in't Hout's analytic technique for the numerical stability of onestep Runge-Kutta methods, we obtain that a multistep Runge-Kutta method for DDEs is stable iff the corresponding methods for ODEs is A-stable under suitable interpolation conditions.