Convergence of Runge-Kutta methods for delay differential equations

This paper deals with the adaptation of Runge-Kutta methods to the numerical solution of nonstiff initial value problems for delay differential equations. We consider the interpolation procedure that was proposed in In 't Hout [8], and prove the new and positive result that for any given Runge-Kutta method its adaptation to delay differential equations by means of this interpolation procedure has an order of convergence equal to min {p, q}, where p denotes the order of consistency of the Runge-Kutta method and q is the number of support points of the interpolation procedure.