On a class of \(P\)-stable mono-implicit Runge-Kutta-Nyström methods
Mono-implicit Runge-Kutta methods show interesting properties [e.g., see \textit{J. R. Cash} and \textit{A. Singhal}, IMA J. Numer. Anal. 2, 211-227 (1982; Zbl 0488.65031)]. In this paper the concept of mono-implicitness is extended to Runge-Kutta-Nyström (RKN) methods. The aim is to construct \(P\)-stable mono-implicit RKN methods. The conditions of the \(P\)-stability and of the order are developed for these methods, which lead to results on the attainable order. Finally, \(P\)-stable methods with 2, 4 and 6 stages are constructed.
scientific article; zbMATH DE number 1311327
scientific article