Analysis of trigonometric implicit Runge-Kutta methods

Nguyen, H. S., Sidje, R. B. and Cong, N. H. (2006) Analysis of trigonometric implicit Runge-Kutta methods. Journal of Computational and Applied Mathematics, 198 1: 187-207. doi:10.1016/

Author Nguyen, H. S.
Sidje, R. B.
Cong, N. H.
Title Analysis of trigonometric implicit Runge-Kutta methods
Journal name Journal of Computational and Applied Mathematics   Check publisher's open access policy
ISSN 0377-0427
Publication date 2006
Sub-type Article (original research)
DOI 10.1016/
Volume 198
Issue 1
Start page 187
End page 207
Total pages 21
Editor Brenner, S.
Goovaerts, M. J.
Mitsui, T.
Ng, M.
B Sommeijer
Wuytack, L.
Place of publication Amsterdam
Publisher Elsevier
Collection year 2006
Language eng
Subject C1
230116 Numerical Analysis
780101 Mathematical sciences
Abstract Using generalized collocation techniques based on fitting functions that are trigonometric (rather than algebraic as in classical integrators), we develop a new class of multistage, one-step, variable stepsize, and variable coefficients implicit Runge-Kutta methods to solve oscillatory ODE problems. The coefficients of the methods are functions of the frequency and the stepsize. We refer to this class as trigonometric implicit Runge-Kutta (TIRK) methods. They integrate an equation exactly if its solution is a trigonometric polynomial with a known frequency. We characterize the order and A-stability of the methods and establish results similar to that of classical algebraic collocation RK methods. (c) 2006 Elsevier B.V. All rights reserved.
Keyword Mathematics, Applied
oscillatory ODEs
variable stepsize
variable coefficients
trigonometric collocation
implicit RK
Mixed Collocation Methods
Nystrom Methods
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: 2007 Higher Education Research Data Collection
School of Physical Sciences Publications
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Citation counts: TR Web of Science Citation Count  Cited 8 times in Thomson Reuters Web of Science Article | Citations
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Created: Wed, 15 Aug 2007, 10:45:53 EST