Continuous Runge-Kutta(-Nyström) methods with reduced phase-errors
type: Item
instance of: scholarly article
title: Continuous Runge-Kutta(-Nyström) methods with reduced phase-errors
zbMATH Open document ID: 0855.65077
DOI: 10.1016/0377-0427(95)00027-5
author: George Papageorgiou
author: Ch. Tsitouras
published in: Journal of Computational and Applied Mathematics
publication date: 1996-07-23T00:00:00Z
review text: New `dense output' formulas are constructed for an explicit Runge-Kutta method of order 6(5) and for a Runge-Kutta-Nyström method of order 8(6). Since the authors' interest is in problems describing free and weakly forced oscillations, the formulas are constructed in such a way that (asymptotically) the phase-error is as small as possible.
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L70
Mathematics Subject Classification ID: 70K40
zbMATH DE Number: 908398
zbMATH Keywords: reduced phase-errors
zbMATH Keywords: phase-lag order
zbMATH Keywords: dense output formulas
zbMATH Keywords: explicit Runge-Kutta method
zbMATH Keywords: Runge-Kutta-Nyström method
zbMATH Keywords: free and weakly forced oscillations
MaRDI profile type: Publication
full work available at URL: 0377-0427(95)00027-5
OpenAlex ID: W2063481587
cites work: A fifth-order interpolant for the Dormand and Prince Runge-Kutta method
cites work: Families of Runge-Kutta-Nystrom Formulae
cites work: Runge-Kutta triples
cites work: Runge-Kutta-Nyström triples
cites work: Interpolants for Runge-Kutta formulas
cites work: Interpolants for Runge-Kutta-Nyström methods
cites work: Practical Aspects of Interpolation in Runge-Kutta Codes
cites work: Fourth- and Fifth-Order, Scaled Rungs–Kutta Algorithms for Treating Dense Output
cites work: Comparing Numerical Methods for Ordinary Differential Equations
cites work: Some new Runge-Kutta methods with interpolation properties and their application to the Magnetic-Binary Problem
cites work: Scaled runge-kutta-nyström methods for the second order differential equationÿ=f(x,y)
cites work: Runge-Kutta pairs for periodic initial value problems
cites work: Interpolation for Runge–Kutta Methods
cites work: Some Practical Runge-Kutta Formulas
cites work: New interpolants for runge-kutta algorithms using second derivatives
cites work: Runge-Kutta interpolants based on values from two successive integration steps
cites work: Interpolating runge-kutta-nyström methods of high order
cites work: Explicit Runge–Kutta (–Nyström) Methods with Reduced Phase Errors for Computing Oscillating Solutions
description: scientific article; zbMATH DE number 908398