Rooted tree analysis of Runge--Kutta methods with exact treatment of linear terms
type: Item
instance of: scholarly article
title: Rooted tree analysis of Runge--Kutta methods with exact treatment of linear terms
zbMATH Open document ID: 1072.65106
author: S. Koikari
published in: Journal of Computational and Applied Mathematics
publication date: 2005-05-04T00:00:00Z
review text: The author's aim is to provide a mathematical foundation of the methods called ETD Runge-Kutta, already proposed in literature. The main feature of these methods is that they treat exactly the linear terms of an ordinary differential equation, while the other terms are numerically integrated by a one-step method. The author assumes the point of view of Runge-Kutta methods, using a Butcher-like tableaux, whose elements are themselves matrices instead of scalar; then he applies the rooted tree analysis. Several classes of formulas are derived. The study of these methods is complete and well-detailed.
reviewed by: Raffaella Pavani
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 2164843
zbMATH Keywords: ETD Runge-Kutta methods
zbMATH Keywords: exact treatment of linear part
zbMATH Keywords: rooted tree analysis
zbMATH Keywords: integrating factor method
zbMATH Keywords: spectral methods
zbMATH Keywords: one-step method
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: j.cam.2004.09.057
OpenAlex ID: W2055729883
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DOI: 10.1016/J.CAM.2004.09.057
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description: scientific article; zbMATH DE number 2164843