Some modified Runge-Kutta methods for the numerical solution of initial-value problems with oscillating solutions
type: Item
instance of: scholarly article
title: Some modified Runge-Kutta methods for the numerical solution of initial-value problems with oscillating solutions
zbMATH Open document ID: 0939.65096
DOI: 10.1023/A:1023204727185
published in: Journal of Scientific Computing
publication date: 2000-06-19T00:00:00Z
review text: In the numerical modelling of oscillatory problems, the phase shift introduced by a numerical scheme is an important attribute in assessing its quality. Thus, methods with high phase-lag order, along with moderately high classical order are sought. This paper introduces two new explicit Runge-Kutta methods with order 5 and phase-lag orders 10 and 12, respectively. The author proposes an embedding scheme where phase-lag is estimated and used for error control.
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 34C10
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 65L50
zbMATH DE Number: 1204428
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: oscillatory problems
zbMATH Keywords: phase-lag order
zbMATH Keywords: error control
author: T. E. Simos
reviewed by: J. C. Butcher
MaRDI profile type: Publication
full work available at URL: a:1023204727185
OpenAlex ID: W72421626
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description: scientific article; zbMATH DE number 1204428