INTERPOLATING RUNGE-KUTTA METHODS FOR VANISHING DELAY-DIFFERENTIAL EQUATIONS

In the numerical solution of delay differential equations by a continuous explicit Runge-Kutta method a difficulty arises when the delay vanishes or becomes smaller than the stepsize the method would hire to use. In this situation the standard explicit sequential process of computing the Runge-Kutta stages becomes an implicit process and an iteration scheme must be adopted. We will consider alternative iteration schemes and investigate their order.