In this paper, we study diagonally implicit Runge-Kutta-Nystr??m methods (DIRKN methods) for
use on parallel computers. These methods are obtained by diagonally implicit iteration of fully implicit
Runge-Kutta-Nystr??m methods (corrector methods). The number of iterations is chosen such that the
method has the same order of accuracy as the corrector, and the iteration parameters serve to make the
method at least A-stable. Since a large number of the stages can be computed in parallel, the methods are
very efficient on parallel computers. We derive a number of A-stable, strongly A-stable and L-stable
DIRKN methods of order p with s* (p) sequential, singly diagonal-implicit stages where s*(p)=[(p+1)/2] or
s* (p)=[(p+1)/2]+1,[?] denoting the integer part function. ?? 1993
