Generalized singly-implicit Runge-Kutta methods with arbitrary knots
type: Item
instance of: scholarly article
title: Generalized singly-implicit Runge-Kutta methods with arbitrary knots
zbMATH Open document ID: 0578.65069
DOI: 10.1007/BF01934384
author: Claus Schneider
published in: BIT
publication date: 1985-01-01T00:00:00Z
review text: This paper generalizes the work of the reviewer on singly-implicit Runge- Kutta methods (methods whose Runge-Kutta matrix has a single real s-fold eigenvalue) to a general family of Nordsieck methods with s internal stages and r external stages (so that r quantities representing y and the first r-1 scaled derivatives of y are carried from step to step). It is shown how to construct singly-implicit Nordsieck methods of order \(s+r-1\) with stage order \(s+r-2\) without restriction on the knots. The similarity transformation is formed which allows efficient implementation when solving the s implicit equations for the s internal approximations, and simple formulas for the r updates at the end of an integration step are established.
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L50
zbMATH DE Number: 3926125
zbMATH Keywords: similarity transformations
zbMATH Keywords: singly-implicit Runge-Kutta methods
zbMATH Keywords: Nordsieck methods
reviewed by: Kevin Burrage
MaRDI profile type: Publication
cites work: Q5558293
cites work: A special family of Runge-Kutta methods for solving stiff differential equations
cites work: An implementation of singly-implicit Runge-Kutta methods
cites work: A Transformed implicit Runge-Kutta Method
cites work: A generalization of singly-implicit methods
cites work: Numerische Lösung gewöhnlicher Differentialgleichungen mit Splinefunktionen
cites work: Q5672034
description: scientific article; zbMATH DE number 3926125