On the generation of mono-implicit Runge-Kutta-Nystrِm methods by mono-implicit Runge-Kutta methods

Mono-implicit Runge-Kutta methods can be used to generate implicit Runge-Kutta-Nystrِm (IRKN) methods for the numerical solution of systems of second-order differential equations. The paper is concerned with the investigation of the conditions to be fulfilled by the mono-implicit Runge-Kutta (MIRK) method in order to generate a mono-implicit Runge-Kutta-Nystrِm method (MIRKN) that is P-stable. One of the main theoretical results is the property that MIRK methods (in standard form) cannot generate MIRKN methods (in standard form) of order greater than 4. Many examples of MIRKN methods generated by MIRK methods are presented.