Continuous extensions to Nyström methods for second order initial value problems
type: Item
instance of: scholarly article
title: Continuous extensions to Nyström methods for second order initial value problems
zbMATH Open document ID: 0849.65052
DOI: 10.1007/BF01731986
author: Arne Marthinsen
published in: BIT
publication date: 1996-11-11T00:00:00Z
review text: The aim of this article is to extend results on continuous, explicit Runge-Kutta methods by \textit{B. Owren} [Ph.D. thesis, Norwegian Institute of Technology, Trondheim, 1989] to explicit Nyström methods for second-order ordinary differential equations \(y''= f(x, y, y')\). After recalling some classical results, the order conditions of continuous Nyström methods (i.e., methods providing a dense output) are discussed. The main contribution consists in a detailed study of the maximum order attainable with an \(s\)-stage, continuous Nyström method.
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 885556
zbMATH Keywords: interpolants
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: Nyström methods
zbMATH Keywords: second-order ordinary differential equations
zbMATH Keywords: order conditions
zbMATH Keywords: dense output
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 885556