On a class of P-stable mono-implicit Runge-Kutta-Nyström methods Original Research Article

By a detailed investigation of the conditions to be satisfied by a mono-implicit Runge-Kutta-Nyström (MIRKN) method in order to be P-stable, a subset of candidate P-stable MIRKN methods is firstly isolated. Then it is shown that this subset effectively contains P-stable MIRKN methods with an even number of stages. Finally, P-stable MIRKN methods with 2, 4 and 6 stages are constructed explicitly.