We present an explicit RungeKutta scheme devised for
the numerical solution of delay differential equations (DDEs) where
a delayed argument lies in the current RungeKutta interval. This can occur
when the lag is small relative to the stepsize, and the more obvious extensions
of the explicit RungeKutta method produce implicit equations. It transpires
that the scheme is suitable for parallel implementation for solving
both ODEs and more general DDEs. We associate our method with a RungeKutta
tableau, from which the order of the method can be determined. Stability
will affect the usefulness of the scheme and we derive the stability equations
of the scheme when applied to the constantcoefficient test DDE
y'(t) = l y(t) + u y(tT),
where the lag T and the RungeKutta stepsize Hn
= H are both constant. (The
case u = 0 is treated separately.) In the case that u <> 0,
we consider the two distinct possibilities: (i) T >= H
and (ii) T < H.
