In this paper, we study diagonally implicit Runge-Kutta-Nyström methods (DIRKN methods) for use on parallel computers. These methods are obtained by diagonally implicit iteration of fully implicit Runge-Kutta-Nyström 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 J.C. Baltzer AG Science Publishers.

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