A new type of singly-implicit Runge-Kutta method
type: Item
instance of: scholarly article
title: A new type of singly-implicit Runge-Kutta method
zbMATH Open document ID: 0954.65058
DOI: 10.1016/S0168-9274(99)00126-9
author: D. J. L. Chen
author: J. C. Butcher
published in: Applied Numerical Mathematics
publication date: 2000-09-04T00:00:00Z
review text: The authors discuss new type of implicit Runge-Kutta methods which combine the singly-implicitness or diagonal-implicitness property with a zero first row in the coefficient matrix of the method. The new feature considered in this paper is the use of a first stage identical to the input approximation (this means that the first row of the coefficient matrix is zero) and the last stage , identical to the output value (this means that the last row of the coefficient matrix is identical with the vector of output value coefficients). The derived methods preserve the feature of the FSAL-methods and also of the DESI-methods [cf. \textit{J. C. Butcher} and \textit{J. R. Cash}, SIAM J. Numer. Anal. 27, No.~3, 753-761 (1990; Zbl 0702.65072)]. It is shown that the derivative of the first internal stage for a singly-implicit Runge-Kutta method can be obtained from the previous step without any loss of performance. Numerical experiments show the efficiency of the proposed methods.
reviewed by: Iulian Coroian
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L20
zbMATH DE Number: 1462297
zbMATH Keywords: singly-implicit Runge-Kutta methods
zbMATH Keywords: FSAL methods
zbMATH Keywords: DESI methods
zbMATH Keywords: initial value problems
zbMATH Keywords: stability of methods
zbMATH Keywords: numerical experiments
MaRDI profile type: Publication
full work available at URL: s0168-9274(99)00126-9
OpenAlex ID: W1995948321
Wikidata QID: Q128066889
description: scientific article; zbMATH DE number 1462297