On a class of \(P\)-stable mono-implicit Runge-Kutta-Nyström methods
type: Item
instance of: scholarly article
title: On a class of \(P\)-stable mono-implicit Runge-Kutta-Nyström methods
zbMATH Open document ID: 0937.65085
DOI: 10.1016/S0168-9274(97)00110-4
author: Tanja Van Hecke
author: M. Van Daele
author: H. De Meyer
author: G. Vanden Berghe
published in: Applied Numerical Mathematics
publication date: 2000-06-14T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 1311327
zbMATH Keywords: Runge-Kutta-Nyström methods
zbMATH Keywords: mono-implicit Runge-Kutta methods
zbMATH Keywords: \(P\)-stability
zbMATH Keywords: order
reviewed by: Rudolf Scherer
describes a project that uses: PMIRKDC
describes a project that uses: MIRKDC
MaRDI profile type: Publication
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full work available at URL: s0168-9274(97)00110-4
OpenAlex ID: W1985874154
description: scientific article; zbMATH DE number 1311327